Studies in History and Philosophy of Modern Physics 46 (2014) 523Contents lists available at ScienceDirectStudies in History and Philosophyof Modern Physics1355-21http://d

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Butterfijournal homepage: www.elsevier.com/locate/shpsbOn the philosophy of cosmology$

George Francis Rayner Ellis a,b,c,n

aMathematics Department and ACGC, University of Cape Town, South AfricabTrinity College, Cambridge University, UKcDAMTP, Cambridge University, UKa r t i c l e i n f o

Article history:Received 1 May 2012Received in revised form9 May 2013Accepted 25 July 2013Available online 24 August 2013

Keywords:Philosophy of cosmologyMultiversesInfinity98/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.shpsb.2013.07.006

at Granada Meeting, 2011.espondence address: Mathematics Departmewn, South Africa.ail address: george.ellis@uct.ac.zae for example Munitz (1962), Ellis (2006eld (2012).a b s t r a c t

This paper gives an overview of significant issues in the philosophy of cosmology, starting off byemphasizing the uniqueness of the universe and the way models are used in description and explanation.It then considers, basic limits on observations; the need to test alternatives; ways to test consistency; andimplications of the uniqueness of the universe as regards distinguishing laws of physics from contingentconditions. It goes on to look at the idea of a multiverse as a scientific explanation of facts about fine-tuning, in particular considering criteria for a scientific theory and for justifying unseen entities. Itconsiders the relation between physical laws and the natures of existence, and emphasizes limits on ourknowledge of the physics relevant to the early universe (the physics horizon), and the non-physicalnature of some claimed infinities. The final section looks briefly at deeper issues, commenting on thescope of enquiry of cosmological theory and the limits of science in relation to the creation of theuniverse.

& 2013 Elsevier Ltd. All rights reserved.When citing this paper, please use the full journal title Studies in History and Philosophy of Modern Physics1. Introduction

Philosophy underlies our approaches to cosmology. One orother basic philosophical stance is usually just taken for granted inpresent day cosmological studies, but this stance is not usuallyexplored. The theme of this paper is that cosmology will benefit bymaking the underlying philosophical issues explicit.

The core issue for the philosophy of cosmology1 is, Whatconstitutes an explanation in the context of cosmology? This hasseveral specific aspects: What kinds of things are we trying toexplain? What kinds of questions do we want our models toanswer? Can we explain what is, by asking what else could be thecase? How do we restrict explanatory models in cosmology whenthey are underdetermined by the data? How do we test whetherthe kinds of explanation we are offering are valid?

The answers depend crucially on our investigative framework:Do we want to tackle only technical issues, restricting attention tophysical cosmology, or do we want to deal with issues of meaningll rights reserved.

nt and ACGC, University of

), Zinkernagel (2011), and(or lack of it) as well, extending the investigation to the bigquestions of cosmology? This is the basic underlying choice wehave to make, which shapes the questions that we ask and thekinds of answers we consider.

If we do enter the latter terrain to do with issues of mean-ing, we need to consider, How much of reality do our modelstake seriously? In some cases, the models used are very limited inscope, being essentially of a purely physical nature, but theyare being used by some to answer questions that are beyondtheir capacity.2 Awareness of this issue may help us resist thattemptation.

Most of this article considers the philosophy of physicalcosmology, but the last section briefly touches on these biggerissues. When considering the physical issues, we should remem-ber that philosophical considerations are necessarily part of thephysics enterprise (Zinkernagel, 2011). Even when dealing withapparently purely technical issues, there will always be philoso-phical assumptions underlying what we are doing.

The sections that follow look successively at: the uniqueness ofthe universe, and the use of models in description and explanation(this section); the basic issues in physical cosmology, and limits onobservations in relation to that program (Section 2); the key need2 See commentary at http://edwardfeser.blogspot.com/2012/01/maudlin-on-philosophy-of-cosmology.html.

www.sciencedirect.com/science/journal/13552198www.elsevier.com/locate/shpsbhttp://dx.doi.org/10.1016/j.shpsb.2013.07.006http://dx.doi.org/10.1016/j.shpsb.2013.07.006http://dx.doi.org/10.1016/j.shpsb.2013.07.006http://crossmark.crossref.org/dialog/?doi=10.1016/j.shpsb.2013.07.006&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.shpsb.2013.07.006&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.shpsb.2013.07.006&domain=pdfmailto:george.ellis@uct.ac.zahttp://edwardfeser.blogspot.com/2012/01/maudlin-on-philosophy-of-cosmology.htmlhttp://edwardfeser.blogspot.com/2012/01/maudlin-on-philosophy-of-cosmology.htmlhttp://dx.doi.org/10.1016/j.shpsb.2013.07.006

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 5236to test alternatives to the standard models: alternative topologies,geometries, and physics (Section 3); ways one can test theconsistency of the standard models (Section 4); issues relatedspecifically to the uniqueness of the universe, and particularly theproblem of distinguishing laws from initial conditions in thiscontext (Section 5); the question of whether multiverse proposals,which deny the uniqueness of the universe, are testable science(Section 6); and the relation between physical laws and thecoming into being of the universe (Section 7), including a critiqueof the alleged occurrence of physically existing infinities that isoften invoked as part of such discussions. Finally, Section 8 looksbriefly at the deeper issues that arise when one looks beyondpurely physical cosmology, and critiques attempts to do so on aninadequate philosophical basis.

1.1. Uniqueness of the universe

The underlying basic problem in studying cosmology is theuniqueness of the universe (Ellis, 2006a; McCrea, 1953; Munitz,1962). There is only one object to look at, and no similar object tocompare it with. Also there is no chance to rerun it in an experiment.This is what makes cosmology unique as a science, and underliesmost of the problems discussed below. It is a unique historicalscience, where no direct experiments are possible on the objectbeing investigated as a whole (although many are possible on partsor aspects of the whole.)

There are other historical and geographical sciences dealing withunique events or entities, but in these cases at least in principle thereare similar events or entities which might exist (there have beenother wars and generals, there are other mountains and seas, theremay be life on other planets, etc.). Cosmology is the unique casewhere there is no similar entity with which we can compare theobject of study, because by definition the Universe is all that there is.3

It is for this reason that we have to be exceptionally carefulin analyzing the relation between data and models in cosmology.We need to extract all the evidence we can, and check our models inall possible ways. Additionally, this uniqueness has implications forexplanation and how we understand the nature of laws and chancein this context. These specific implications will be discussed inSection 5.1.2. Use of models in description

Explanation depends on our ideas of what exists, and so ispreceded by descriptive models based on observations. But thesewill then include descriptions of causal factors as envisaged byexplanatory models, so the descriptive and causal models will notbe independent. In any case, models of any physical system arealways an idealization: they include some items while excludingothers. The question How accurate are they? depends on thekind of question we wish to answer. So the first issue is as follows1.speWhat kinds of things will they describe?If the aim is just to deal with physical cosmology, the kinds ofentities are fairly obvious (geometry, matter, fields). But thenthe issue is as follows:2. How general will they be?The majority of models used in cosmology are perturbedFriedmannLematreRobertsonWalker (FLRW) models(Dodelson, 2003; Ellis, Maartens, & MacCallum, 2012). But ifone wants to explore3 There is thus a tendency to capitalize it (The Universe) because it names acific entity. the full range of cosmological models that are consistentwith observations, or

the range of all cosmologies that might conceivably have comeinto existence, irrespective of whether they are compatiblewith observations or not, this will not be enough. This fullrange of models provides a conceptual framework for under-standing what actually exists, because it enables us to comparewhat exists with what might have existed, and so to ask, whydid these other kinds of universe not come into existence?If we don't describe them, we can't ask these questions.Each model has a domain of validity which can be specified bywhat it includes and what it excludes; these should be statedclearly, and not exceeded when it is used in explanatory mode.In particular, there are always averaging scales in physicaldescriptions, albeit often implicit or hidden. One shouldconsider,3. What scales of description are included? What detail will theyencompass?There will always be smaller scales not included in our model.And the same may be true at large scales: we may or may nottry to describe the entire universe, including domains beyondwhat is observable.The further core issue is as follows:4. How will the proposed models of what exists be tested?Many models used in cosmology make major claims aboutunobservable entities and regions. An issue we pursue below(Section 6) is to what degree such claims can be called scientific.

1.3. Use of models in explanation

But our models go beyond description: they aim at explanation.So the issue here is as follows:1. What kinds of causation do we envisage in cosmology?Physical effects take place in astrophysical processes, determiningwhat happens on the basis of the initial data and the astrophysicalcontext. But cosmological claims often go further than that: theytry to explain the very existence of the universe. The kinds ofcausation envisaged here test the limits of science. So a funda-mental issue is as follows:2. What are the limits of our causal models? How far do we takeexplanation? What do we take for granted, and not try toexplain?Each causal model has a domain of validitywhich should bestated clearly and not exceeded.We will be able to use testable physics up to some point, butafter that we will be in the domain of speculation. A further keyissue therefore is3. To what degree are our proposed causal models testable?This is different from exploring what exists (see Section 1.2),because it relates to the possibility of testing the physicsunderlying what we propose. Exploring the limits will neces-sarily at least initially involve presently untestable proposals,but the problem arises if they will in principle be untestablealways, because of the extreme energies involved. Their statusas scientific explanation will then be in questionno matterhow attractive they may be from some specific philosophicalviewpoint. In many cases in cosmology, the situation is not

Known Physics - Outcome 1as some writings suggest. Instead it is

Known Physics - Hypothetical Physics - Outcome 2We will encounter this in a variety of contexts.

