ETERN4 - University of Cambridge · 2012. 1. 27. · Alan Guth Massachusetts Institute of T...

OUTLINE: Eternal Inflationand Its Implications

1) Background: Ination is a big success.

2) Why should I take eternal ination and the multiverse seriously?

3) What does eternal ination buy me?

4) What does eternal ination cost me?

Alan Guth

Massachusetts Institute of Technology

Stephen Hawking 70th Birthday Conference, January 5, 2012 {6{

1. Background: Inflation is A Big Success

Alan Guth



Successes of Inflation

1) The universe is big| about 1090

particles!

2) Hubble expansion| what was therepulsive driving force?

3) Homogeneity and isotropy| in theconventional big bang (without ina-tion), cosmic microwave backgrounduniformity requires communication� 100 times speed of light.

4) Flatness Problem | why was themass density at t = 1 sec equalto the critical density to 15 decimalplaces?

5) Why no magnetic monopoles?

6) Nearly scale invariant, adiabatic,Gaussian density perturbations.

Alan Guth



CMB:Comparisonof Theory

andExperiment

Graph by Max Tegmark,for A. Guth & D. Kaiser,Science 307, 884

(Feb 11, 2005), updatedto include WMAP7-year data.

Alan Guth



2. Why Should I Take Eternal Inflationand the Multiverse Seriously?

Alan Guth



Eternal InflationIn Our Pocket

Our own universe appears to have � > 0, so it is entering a periodof ination.

If our vacuum is stable, then our visible universe will becomeeternal. Life will die out, but the inating region will expandforever, without any limit on its volume.

If our vacuum is metastable, it has to have a decay rate � � H4to prevent eternal ination. Otherwise the volume will continueexpanding forever despite the decays. Tunneling events in ourown pocket universe will create an in�nite number of others.

Alan Guth



Almost All Models Are Eternal

Essentially all models of ination lead to (future) eternal ination.

Crude explanation: inating false vacuum is metastable, butdecay rate � expansion rate. Therefore the volume of falsevacuum increases exponentially with time.

Once ination starts, it never stops. The inating region neverdisappears, but pieces of it undergo decay and produce \pocketuniverses" ad in�nitum.

Alan Guth



Three strong winds blowing in the direction of the multiverse|a diverse multiverse where selection e�ects play an importantrole.

1) Theoretical Cosmology: Almost all versions of ination leadto eternal ination; once ination starts, it never stops.

2) String Theory: Most string theorists are convinced thatthere is no unique vacuum. Instead, there are at least � 10500long-lived metastable states, any one of which can serve asthe substrate for a pocket universe.

3) Observational Cosmology: The cosmological constant �.The most plausible known explanation for small � is theanthropic one, using the multiverse. That is, the set of stringtheory vacua is expected to include many with � as small aswhat we observe, eternal ination can populate these vacua,and life is expected to form only where � is small.

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3. What Does Eternal Inflation Buy Me?

Alan Guth



What Does Eternal Inflation Buy Me?

a) Independence of Initial Conditions

With some assumptions, an eternally inating universe approaches asteady-state equilibrium, so the initial conditions do not a�ect late-time predictions. (This depends on the measure question, but is truefor many proposed measures, including all my favorites.)

Alan Guth



b) Possible Explanation for Small VacuumEnergy Density

The vacuum energy density is at least 120 orders of magnitudesmaller than expected, and there is no known, accepted, dynam-ical explanation.

But string theory strongly suggests that there are at least � 10500long-lived vacuum-like states, so we expect many of these to havevacuum energy densities as small as what we observe.

If eternal ination populates these vacua, and selection e�ectscause life to predominantly form in these vacua, then the smallvacuum energy density is explained. That is, maybe almost allliving things see a small vacuum energy density, even if it is veryrare in the multiverse. [Refs: Weinberg, 1987; Martel, Shapiro, and Weinberg,1998.]

Alan Guth



c) Avoidance of Thermal Equilibrium Phase

I am not aware of any papers that make this argument (in full).

Need to avoid thermal equilibrium:

� Suppose, for example, that reality can be described by some quantumsystem with a maximum possible entropy. Then the system will reachthermal equilibrium and undergo Poincar�e recurrences forever, and allmicrostates will occur and re-occur with equal probability.

� Life (including observers like us) will continue to occur in the thermalequilibrium phase, but with overwhelming probability the worlds that theywill observe will look nothing like ours. Boltzmann brains.

� We think that the world we see looks the way it does because of itsbig-bang history. But in thermal equilibrium, probabilities are determinedONLY by state counting. For example, a state that looks just like ourworld except that TCMB = 10 K would have more microstates, and wouldbe much more likely than 2:7 K. [Ref: Dyson, Kleban, & Susskind (2002).]

Alan Guth



c) Avoidance of Thermal Equilibrium Phase, Cont.

If the semiclassical global picture of eternal ination is valid,then new pocket universes are constantly being created and newregions of phase space are constantly being explored. Poincar�erecurrences do not happen.

For this to happen, the available classical phase space must bein�nite, or the quantum mechanical Hilbert space must be in�nite-dimensional.