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 523 7As is true also for description (Section 1.2), causal models willnever be complete: they will always omit some part of the causalnexus, inter alia because that involves all scales from the smallestto the largestand as indicated in the last section, we cannot fullyrepresent all the causal variables at play, let alone the interactionsbetween them. Our models will represent some causal influencesbut not all. So as always, the moral is Don't confuse causal modelswith reality! They will always of necessity be partial descriptionsof the whole. One should respect their limits.

1.4. Epistemology and ontology

As in all cases of scientific explanation, in cosmology we arerelating our knowledge to an external reality, and the key scientificrequirement is to test those models by observational and experi-mental means against what is actually out there. But our observa-tional access to the vast distant domains of the universe is strictlylimited. This means that our model building is under-determined,because access to data is restricted in three crucial ways.1.uniSpeed of light limitsAs we look to distant domains in the universe, we see what isthere only through photons that travel towards us at the speed oflight; so we can't see things as they are today, we only get dataabout things as they were in the past (Ellis, 1971a). To understandwhat things are like today, we have to extrapolate from theobservable past to unobservable present events at a distance fromus; and that is a model-dependent exercise.2. Observational horizonsAs we peer back into the past, because the observable part of theuniverse has been in existence only for a finite time, there areparticle and visual horizons limiting our causal and visual contactwith distant domains (Ellis & Stoeger, 1988). We can only see outto matter that is presently about 42 billion light years distant4;the rest is unobservable for ever, except perhaps by means ofcosmological neutrinos and gravitational wavesboth of whichare extraordinarily difficult to detect. And their scope too islimited by associated horizons. We will never have access to dataabout most of the universe (except if we live in a small universe,discussed in Section 3.1; but this is probably not the case).3. The physics horizonWe are also faced with a limit to our ability to test the physicsrelevant to understanding processes in the early universe.Hence there are profound limits on our ability to test explana-tions of what was going on then.These three limitations will necessarily be central to any studyof epistemology of cosmology; they will be very apparent in thediscussion that follows.4. Detection limits and selectionFinally one must as always take selection and detection effectsinto account, asking, What exists that we cannot see becauseit emits no radiation? What emits radiation that we do notdetect? What do we see but not recognize for what it is? (henceexcluding it from our catalogs of sources). These effects (Ellis,Perry, & Sievers, 1984) are crucial in determining what weactually see and measure.

1.5. Philosophy and cosmological issues

Because of these limits of observability and testability, asemphasized by Butterfield (this issue), our cosmological modelsare underdetermined by observations: we have to make4 This is three times the Hubble scale distance; that factor is because theverse is expanding. See Ellis & Rothman (1993).theoretical assumptions to get unique models, both as regardsphysics and geometry. That is one reason why philosophy isinevitable in the study of cosmology: even if this is not oftenexplicitly recognized, it is part of the territory, even in studyingpurely physical cosmology. And even with as much data as onewould like, and even if one could use this to fix our cosmologicalmodel uniquely, we would still be left with the task of interpretingthis model. Even if under-determination could be eliminated at themodel level, this does not imply that there is no under-determination at the level of interpretationi.e. about what themodel implies for our understanding of the world (see Section 2 ofZinkernagel, 2011).

Of course this is much more apparent in tackling foundationalissues and big questions, which go beyond purely physicalcosmology (both are considered below). Proclaiming that philoso-phy is useless or meaningless will not help: cosmologists neces-sarily indulge in it to some degree, whether they acknowledge thisfact or not. Poorly thought out philosophy is still philosophy, but itis unsatisfactory. Rather than denying its significance, we shouldcarefully consider the philosophycosmology relation and developa philosophy of cosmology of adequate depth.2. Understanding cosmology: basic issues

There is consensus that we live in an expanding universe thatstarted off in a Hot Big Bang era dominated by matter in equilibriumwith very hot radiation, and is now of vast scale with galaxiesreceding from each other at an accelerating rate (Dodelson, 2003;Ellis et al., 2012; Harrison, 2000; Silk, 2001). When considered onvery large scales, the universe is very smooth and is almost isotropicabout us. The dynamics of the universe is governed by gravity,which is represented through the Einstein Field Equations. Weobserve distant regions by means of radiation of all wave lengthsthat reaches us at the speed of light, so we necessarily look backinto the past as we look further out. We also obtain cosmologicaldata by examining what exists here and now (galaxies, stars,planets, baryonic matter), since it all had its ultimate origins inthe physical conditions in the very early universe.

2.1. The basic program

The basic program relies on two elements: seeing what is there(based on numerous observations deriving from all the various kindsof telescopes) and fitting parametrized perturbed FLRW models tothis data. These models involve physical theory: causal models givephysical explanations of the dynamics, through applying the Einsteinfield equations with suitable matter models. Thus the basic conceptof explanation here is explanation of large scale dynamics andstructure through local application of physical laws. Note that onefits the parameters of both the background model and of theperturbation spectrum for different matter components: one ismodeling what matter is here now, and how it got there.

The basic ingredients of the resulting concordance model(Dodelson, 2003; Ellis, 2006a; Ellis et al., 2012; Harrison, 2000;Silk, 2001), based on perturbed FLRW models of the universe, are: An inflationary era prior to the hot big bang stage, includinggeneration of a seed perturbation spectrum; The end of inflation, reheating, and baryosynthesis;

The Hot Big Bang epoch, including neutrino decoupling,

nucleosynthesis and baryon acoustic oscillations (BAO);

Decoupling of matter and radiation, leading to emission of the

blackbody Cosmic Microwave Background Radiation (CMB);

Dark ages, followed by structure formation and first light, then

emergence of more complex structures in a bottom-up way;

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 5238

C

Figobsobs

CMB 2-sphere Existence of dark matter, dominating gravitational dynamics atgalactic to cluster scales; Existence of dark energy, dominating cosmological scale grav-itational dynamics at late times.

The concordance model makes no claims as regards the spatialtopology of the universe; it is implicitly understood that it has thesimplest (simply connected) topology.Fig. 2. The CMB 2-sphere. Microwave background radiation anisotropy over theentire sky is depicted, with the dipole due to our motion removed. This images theLast Scattering Surface (LSS), with our galaxy superimposed in the foreground.Anisotropy is present at one part in 100,000, representing primordial fluctuationsthat are the seeds for large scale structure formation at much later times. Thematter emitting this radiation is the most distant matter we can see inthe universe: their world lines constitute our visual horizon. This 2-sphere is theintersection of our past light cone with the LSS: we cannot see the matter on theLSS to the interior of this 2-sphere (see Fig. 1).2.2. Limits on observations

Not only is no direct experiment possible on the whole, orobservations of similar entities; additionally, because of its vastscale, but also our ability to examine the nature of the oneuniverse in which we exist is very restricted.

In effect we can only see the universe from one spacetimeevent: here and now (see Fig. 1). All we can see (on acosmological scale) lies on a single past lightcone; hence ourcosmological models are underdetermined by possible observa-tions: we have to make theoretical assumptions to get uniquemodels, both as regards physics and geometry. The observationalsituation is shown in Fig. 1.

Conformal coordinates are used so that fundamental worldlines are vertical lines, surfaces of homogeneity are horizontalplanes, and null cones are at 7451. Spatial distances are distortedbut causal relations are as in flat spacetime. The start of theuniverse is at the bottom. The universe was opaque until the LastScattering Surface (LSS), where radiation decoupled from matter,and propagated freely from then on as cosmic microwave blackbody radiation (CMB), nowadays peaked in the microwave regionat 2.75 K. Our world line is at the center of the diagram; thepresent event here and now is about 14 billion years afterdecoupling. We see a distant galaxy at the instant it crosses ourpast light cone.

All events before the LSS are hidden from our view. As the LSSis where the freely propagating cosmic microwave background(CMB) originates, it contains the CMB 2-sphere we see when wemeasure temperature fluctuations in the CMB across the sky(Fig. 2). The matter we see in this way is the furthest matter wecan see by any electromagnetic radiation; hence it forms the visualhorizon (Ellis & Rothman, 1993; Ellis & Stoeger, 1988).