Alan Guth



d) Explanation of Fine-Tuning:Infinite vs. Finite Phase Space

Can Hamiltonian evolution, consistent with Liouville's theorem, leadto �ne-tuning of parameters?

For �nite phase space, NO:

Time evolution merely pushes the probability distribution aroundin phase space. What is rare at one time is rare at all times.

BUT: if available phase space is in�nite, the answer is YES!!

Alan Guth



Can Hamiltonian evolution, consistent with Liouville's theorem, leadto �ne-tuning of parameters?

Example (due to Larry Guth):

H = tan�1(�pq) :

(Time independent, bounded from below.)

_p =p

p2q2 + 1_q = � q

p2q2 + 1:

For any normalizable initial probability distribution, for any � > 0,and for any Æ > 0, there exists a T such that

t > T =) P (jqj < Æ) > 1� � :

Alan Guth



e) Explanation of The Arrow of Timewith Infinite Phase Space

In an in�nite phase space, achieving an arrow of time fromessentially arbitrary initial conditions is not a problem.

To see how this works in principle, consider a gas of particles asan example. Consider choosing initial conditions for each positionand velocity from some normalizable distribution.

Let the system evolve for a long time. The momentum distribu-tion will remain approximately �xed, but the position distributionwill spread without limit. Coarse-grained entropy will grow.

Alan Guth



Key point: there is no maximum entropy! Whatever the initialentropy was, it was small compared to the maximum.

If the system is evolved backwards in time, entropy will alsoincrease in the time-reversed direction.

The argument here shows, by a simple example, how in principlean arrow of time can emerge from random initial conditions.To see how this works in detail, in eternally inating models,see R. Bousso, \Vacuum Structure and the Arrow of Time,"ArXiv:1112.3341 [hep-th].

Alan Guth



4. What Does Eternal Inflation Cost Me?

Alan Guth



What Does Eternal Inflation Cost Me?| A Problem in Defining Probabilities

Anything that can happen will happen | an in�nite number oftimes!

To separate the probable from the improbable, we need tocompare in�nities.

Example of ambiguity: what fraction of the positive integers areodd? Normal answer: 1/2. BUT, consider listing the integers as1; 3; 2; 5; 7; 4; 9; 11; 6 ; : : :, always writing two odds and thenthe next even. Each positive integer appears once and only once,yet it looks like 2/3 of the integers are odd!

Probabilities can be de�ned by introducing a cuto�, but in thiscase the answers can depend strongly on the type of cuto�.

Alan Guth



The Measure Problem

A measure is a prescription for de�ning probabilities in aneternally inating universe.

A measure is a prescription for regularizingRd4x

pg for the

multiverse: how can one say that one type of event is twice asfrequent as another type.

Alan Guth



Is the Measure Problem a Show-Stopper?

Don't think so.

The description of the multiverse itself is not a problem (See Guth& Vanchurin, arXiv:1108.0665 [hep-th]).

Can imagine describing multiverse on a lattice that grows expo-nentially with time.

The update rule is de�ned by the laws of physics.

The in�nite system is mathematically well-de�ned, just like theintegers.

There have been claims that time must end, but Vanchurin claimto have shown that there is no reason to assume that timeends.

Alan Guth



Multiverse itself is a mathematically well-de�ned system, whichis even well-motivated by what we understand of fundamentalphysics.

Measure problem arises only when we try to count events in themultiverse.

The fact that we don't understand the measure problem is noreason to think eternal ination is o� track.

Nature is not required to behave in a way that we �nd easyto understand.

(Arthur Eddington refused to believe that stars could collapse toblack holes, because we would not understand where this wouldlead.)

Alan Guth



Status of the Measure Problem?

A number of possible pitfalls have been discovered, rulingout many proposals. Examples: the youngness problem, theBoltzmann brain problem, the Q-catastrophe.

A number of successful prescriptions for the measure have beenproposed. These include the scale-factor cuto� measure, thecomoving apparent horizon cuto� (CAH+) measure, the causalpatch measure, Nomura's quantum meausure, etc.

Some of these measures depend on initial conditions, and othersdo not.

No general principle has been found to determine the measure.

There is promising research, starting with Garriga and Vilenkin(Holographic Multverse, arXiv:0809.4257 [hep-th]) that attemptsto describe the regulator as a short-distance cuto� on a dualconformal �eld theory de�ned on future in�nity.

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OUTLINE: Eternal Inflationand Its Implications

1) Background: Ination is a big success.

Explains why the universe is big, expanding, homogeneous,

at, devoid of visible monopoles, and has the density pertur-bations that it does.

2) Why should I take eternal ination and the multiverse seriously?

Essentially all inationary models lead to eternal ination.

The landscape of string theory.

The evidence for a very small but nonzero cosmologicalconstant.

Alan Guth



3) What does eternal ination buy me?

Independence of initial conditions (?)

Explanation of the cosmological constant

Avoidance of a thermal equilibrium phase

With in�nite phase space, �ne-tuning and the creation of anarrow of time can be achieved by Hamiltonian evolution.

4) What does eternal ination cost me?

The measure problem | which is still open.

Alan Guth



ETERN4 - University of Cambridge · 2012. 1. 27. · Alan Guth Massachusetts Institute of T...

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