The Hot Big Bang (HBB) epoch is from the end of inflation(extremely soon after the start of the universe) until decoupling atHere and now

Distant galaxy

CMB 2-sphere

an only observe on past light cone

LSS

Hidden

Start of universe

furthest matter we can see

Nucleosynthesis: Very early past world line

1.4 x 1010years

. 1. The basic observational situation in cosmology. A spacetime diagram of theervable universe domain in conformally flat coordinates, showing the limits toervations.the LSS. Nucleosynthesis took place shortly after the start of theHBB epoch, and determined the primordial abundance of lightelements in our region, which we can estimate from nearby stellarspectra. The region of spacetime that actually influences us hereand now is much smaller than the visual horizon, see (Ellis andStoeger 2009a).

2.3. Major questions

A series of major questions arise as regards the concordancemodel.1. What are the cosmological parameters?A series of parameters (the rate of expansion, densities ofvarious matter components, the ratio of scalar to tensorperturbations, and so on) characterize the standard cosmolo-gical model, and determine important aspects of its nature(Dodelson, 2003; Spergel et al., 2007; Tegmark, Zaldarriaga, &Hamilton, 2001).Massive new data sets are being collected that will refine themand decrease uncertainty as to their values (Ade et al., 2013a).An important issue is how to break degeneracies, which hasbeen well studied (Howlett et al., 2012). There are also datawhich are not easily fitted with the concordance model(Lithium-7 abundance, lack of observation of population IIIstars, and a possible Axis of evil in the CMB data). These arediscussed in Hamilton's paper (this issue).2. What is the spatial curvature?One key issue is observationally determining whether the spatialcurvature is positive, negative or zero. This does not depend onwhether the space sections have the simplest (simply connected)topology. It can be determined by sufficiently sensitive astronom-ical observations of densities and the expansion rate, whichtogether determine the dimensionless curvature parameterkk/a2, where k+1 (positively curved space sections), 0 (flatspace sections), or 1 (negatively curved space sections). Ifk+1, the universe will close up on itself if its geometry continuesunchanged outside the part we can see. The value of k is key to thedynamics of the universe: a bounce is possible in the past, andrecollapse is possible in the future, only if k+1. The present dataare not sufficient to determine this sign (Ade et al., 2013a).A number of data analyses determining cosmological parametersset k0 for convenience. They are missing a key parameter.

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 523 93. What do they tell us about inflation?The values of these parameters determine the ratio of tensor toscalar perturbations, and so give key information about thenature of inflation (Bond, Contaldi, Lewis, & Pogosyan, 2004;Ma, Zhao, & Brown, 2010). They also test alternatives toinflation (see Brandenberger, 2009, 2012, and referencestherein). But this is difficult because inflation is not a specificwell-defined theory: a large variety of alternative inflationaryproposals create a lot of flexibility in what is possible, so it isdifficult to disprove the whole family. However detailed ana-lyses of data such as the CMB anisotropy power spectrum andpolarization can rule out many inflationary models (Ade et al.,2013b).4. How did structure formation take place?Key elements of structure formation are understood: quantumperturbations generated in inflation led to small inhomogene-ities that generate baryon-acoustic oscillations leading toinhomogeneities on the last scattering surface, which then actas seeds allowing gravitational instability to generate structurein a bottom-up way after decoupling (Dodelson, 2003). But thedetails are unclear, particularly because as non-linearity sets inafter decoupling, when the first stars have formed and complexastrophysical processes occur associated with reheating ofmatter.Additionally, an important issue is unresolved: we have the wholequantum-to-classical transition to account for: that is, how doesquantum uncertainty give way to classical definiteness in thepost-inflationary era? Current decoherence-based approaches tothis question are insufficient to resolve the issue; this mustnecessarily involve some resolution of the measurement problemin quantum theory (see Caate, Pearle, & Sudarsky, in press;Sudarsky, 2011 and references therein). This is a major lacuna inthe physical explanation of structure formation in the earlyuniverse.5. What is the nature of dark matter?The Planck satellite observations indicate the total massenergydensity of the universe is 4.9% baryonic matter and 26.8% darkmatter the other 68.3% is the dark energy density (Ade et al.,2013a). Thus dark matter is estimated to be 84.5% of the matter inthe universe. We know it is non-baryonic, but do not know whatit is. However potential candidates abound. Experimental andobservational searches are under way to determine its nature(Albrecht et al., 2006; Bertone, Hooper, & Silk, 2005).6. What is the nature of dark energy?The existence of dark energy is established by observations of TypeIa supernovae, BAO, weak gravitational lensing, and the abundanceof galaxy clusters, combined with CMB observations (Ade et al.,2013a). In particular, decay of supernovae in distant galaxiesprovides a usable standard candle (maximum brightness is corre-lated to decay rate) that, taken together with redshifts, gives areliable detection of non-linearity in the redshift-distance relation,showing the universe is presently accelerating. Consequently cos-mological dynamics is presently dominated an effective positivecosmological constant, with 0.7. But its nature is completelyunknown, and major efforts are under way to understand it(Peebles & Ratra, 2003). It may just be a cosmological constant,or it may be some more complex matter field (quintessence).Simple estimates of vacuum energy based in quantum field theorygive the wrong answer by at least 70 orders of magnitude(Weinberg, 1989). This is a major perplexity facing theoreticalphysics. One possible resolution is some form of unimodulargravity, leading to a trace-free form of the Einstein equations (seeEllis, van Elst, Murugan, & Uzan, 2011).7. What happened at the start of the universe?It seems that there was a start of some kind to the presentexpansion epoch of the universe (as it is not in a steady state).What was the nature of this start? How did it happen? (insofaras we can meaningfully ask that question). I return to this inSections 7.3 and 8.

3. Testing alternatives to the concordance model

It is a sound general principle that one only fully understandswhat exists if you have a good idea of what does not exist: youdon't understand the model you have unless you understand thealternatives. One should therefore ask as follows:

What else could be the case?In order to understand what it is, this is particularly true in the

case of cosmology, where one cannot go out and examine otherphysical examples of universes: one can however consider otherhypothetical universes, and ask why they do not exist rather thanthe specific one we in fact happen to live in. In particular, differentmodels may explain the same datathere is a degeneracy inparameters with the same observational outcomes, for exampleand we need to examine all the family that can explain the samedata, in order to decide between them (Ellis et al., 2012). It is notgood enough to choose the first model that fits the data, whenthere may be many.3.1. Alternative topologies

FLRW models are necessarily closed if they have positivecurvature (k+1), but they need not thereby have the simplest(simply connected) topology. They can have closed finite spatialsections with complex topologies even if k0 (locally flat) ork1 (locally negatively curved) (Ellis, 1971b). While in generalwe can't tell what the topology of the spatial sections is, becausethey extend beyond our visual horizon, there is one exceptionalcase: we might possibly live in a small universe with closedspatial sections where the closure scale is less than the size of thevisual horizon (Ellis & Schreiber, 1986; Lachieze-Ray & Luminet,1995). In that case, we can see right round the universe sincedecoupling, and can see many images of the same galaxy atdifferent times in its historyincluding our own. Local physics willbe the same as in the usual models, but there will be a large-scalecut off in wavelengths because of the compact topology.

This scenario is attractive in various ways, because these arethe only cases where we can see the entire universe (Ellis &Schreiber, 1986); but is quite difficult to test observationally.However it is in principle testable by discrete source observations,and by checking for identical circles in the CMB sky (Cornish,Spergel, & Starkmann, 1998). Many simple cases have beenexcluded through such observations, but there remains a smallpossibility it may be true. If so, it would be a major feature of theobserved universe. It is a possibility that should indeed be fullyobservationally tested.3.2. Anisotropic (Bianchi) models

Another question is what difference can anisotropy make todynamics and observations? This has been extensively investi-gated through use of the Bianchi spatially homogeneous butanisotropic models (Wainwright & Ellis, 1996). Using such modelsone can put observational limits on early universe anisotropy,particularly by studying CMB anisotropies and element productionin such universes.

There is no evidence at present that there were indeedsignificant such anisotropies. But the point is that one cannotask these questions unless you have such models. Indeed it isironic that most papers on inflation say it can resolve anisotropy

Here and now

Scattering event: Radiation isotropic?

KSZ test of Copernican Principle:

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 52310and inhomogeneity, but then only consider FLRW models, whichare by definition spatially homogeneous and isotropic everywhere.You can't derive the conclusion on this basis, because these modelswere never anisotropic or inhomogeneous, so they can't be used toinvestigate the decay of either anisotropy or inhomogeneity. Theyare homogeneous and isotropic by fiat, not because of inflationaryprocesses.

3.3. Dark matter and modified gravity

One of the key issues is that dark matter is predicted to exist onthe basis of astronomical observations, but is not yet understood.It is crucial to check that these observations do indeed indicateexistence of dark matter, rather than that our theory of gravityis wrong.

Consequently it is important to investigate alternatives such asMONDmodified Newtonian dynamics, and its general relativisticcousins (Bekenstein, 2012). There are a variety of such models, butthey are restricted in various ways (Starkman, 2012) One shouldnote here that we get evidence on dark matter from gravitationaldynamics in galaxies and clusters, from structure formationstudies, and from gravitational lensing observations. Any theorymust handle all these aspects.

3.4. Dark energy and inhomogeneity

One of the major problems for cosmology, and indeed theore-tical physics, is the unknown nature of the dark energy causing aspeeding up of cosmological expansion at recent times (Weinberget al., 2012): Is it a cosmological constant? Is it quintessence(some dynamical form of matter?). What else might it be? Andhow are the observations compatible with estimates of the energydensity of the quantum vacuum, some 70120 orders of magni-tude larger than the observed energy density? (Weinberg, 1989).

Again one needs to investigate the possibility that the observa-tions signal a breakdown in General Relativity rather than theexistence of dark energy. Many investigations are under wayconsidering possible modifications of General Relativity that couldaccount for the observations, such as including higher-order termsin the Lagrangian. But given the significance of the problem, oneneeds to explore all possible other routes for explaining theobservations.

It is therefore of considerable importance that there arespatially inhomogeneous geometrical models that in principlecan explain the data without any need for any modification ofgravity, or any exotic physics (Clarkson & Maartens, 2010; Elliset al., 2012). Because we observe spherical symmetry around us tohigh accuracy, we need to use spherically symmetric (LematreTolmanBondi or LTB) inhomogeneous models where we aresomewhere near the center. Now many people don't like thisphilosophically, but that's too bad: if the observations say that isthe way things are, we have to accept it, and adjust our philosophyto fit the facts.

Three related questions arise:(i) Can we observationally put limits on late universeinhomogeneity?(ii) Can we test the Copernican Principle (the assumption we areat a typical place in the universe) rather than taking it as anuntestable philosophical a priori assumption?Probes Interior

(iii)CMB 2-sphere

Can we do away with dark energy through inhomogeneousmodels?Fig. 3. KSZ test of Copernican principle. We can see if the CMB is isotropic outthere, at a distance down our past light cone: then the almost EGS theorem appliesand confirms we live in an almost-FLRW universe. This test probes the interior ofthe CMB 2-sphere on the LSS.The answer is that in principle the answer to all these questionsis Yes. The supernova data could be revealing inhomogeneityviolating the Copernican Principle on scales close to the Hubblescale, rather than existence of dark energy. Such models are able toexplain both the supernova and the number count observations,without the presence of any cosmological constant or dark energy.Indeed that's a theorem: Mustapha, Hellaby, and Ellis (1999)showed that one can run the Einstein field equations backward,starting with any such a set of observations and then determininga LTB model that will fit them. This can be done whether there is acosmological constant or not.

So can such models explain the rest of the data provided bycurrent precision cosmological observations? Maybe, maybe not.A variety of tests have been developed based on Supernova observations down the past null cone (Clarkson,Bassett, & Lu, 2007), Relating CMB anisotropies and BAO measurements in suchmodels (Clarkson & Maartens, 2010), The Kinematic SunyaevZeldovich (kSZ) effect (Clifton, Clarkson,& Bull, 2012).

The latter test in effect enables one to see the interior region ofthe CMB 2-sphere on the LSS (see Fig. 3) because of the scatteringof radiation by hot gas that underlies the kSZ effect. Thus it isessentially an observational implementation of the almost-EGStheorem (Stoeger, Maartens, & Ellis, 1995). This theorem provesthat if the CMB radiation is seen by an expanding family ofobservers to be almost isotropic everywhere in an open set U,then the spacetime geometry of U is that of a perturbed FLRWuniverse.

At present it seems the kSZ based tests are indeed confirmingthe homogeneity of the universe on Hubble scales. Thus apreviously untested philosophical assumption is being trans-formed into an observationally tested aspect of present daycosmology.

Another possibility is Uniform thermal histories: Testing that distant matter weobserve has the same thermal history as nearby matter, result-ing in the same kinds of structures being formed in distantregions as nearby (Bonnor & Ellis, 1986).

Tests of distance element abundances fall in this category (seeSection 4.5).

Some people claim these tests are unnecessary: it is philosophi-cally implausible that we live in an inhomogeneous universe, and soit is a waste of time checking the Copernican (homogeneity)

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 523 11principle. I completely disagree. A set of testable alternatives exists,leading to interesting observational proposals; it is important to dothese tests, both because the CP is the foundation of the concordancemodel of cosmology, and if it is not valid one could perhaps do awaywith the need for dark energyone of the key mysteries in presentday cosmology.

These tests have the effect of turning a previously untestedphilosophical assumption at the foundations of standard cosmol-ogy into a scientifically testable hypothesis.5 I regard that as a bigstep forward: it is good physics and good science. Philosophicalassumptions may or may not be true: we should test themwhenever we can.4. Testing consistency

Because of the uniqueness of the universe as discussed above,consistency tests are of crucial importance: we should in allpossible ways check our models for consistency of all the differentstrands of evidence supporting the model. There are three aspectsof such consistency:(i)5

of thtrueConsistency of observations with the background FLRWmodel; testing the Copernican Principle, as just discussed, isone such test;(ii) Consistency of observations with structure formation modelsbased on perturbations of the background model;(iii) Consistency of the observations with each other.I list here the most important such tests.

4.1. Ages: checking the universe is older than its contents

This is perhaps the most crucial test of all: if it comes outwrong, it has the capacity to destroy the standard model. Indeedthis is why Hubble never believed in the idea of an expandinguniverse: the value of the Hubble Constant that he obtainedwas wrong, and this test came out inconsistent with the FLRWmodels of his time. With present Hubble constant estimates, thisworks out acceptably. But it is crucial to keep checking asestimates of ages change.

4.2. CMB-matter dipole agreement

The standard interpretation of the CMB dipole anisotropy isthat it is due to our motion relative to the cosmic rest framedefined by the CMB. A consequence is that there must be a paralleldipole in number counts of all classes of astronomical objects:radio sources, for example (Ellis & Baldwin, 1984). If this dipoleagreement were not to exist, it would call into question thecosmological interpretation of either the relevant sources, orthe CMB. It would undermine the whole of the standard modelif the CMB were not of cosmological origin (as suggested forexample by the quasi-steady state theory). The sensitivity andstatistics are difficult, but it seems this test has been passed so far;again it is crucial to keep checking.

4.3. Cosmic distance-duality relation

A key feature of standard models is the cosmic distance-dualityrelation, also known as the reciprocity theorem (Ellis, 1971a),stating that angular diameter distances are equal to luminosityValidity of an almost-FLRW geometry is not proved by the standard analysese CMB anisotropy power spectrum (e.g. Dodelson, 2003): it is assumed to beat the outset of those analyses.distances up to a redshift factor. This relation underlies thestandard (magnitude, redshift) observations of distant sources,CMB intensity observations, and gravitational lensing intensityobservations. If it were not true, then the foundational assumptionthat our observations are based on photons moving on nullgeodesics in a Riemannian spacetime would be proved wrong.

Tests are indeed possible. Khedekar and Chakraborti (2011) reportone based on the HI mass functions, and Holanda, Goncalves, andAlcaniz (2012) propose a test using measurements of the gas massfraction of galaxy clusters from SunyaevZeldovich and X-ray surfacebrightness observations. They find no significant violation of thedistance-duality relation. A more sensitive test comes by checkingthe CMB radiation spectrum deviation from a Planck spectrum (Ellis,Poltis, Uzan, & Weltman, 2013), which also confirms the relation.

4.4. CMB temperature at a distance

If the standard interpretation of the CMB is right, its tempera-ture must change with redshift z according to the formula T(z)T0(1+z). Hence we need to find distant thermometers to measurethe CMB temperature at significant redshifts. One such thermo-meter is interstellar molecules (Meyer, 1994); it turns out one canalso use the SunyaevZeldovich effect to test this relation(Avgoustidis, Luzzi, Martins, & Monteiro, 2011).

This again is an important test: it checks that the CMB is what itis believed to be, rather than some local effect. So far this test too ispassed.

4.5. Primordial element abundances with distance

If the universe is spatially homogeneous then element productionmust also be spatially homogeneous; so primordial element abun-dances for galaxies at high z should be the same as nearby. Thisseems to be the case, although there is some query as regardslithium; if that problem persists, it could be an indication of aninhomogeneous universe (Regis & Clarkson, 2010). The importance ofthis test is that it checks conditions at very early timeslong beforethe LSSfar out from our world line (see Fig. 4). This is a special caseof tests of uniform thermal histories for distant matter (Section 3.4).

4.6. Structure formation consistency tests

Structure formation depends on the densities of baryonicmatter, radiation, and dark energy, as well as the primordialperturbation scalar spectral tilt (Jaffe et al., 2001). Evidence fromMAXIMA-1, BOOMERANG & COBE/DMR CMB observations allconverge on the same values.

4.7. Consistency of observations with each other

Do ages determined in different ways agree with each other?Do different estimates of the dark energy density agree with eachother? They do indeed do so, to a good approximation: hence theidea of a concordance model of cosmology (Ostriker & Steinhardt,1995; Wang, Caldwell, Ostriker, & Steinhardt, 2000). That phraseemphasizes the consistency of all the different lines of evidencethat point to the same model (Ade, 2013a).5. The uniqeness of the universe

As mentioned in Section 1.1, the key feature that separatescosmology from all other sciences is the uniqueness of the universe.There is only one object to look at; there is no similar object tocompare it with. We can of course investigate almost countlessaspects of the universe; but they are all aspects of one single object,

Helium here and now

Helium abundance

Nucleosynthesis Nucleosynthesis far out

Elements with distance: Testing the hidden eras

Fig. 4. Distant element abundances. Testing element abundances at high redshiftenables us to investigate conditions at very early times (long before the LSS) atlarge distances from our world line. Nucleosynthesis occurs during the first 3 minof the history of the Hot Big Bang, and is sensitive to the expansion rate at thattime; which is determined by the geometry and matter content then.

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 52312the single universe domain we can observe. It is not just that wecannot observe other universes: we also cannot experiment on otheruniverses, nor re-run this one. We have one unique object with oneunique history that we want to understand. No other science has thisfeature. We study specific mountains, oceans, planets, stars, galaxies;but there are other mountains, oceans, planets, stars, galaxies withwhich they can be compared. In the case of cosmology, because thereis only one universe there is no chance of discovering otheruniverses. We might discover other expanding universe bubblesthrough bubble collisions; but those bubbles are part of the oneuniverse (Rees uses the term megaverse).

It is at this point that we inevitably move from more technicalissues to more philosophical ones.

5.1. The philosophy of the historical sciences

There are other historical sciences beside cosmology (forexample, the study of the origin of the Galaxy, the origin of theSolar System, and the origin of life on Earth), and the way theyrelate to theory is different than in the case of the experimentalscienceswhich is why they are often so much more controversial.But in all the other cases there are at least in principle otherexamples we can consider and about which we can one day hopeobtain data (the most difficult example being the origin of life, buteven that may have occurred elsewhere in the universe). This isnot the case as concerns cosmology. It is the unique historicalscience. Hence we need to extract all evidence we can, and checkour theories in all possible ways, as discussed above, just becausewe can't generate extra data by experimental means, as one can dofor example in the case of particle physics. But there are furtherconsequences we now look at.

The issue in all historical sciences is the tension between generallaws and specific applications: how does one relate the influence ofuniversal aspects (necessity) to that of contingent events(chance)? What is the role of specific initial conditions, as againstthat of general laws of universal validity? (see Section 5.2). Inparticular, a key question is, does cosmology have space for non-epistemic probabilities? I return to this in Section 8.55.1.1.1. Cosmic varianceThe specific situation where this matters is the idea of cosmic

variance: the difference between what our statistical set of modelspredicts, and the specific unique outcome we actually encounter.In particular, the observed CMB angular power spectrum issignificantly lower at large angles than predicted by theory. Theissue is whether this large angle discrepancy between theory andobservation is in need of an explanation, or is it just a statisticalfluke due to chance that needs no explanation? This is aphilosophical question that gains a bit of bite because just such acut-off at large angular scales is predicted to occur in smalluniverses (Section 3.1). The usual view is that it is just a statisticalfluke. Starkman, Copi, Huterer, and Schwarz (2012) discuss othersuch anomalies in the CMB observations.

The deeper issue in this regard is the common assumption thatthe universe should not be fine tuned: it is taken for granted thatit should in some sense be of a generic nature. This is a completephilosophical change from what was taken for granted in cosmol-ogy up to the late 1970s: until then it was taken for granted thatthe universe had a very special nature. This was encoded in theidea of a Cosmological Principle, taken as a foundational presuppo-sition of cosmology (Bondi, 1960). The pendulum has swung to theopposite extreme, with people searching for all sorts of explana-tions of fine tuning. But it should be stressed that no physicallaw is violated by whatever fine tuning there may be. Theimprobability of existence of fine tuning is a perfectly validargument in the framework of assuming that there are multipleentities that occur in the universe and are subject to statisticallaws; but there is no possible evidence or proof that the universeitself is subject to any such laws.

So a key philosophical question is as follows: Is the universe probable?That the universe is probable, or at least not too improbable(i.e. it is generic), is an untestable philosophical assumption under-lying much present day work, presumably based in the idea ofprobability in an ensemble of possibilities. But if only one universe isrealised, this ensemble is hypothetical rather than actual, and there isno conclusive reason that it should be probable: the requisiteensemble for that argument does not exist. Maybe the universe ISfine tuned!indeed there is a lot of evidence this is indeed the case(see the discussion of the Anthropic Coincidences in Section 6.1).Additionally of course there are major problems in determining aviable measure to use to determine what is and what is not probable(Gibbons & Turok, 2008; Guth & Vanchurin, 2012; Linde & Noorbala,2010; Mersini-Houghton & Perry, 2012).

Whatever one's attitude, one should recognize that the conceptof fine tuning is a philosophical issue. Worries about fine-tuningare not unique to cosmology. For example it is also discussed inrelation to the hierarchy problem in the Standard Model of particlephysics. But cosmology can be construed as being concerned withwhy the laws of physics are as they are, with explanation at ahigher level than just in terms of what the laws of physics imply.That is, unlike all other sciences, it can be construed as beingconcerned with what underlies the laws of physics. This illustrateshow cosmology is a unique physical science.5.2. Laws and initial conditions

The further key point arising is that because of the uniquenessof the universe, it is not clear how to separate laws (genericrelations that must always be true) from initial and boundaryconditions (contingent conditions that need not be true). Invokingthese provides two rather different kinds of explanation. In effect,they are the difference between necessity and chance.

Given the unique initial conditions that occurred in the oneexisting universe,

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 523 13 We don't know what aspects of those initial conditions had tobe that way, and what could have been different. Some relationships that locally appear to us to be fundamentalphysical laws may rather be the outcome of specific boundaryor initial conditions in the universe: they could have workedout differently.

The prime example is the existence of the second law ofthermodynamics with a specific uniquely determined arrow oftime. No choice of the arrow of time is determined by localfundamental physical laws, which (with one very weak exception)are time symmetric. It seems to be the consensus nowadays thatthe unique one-way flow of time embodied in the cruciallyimportant second law of thermodynamics (Eddington, 1928) isnot after all a fundamental physical law: it is due to special initialconditions at the start of the universe (Carroll, 2010; Ellis &Sciama, 1972; Penrose, 2011).

Another example is the claim that the constants of naturefundamental determinants of local physics (Uzan, 2010)aredetermined by the string theory landscape, and so may vary fromplace to place in the universe. On this view, local physics isvariable and context dependent (Rees, 1999; Susskind, 2006).Effective physical laws are then only locally valid (althoughdetermined by an underlying scheme that is globally valid). Thisis one of the drivers for searches to see if the constants of naturemay vary with position in the universe (Uzan, 2010).

It must be emphasized that neither of these proposals for aglobal influence on local physics can be proven to be the case.Certainly the first is widely believed to be a necessary outcome oftried and tested physics, because otherwise we have no goodexplanation for the origin of the arrow of timeone of thefundamental aspects of local physics. The second is taken by manyto be strongly implied by our best possible approach to a unifiedtheory of fundamental interactions, however this is much morespeculative as it is less well grounded in tested physics.6. Multiverses: denying the uniqueness of the universe

One response to the issues raised in Sections 5.1 and 5.2 is todeny the uniqueness of the universe: to claim we live in amultiverse (Carr, 2009). Various motivations are given for thisproposal:1. It is claimed as the inevitable outcome of the physical originat-ing process that generated our own universe, e.g. as an out-come of the chaotic inflationary scenario or of the Everettinterpretation of quantum theory.2. It is proposed as the result of a philosophical stance underlyingphysics: the idea that everything that can happen happens orwhatever is possible is compulsory3.6 Stenger (2011) argues there is no fine tuning. Barnes (2012) gives acomprehensive response to Stenger.It is proposed as an explanation for why our universe appearsto be fine-tuned for life and consciousness, giving a probabil-istic explanation for why we can exist.

While the first is often claimed from the physics side, it is thethird that is more often the motivation from the philosophical side.

6.1. Fine tuning: the anthropic issue

Examination of theoretically possible alternative universe mod-els shows that there are many very specific restrictions on the waythings are that are required in order that life can exist. Theuniverse is fine-tuned for life, both as regards the laws of physicsand as regards the boundary conditions of the universe (Barrow &Tipler, 1986).As mentioned in Section 5.1, a multiverse with varied localphysical properties is one possible scientific explanation of thisapparent fine tuning: an infinite set of universe domains withvarying physics may allow almost all possibilities to occur, so thatsomewhere things will work out OK for life to exist just by chance(Carr, 2009; Rees, 1999, 2001; Susskind, 2006; Weinberg, 2000).

Note that for this to work as a scheme of explanation, it mustbe an actually existing multiverse: this is essential for any suchanthropic argument. The point is that if such an entity actuallyexists, then probability theory can be applied to estimate like-lihood in an actually existing ensemble, which is constrained bythe nature of the physical processes that led to its existence. If oneis considering a hypothetical ensemble, this is just a mentalconstruction, and this has no causal effect on whatever eventsand objects actually exist in the real universe.

A specific example of the argument is given in Just Six Numbers(Rees, 1999), stating that in order that life can exist, there must befine tuning of the following physical constants:1. Nelectrical force/gravitational force1036

2. Estrength of nuclear binding0.007

3. normalized amount of matter in universe0.3

4. normalized cosmological constant0.7

5. Qseeds for cosmic structures1/100,000

6. Dnumber of spatial dimensions3He explains (Rees, 1999),

Two of these numbers relate to the basic forces; two fix the sizeand overall texture of our universe and determine whether it willcontinue for ever; and two more fix the properties of space itselfThese six numbers constitute a recipe for a universe. Moreover,the outcome is sensitive to their values: if any one of them were tobe untuned, there would be no stars and no life An infinity ofother universes may well exist where the numbers are different.Most would be stillborn or sterile. We could only have emerged(and therefore we naturally now find ourselves) in a universe withthe right combination. This realization offers a radically newperspective on our universe, on our place in it, and on the natureof physical laws.

Note that this assumes the basic structure of physics isunchanged; it is only the constants of physics that vary.

Usually such studies consider varying only one or two con-stants of nature, at a time, but one can envisage multiverses with amuch more general variety of possibilities; one can vary manyphysical parameters simultaneously (Aguirre, 2005). Physical pos-sibility is constrained by laws of physics, but as in the case ofLeibniz's modal metaphysics (Look, 2013), one can look at widerpossibilities: Tegmark (2004) has metaphysical or logical possibi-lity in mind when he proposes that all possible mathematicalstructures are physically realized. In the end, what one assumes tobe possible in a multiverse is a philosophical choice, constrainedby philosophical considerations. However no physical or observa-tional test is possible of whatever assumptions one makes.

Rees focuses on only six parameters, but there are in fact manyother physical constants that must be fined tuned if life is to bepossible (Barnes, 2012; Barrow & Tipler, 1986; Ellis, 2006a).6 Oneparticularly important application of this idea is to explain the smallvalue of the cosmological constant (dark energy) by such an anthro-pic argument (Rees, 1999; Susskind, 2006; Weinberg, 2000), theobserved value being different by 120 orders of magnitude from thevalue of the vacuum energy predicted by quantum field theory

No observational data whatever are available!

Observable universe domain

Extrapolation to unobservable universe domain

Observable universe domain

Extrapolation to unobservable universe domain

Fig. 5. Observational limits outside our past null cone, at two different scales.No observational data are available however anywhere beyond the shadedtriangles, no matter what observational techniques are used. The assumption madein multiverse theories is that we can extrapolate from the observable domain todetermine the nature of the situation at 100 Hubble radii, 101000 Hubble radii, ormuch, much more distant from us (the word infinity is often used). This is anextrapolation on a truly grand scale. We cannot remotely test if it is true or not.Statements about what is out there are faith-based statements rather thanempirically testable proposals.

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 52314(Weinberg, 1989). Too large a positive value for results in nostructure (stars and galaxies) forming as the universe expands, andhence no life being possible; too large a negative value results in theuniverse recollapsing, with too short a lifetime for the universe toallow life to emerge. Thus in a multiverse where takes all possiblevalues, anthropic considerations require that the value of weobserve will be small in fundamental units, thus justifying the valuewe observe. It provides a scientific explanation of this otherwiseextremely implausible value.

But I stress that no specific value of can either prove ordisprove the existence of a multiverse: the argument is based inthe idea of meaningful probabilities, and so assumes a multiverseexists at the start. It is inapplicable if this is not the case. Thisargument provides a useful consistency test of the multiversehypothesis, but not a proof it is correct.

This example makes clear the true nature of the multiverse lineof thought: making the extremely improbable appear probable. Itis a potentially viable explanatory model of fine tuning in theuniverse domain we inhabit and observe. However as mentionedin Section 5.1, even if a multiverse is assumed to exist, it is notclear that a meaningful probability measure is available (see Guth& Vanchurin, 2012; Linde & Noorbala, 2010 for many options). Theoutcomes of those proposed may not favor either the single-field,slow-roll inflation (Gibbons & Turok, 2008), which is indicated bythe recent Planck satellite measurements (Ade, 2013a), nor amultiverse (Mersini-Houghton & Perry, 2012). It is also not clearthat that an infinite universe necessarily allows all possibilities tooccur (see Section 4.1 of Zinkernagel, 2011). In short, the prospectsfor a viable explanation in probabilistic terms in this way are notfully secure.

6.2. Testability

The problems in testing the multiverse are discussed in depthin Ellis (2007, 2013a).

The key observational point is that all the other domainsconsidered in multiverse explanations are beyond the particlehorizon (depicted in Fig. 1) and are therefore unobservable. Theseobservational limits are made clear in Fig. 5. The assumption isthat we can extrapolate from the observed domain to 100 Hubbleradii (roughly: the Hubble radius is the size of the visibleuniverse), 101000 Hubble radii, or much much more. Indeedthe word infinity is casually tossed around in many of themultiverse writings, but we should bear in mind that if we couldsee to 1010,000,000 Hubble radii we would not remotely have testedwhat is claimed, because that is still not even the first step towardsinfinityand we can only see to 42 billion light years.

This sort of extrapolation thus involves an extraordinary claim.It is an explanation whose core feature is the assumption of hugenumbers of entities as large as the entire visible universe that arein principle unobservable. The idea is that the theory (anthropicexplanation of in this way) is so good you should not worryabout the basic epistemic aspect of the theory that is genericallycompletely untestable (see below for the possible exceptionalcases).

Some claim such a multiverse is implied by known physics,which leads to chaotic inflation (Linde, 2003), with differenteffective physics necessarily occurring in the different bubbles ofchaotic inflation (Susskind, 2006). But this is not the case. The keyphysics (e.g. Coleman-de Luccia tunneling or the hypothesizedinflaton potential, the string theory landscape) is extrapolatedfrom known and tested physics to new contexts; the extrapolationis unverified and indeed is unverifiable; it may or may not be true.

For example, the parameter values that led to eternal chaoticinflation may or may not be the real ones occurring in inflation,assuming that inflation happened. And in particular, the supposedmechanism whereby different string theory vacua are realised indifferent universe domains is speculative and untested. Banks(2012) expresses it this way:

The String Landscape is a fantasy. We actually have a plausiblelandscape of minimally supersymmetric AdS4 solutions of super-gravity modified by an exponential superpotential. None of thesesolutions is accessible to world sheet perturbation theory. If theyexist as models of quantum gravity, they are defined by conformalfield theories, and each is an independent quantum system, whichmakes no transitions to any of the others. This landscape hasnothing to do with CDL tunneling or eternal inflation Given thevast array of effective low energy field theories that could beproduced by the conventional picture of the string landscape oneis forced to conclude that the most numerous anthropicallyallowed theories will disagree with experiment violently.

The physics is hypothetical rather than established! Thisextrapolation is untested, and indeed may well be untestable:it may or may not be correct (cf. Section 1).

To sum up: the multiverse proposal is not based on known andtested physics. We will probably never know if it is based in actualrather than hypothetical physics.

Caveat 1: A Disproof Possibility: There is however one casewhere the chaotic inflation version of the multiverse can bedisproved: namely if we observe that we live in a smalluniverse, and have already seen round the universe. In thatcase the universe is spatially closed on a scale we can observe,and the other claimed domains don't exist. As mentioned above(Section 3.1), we can test this possibility by searching foridentical circles in the CMB sky. This is a very important testas it would indeed disprove the chaotic inflation variety ofmultiverse. But not seeing them would not prove a multiverseexists: their non-existence is a necessary but not sufficientcondition for a multiverse.Caveat2: A Proof Possibility? An interesting recent developmentis the idea that proof of existence might be available throughbubble collisions in the multiverse. Bubbles in chaotic inflationmight collide if the rate of nucleation is large relative to the rateof expansion, and this might be observable in principle bycausing recognizable circles in the sky, with different proper-ties in their interior as opposed to the exterior. This is an

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 523 15intriguing idea, notwithstanding the difficulties of predictingwhat would happen if spheres with different physics inter-sected each other. The clincher would be if one could demon-strate different values of some fundamental constants insideand outside such circles (Olive, Peloso, & Uzan, 2011): thatwould vindicate the idea of different physics occurring indifferent domains, the core feature of a multiverse explanation.However, not seeing such circles does not disprove the multi-verse idea: these collisions would only occur in restrictedcircumstances in some multiverse instantiations. But this iscertainly worth looking for. Indeed it is the only knownobservational test that would give genuine support to thephysics of the multiverse proposal.However a conceptual problem with the idea of bubble colli-sions is noted in Rugh and Zinkernagel (2013). Such bubblecollisions threaten the satisfaction of the Weyl principle in themultiverse, and hence the often assumed notion of a well-defined global multiverse time. More generally, the cosmicmeasurement problemthe still unexplained quantum-classical transitionmay undermine even the idea that partsof the multiverse causally and temporally precede our universe.Caveat 3: Negative curvature? There are some theories claimingthat a multiverse predicts the universe must have open spatialsections (Freivogel, Kleban, Martinez, & Susskind, 2006;Susskind, 2006)but that only holds for some multiversetheories. The theories are extremely malleable. Some of themare constrained to obey the supposed 10500 possibilities of thestring theory landscape. But we don't know what thesepossibilities are, we don't even know if they include the physicswe actually experience, and the status of this landscapeproposal is disputed in the string theory community.

6.3. Criteria for a scientific theory

Given that generically a multiverse proposal is not testable inany ordinary way, the question arises: is it science? We need toconsider what is the core nature of a scientific theorya philoso-phical question. The kinds of criteria usually invoked are,1. Satisfactory structure: (a) internal consistency, (b) simplicity(Ockham's razor), (c) beauty or elegance;2. Intrinsic explanatory power: (a) logical tightness, (b) scope ofthe theoryunifying otherwise separate phenomena;3. Extrinsic explanatory power: (a) connectedness to the rest ofscience, (b) extendabilitya basis for further development;4. Observational and experimental support: (a) the ability to makequantitative predictions that can be tested; (b) confirmation:the extent to which the theory is supported by such tests.

It is the last one that characterizes a theory as scientific, incontrast to other types of theories that would like to be classedas scientific but are rejected by mainstream scientists, such asAstrology or Intelligent Design. Their adherents claim that they allsatisfy the other criteria; it is predictive observational test andexperiment that separates establishable sciences from these clai-mants. This is what led to the rise of science and its extraordinarysuccess; it should not be watered down without utmost care inconsidering the consequences.

One must beware the non-uniqueness of both Occam's razorand criteria of beauty. Is the multiverse idea beautiful? It dependson the eye of the beholder. Does it satisfy Occam's razor? Onesingle entity (a multiverse) explains everything one wants toexplain: the height of economy! But wait a minute: that oneentity consists of countless billions of entire universe domains,each as large as the universe region to be explained, and eachcontaining a huge number of galaxies. Besides, these domains areoften stated to be infinite. In this light it is a most extraordinarilyextravagant postulation of innumerable unobservable uni-versesall to explain one single entity (the observable universe).It hardly can be characterized as an exercise of parsimony, asadvocated by William of Ockham (It is futile to do with morethings that which can be done with fewer).

6.4. Justifying unseen entities

There are different notions of unseen or unobservable invarious physics contexts; whereas there is a very clearcut sense inwhich the multiverse is unobservable. Probabilistic predictionsprovide sufficient grounds for taking unobservables to be real ingeneral, but not in cosmology because in general the unobserva-bles have consequences in many different contexts and so the theirhypothesized existence can be tested in different contexts. In thecase of cosmology it can only be tested in one context, i.e. it is anad hoc explanation for one instance. However a broader traditionalphilosophical issue arises from this discussion: When can existence of unseen entities be justified?Examples are the metric tensor in general relativity theory, theelectric field, dark matter, and dark energy in cosmology. Whatjustifies thinking of these as real? Or should they rather bethought of as fictitious entities which are useful, perhaps evenindispensable for our theorizing, but with no physical exis-tence?My own view is that unseen entities can be taken as real if1. They form an essential link in a chain of argument with well

supported foundations,2. They have demonstrable predictable effects on the physical

world of matter which we see around us, that are inagreement with experimental phenomena, and

3. There is no other plausible explanation for the samephenomena.One should test any such proposed entity in a variety ofcircumstances. This applies to: entities such as the metric tensor,the electric field, dark matter, dark energy, other people's emo-tions, the mind, a soul; and modify the proposal if the outcomeseems unsatisfying

Are these criteria satisfied by the proposal of a multiverse? Inmy view, the proposal does not satisfy 1., because the foundationsare not well supported; nor 2., because the outcomes of multiversehypothesis are not predictable; nor 3., because for example thephenomenon in question might simply be sheer chance: as statedbefore (Section 5.1), probability need not apply to the universe.This is where underlying philosophical presuppositions come in.The outcome depends on those assumptions; and we have reason-able grounds for choosing to emphasize the importance of 4.(observational and experimental support); and this is where themultiverse proposal very short. Multiverse adherents also claim itis strongly supported by criterion 3 (Extrinsic explanatory power);but as noted above, the areas of physics that it is strongly linked to,such as string/M theory, are speculative and unproven rather thanexperimentally well-established domains. These areas are fashion-able but not necessarily correct descriptions of the real world. Onepoint of clarification here: claims have been made of probabilisticprediction of the value of the cosmological constant, similar towhat is seen (Weinberg, 2000). But these are statistical predic-tions: they have no meaning if there is only one universe. They areconsistency tests of such a multiverse proposal, but cannot betaken as proofs, for they take for granted what is to be proven.They are probabilistically suggested but not sufficient conditionsfor existence of a multiverse.

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 52316In these sections we are touching upon the topic of scientificinference and its philosophy of inductive reasoning, with justifica-tion by abduction to infer a postulated hitherto unseen entitybecause of its unifying explanation of disparate phenomena.We consider a piece of evidence to confirm (or disconfirm) ahypothesis because the evidence makes the hypothesis more (orless) likely to be true, as can be formalized by using Bayes'Theorem as a formal model of inference. The problem in this caseis that there most probably will be no available evidence to use insuch inference.

6.5. Multiverses: the big issue

The multiverse program involves downgrading criterion 4(Observational and experimental support) relative to the others(Satisfactory structure, Intrinsic explanatory power, Extrinsicexplanatory power). This is dangerous thing to do in that thisamounts to a redefinition of what constitutes genuine science,because criterion 4 is at the heart of the scientific method. Thisopens the door for all sorts of enterprises that are presently notconsidered genuine science to be reclassified as true science.In order to explain one single entity, multiverse explanationssuppose billions or even an infinite number of unseen anduntestable entities at the same level of complexity as that to beexplained. They cannot be adequately justified according to thecriteria just discussed. But the very nature of the scientificenterprise is at stake in the multiverse debate: the multiverseproponents are proposing weakening the nature of scientific proofin order to claim that multiverses provide a scientific explanation.This is a dangerous tactic; and it does not solve the ultimate issuesit is claimed to solve, as discussed below.

Bill Stoeger responds to this (private communication), If aparticular type of multiverse model (i) were an essential elementin a well-supported theory about the origin of our observableuniverse and its characteristics, and (ii) that theory enjoyed longterm success in bringing progressively more aspects of our uni-verse into a coherent overall picture, and (iii) provided a basis forother fruitful advances in cosmology and physics (better thanother competing theories), then, it seems to me that we couldlegitimately maintain scientifically that that multiverse exists.It seems to me that, at least in principle, it is possible to fulfillall three in the case of a multiverse. The proposal certainly mustaccount for all or most of thosebut prediction is somethingdifferent from that.

This is perhaps a viable standpoint. However it seems to me themultiverse proposal is presently a long way from meeting theseconditions, and it may never do so. Overall it is a very interestingphilosophical proposal, based on speculative science. As such it is agood contribution to cosmology; but it is unproven and indeedprobably unproveable; this status should be acknowledged. Beliefin its correctness is, at present, just that: it is a belief. It is notestablished fact.7 A similar discussion of infinities in a k0 or k1 FLRW model with itssimplest topology was given by Ellis & Brundrit (1979), where it was suggested thisimplication of infinite duplications is a philosophical argument against suchinfinities occurring.6.6. Infinities

One particular area where one should be cautious is as regardsthe often claimed existence of physically existing infinities: eitherof universes, or of spatial sections and matter in some physicallyexisting universe. In the multiverse context, it is claimed both suchinfinities exist (Vilenkin, 2007). However if they do indeed occur,they don't occur in a finite time: they are always in the process ofcoming into being in the future (Ellis & Stoeger, 2009b). They don'texist at any finite time.

One should remember here the true nature of infinity: it is anentity that can never be attained, it is by definition always beyondreach, so no physical process can create an infinity of anything.David Hilbert stated: the infinite is nowhere to be found in reality,no matter what experiences, observations, and knowledge areappealed to (Hilbert, 1964). I will refer to this as Hilbert's GoldenRule:

If an essential use of infinity occurs as a core part of anyexplanatory model, it's not science.

Here one should distinguish between essential and inessentialuses of infinity. An inessential use of infinity occurs if it just stands for a verylarge number (as for example in studies of asymptotic flatness).In this case, one should refer to that very large number ratherthan invoking infinity. Good physics resides in determininghow large that number should be.For example, when one calculates outgoing radiation from anisolated gravitational system such as a binary pulsar, when hasthe variable r representing distance from the system becomeinfinite for all practical purposes? I propose the name finiteinfinity for a sphere surrounding the object at this distance(Ellis, 1984); for the solar system or a binary pulsar, it occurs atabout one light year's distance from the center (Ellis, 2013b).Considered at this distance, the solution is asymptotically flatto high accuracy, and one can calculate the mass of the system,outgoing radiative energy, a news function, and so on. If oneextends the solution to larger radii, the further one goes, themore inaccurate is the representation of what is actually there(the other stars, black holes, and so on that actually occur arenot represented by the asymptotically flat model). Similarconsiderations arise in the thermodynamic limit in statisticalmechanics; the number N of particles cannot be infinite inpractice. Good physics resides in determining how large N mustbe in order to have effectively reached that limit. An essential use of infinity occurs if one uses its paradoxicalproperties (such as 2 11, or 1+11) in an essentialway in a physical argument. In these cases, the argumentshould be rejected, because it refers to physical conditions thatcan never be attained in physical reality (as well as beingstrongly contra-indicated by Occam's Razor).An example is Vilenkin's (2007) book on multiverses, where heemphasizes precisely these paradoxical properties to makemany claims about their implications: an infinite number ofrepetitions of every event that occurs in our history occurs inother universes in the multiverse, because (given the impliedexistence of infinities of galaxies) the probability that they willoccur is unity.7

Another example is Deutsch's use of uncountable infinities offungible particles' (to be fungible is to be identical in literally everyway, see Deutsch, 2011a) in order to obtain the Born rule in hisversion of the Everett multiverse proposal (Deutsch, 2011b).Classical events are to be realised through existence of uncoun-table infinities of these hypothetical entities (Rae, 2011).

Both classical and quantum field theories have several exam-ples of references to the continuum (including the continuum limitand the notion of an infinite number of degrees of freedom).I interpret the above to suggest that spacetime must be quantized;then these infinities will hopefully go away.

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 523 17In any case, any claim of physically existing infinities iscompletely untestable: if we could see them, we could not countthem in a finite time, because by the very nature of infinity,the counting can never be complete. So we can never prove theclaimed physical existence of an infinity of any kind entitieswhatever; all we can ever prove is that a very large number exist,which is a completely different situation.

Hence if science is taken to refer to statements that are at leastin principle testable, any such claims are not genuine science.Insofar as they are proposed as an essential part of any multiverseproposal, they weaken yet further the claim of that theory to be ascientific theory.7. Physical laws and different kinds of existence

This section considers first (Section 7.1), the physics horizonthat limits our ability to test the physics applicable to the earlyuniverse. Then it considers (Section 7.2) physical and non-physicalrealities that are implicitly assumed to exist by physical cosmologytheories. Section 7.3 relates this to the pre-existing entities that areassumed by various theories of creation of the universe.

7.1. The physics horizon

Limits to testability: As has already been mentioned, a key issuein our attempts to use physical laws to understand the universe inwhich we live is the limits to what is testable in the laboratory andin the solar system. To tackle causation in the very high energies inthe very early universe, we have to extrapolate known physicallaws to domains where they are untested and maybe untestable.

We hit the Physics Horizon: that is, the limits not just on what istestable now, but also on what it will ever be possible to test in alaboratory or accelerator. Physics at higher energies is not con-firmed, and indeed is not confirmable. Different extrapolations arepossible from known and testable physics, with different out-comes (see Section 1.3).

This is relevant to the very early universe (before inflation)with the very high energies involved: hence uncertainty increasesmore and more as we consider physics further and further to thepast in the very early universe. Particularly, it applies to theories ofthe creation of the universe itself. Whatever we may assume aboutsuch creation, we certainly cannot test the relevant physics,pre-physics, or metaphysics, whichever controls what happensassuming one of these ideas makes sense in this context.

Of course we must explore all alternatives: Models based in the wave function of the universe,

Pre-big bang and cyclic cosmologies,

Brane cosmology and string cosmology,

Loop quantum cosmology8 Example: when I was working on singularity theorems in General Relativity,we regarded a solution as excluded if it implied negative kinetic energies. This is nolonger taken to be the case.(see Ellis et al., 2012 for summaries of these proposals). But allof them are highly speculative untested physics, and most sufferfrom mathematical problems such as ill definition, or divergences,or arbitrary assumption of a matter behavior that is nothing likewhat we have ever encountered in a laboratory.

We must test the outcomes of such theories as we can, but onemust be cautious about testing them only by matching the CMBanisotropies, which they all laudably strive to achieve. The basiclogical point is that, if we call a cosmological hypothesis H and atestable outcome O, {H-O} does not imply {O-H}. For exampleCMB predictions are crucialthey are necessary for a viablecosmological theorybut by themselves are not sufficient toestablish any specific such theory.Respecting known physics: We have to extrapolate beyondknown physics in exploring these issues, but in trying out suchspeculative physical ideas, one should not just abandon basicphysics constraints on what is possible, as seems to be happeningin some of the cosmology literature. Particular examples are: one should avoid theories with a varying speed of light, unlessyou show how to reliably determine distances independent oflight (Ellis and Uzan, 2005); one should avoid dark energy theories with w:dp/do1,unless you have a truly viable theory of how this can emergefrom the underlying physics (rather then being due to negativekinetic energy), and can explain how it won't lead to majorinstabilities (due to the negative inertial mass density).

Currently, there is a culture of allowing anything whatever inspeculative cosmological theoriessometimes abandoning basicprinciples that have been fundamental to physics so far. Sciencewriter Margaret Wertheim attended a 2003 conference on stringcosmology at the Santa Barbara KITP, and reported as follows(Wertheim, 2012):

That string cosmology conference I attended was by far the mostsurreal physics event I have been to, a star-studded proceedinginvolving some of the most famous names in scienceAfter twodays, I couldn't decide if the atmosphere was more like a children'sbirthday party or the Mad Hatter's tea partyin either case,everyone was high the attitude among the string cosmologistsseemed to be that anything that wasn't logically disallowed mustbe out there somewhere. Even things that weren't allowed couldn'tbe ruled out, because you never knew when the laws of naturemight be bent or overruled. This wasn't student fantasizing insome late night beer-fuelled frenzy, it was the leaders of theore-tical physics speaking at one of the most prestigious universitycampuses in the world.

This illustrates why the claims emanating from this approachshould be regarded with great caution: they are in many casesunsupported by evidence and are based on arbitrary assumptionsthat don't satisfy usual physical criteria. Once the gold standard ofexperimental support has been dropped and basic scientificprinciples are disregarded,8 why should such theories be regardedas good science?

7.2. Physical and non-physical realities

Underlying one's view of the nature of cosmology is the issue ofwhat kinds of entities are supposed to exist: a significant philo-sophical issue. Obviously one assumes existence of matter andfields, and (as we use General Relativity as our gravitationaltheory) of spacetime. But these are not the only kinds of entitieswe assume exist. As well as these physical entities, we have toassume existence of at least two other kinds of entities that are notthemselves physical.

Physical laws: First we assume the existence of physical laws.These are not the same as matter or fields: rather they are whatshape the behavior of matter and fields. Equivalently one can talkof the existence of possibility spaces for matter and fields (Ellis,2004). These have two aspects: first there is a space of all possiblestates for the system (called a phase space in physics), which mustrepresent any physical constraints on such states. Second there is aset of flows on that space, giving a phase portrait representing the

G.F.R. Ellis / Studies in History and Philosophy of Modern Physics 46 (2014) 52318possible dynamical histories of the systems represented. Togetherthese are essentially equivalent to the laws that shape the physicalbehavior, just as a set of dynamical equations are essentiallyequivalent to the set of all their solutions.

These laws, and the associated possibility spaces, are notculturally determined or variable (although their specific repre-sentations are culturally variable). They embody the essentialnature of matter, and are eternal, unchanging, and omnipresent,with their outcomes crucially shaped by the values of specificfundamental constants (Uzan, 2010).

Mathematics: Second we have to assume the existence in someform or other of mathematics. I follow the philosophical doctrineof mathematical Platonism supported by Frege, Quine, and Lewis(see Linnebo, 2011), as well as by Penrose (1997, 2006) and Connes(Changeux & Connes, 1998). This assumes that mathematics isdiscovered rather than invented, hence exists in some kind ofeternal and unchanging form independent of matter and mind, oftime and place. That is, mathematics has some kind of Platonicexistence in a space of logical possibilities, which we explore bylogical argumentation. In some mysterious way it underlies orunderpins the nature of physical laws (Penrose, 1997, 2006).

These possibility spaces are both unchanging and eternal: theyare the same everywhere in the universe, and are independent ofhuman existence, although the way we express them will beculturally determined. We discover them and explore themthrough the processes of our mind (Churchland, 2012). They areparticular cases of the possibility spaces discussed below (Section 8.5).7.3. Pre-existing entities

Where this specifically matters is as regards the relationbetween the laws of physics and creation of the universe. Thekey issue here is as follows: What if anything was there pre-existing the universe?According to the way this is talked about by various cosmol-ogists (e.g. Hawking & Mlodinow, 2010; Krauss, 2012; Vilenkin,1982), the