Horizon Physics & String TheoryPlan:

I. Classical spacetime, particle motion, and horizons

II. Two important examples observed in nature:

--Cosmological horizons and the origin of structure *Beautifully simple theory of seeds for structure, quantum uncertainty principle in expanding universe

*Yet, sensitivity to quantum gravity and a role for string theory in empirical science. (including spinoffs: improved understanding of theory and observational constraints).

--Black hole physics *major puzzles for quantum gravity and a role for string theory in their resolution.

To build up to this, we'll start from some basic principles and familiar geometry:

Nothing moves faster than light does on the spacetime geometry.

Particles not subject to non-gravitational force take the shortest path.

Let's start with flat spacetime (with no matter or radiation to cause curvature).

Actually, let's start just with flat space (no time). Pythagorean theorem:

Can rotate or shift the picture without changing this relation.

Now include time:

Can boost or shift without changing:

More on `boost' (for those who like equations):

Boost speeds up massive particle motion, but the light cone (and the speed of light c) is fixed.

Generalize to curved spacetimes:

What do we mean by curvature?

This is intrinsic to the spacetime (not embedded in larger system). Basically a measure of how lengths change as we move in the spacetime.

space (two dimensional):

spacetime: neighboring initially parallel trajectories move apart or together

In flat spacetime, an observer has access to light rays from all of space if they wait long enough. Can send signals from any finite-energy massive trajectory to another.

If the observer accelerates uniformly, they can lose contact (`Rindler Horizon') but this takes an infinite amount of energy.

Horizons:The Einstein equations have solutions in which observers lose contact with each other (can't communicate even with light rays).

The energetics of light and matter probing such a geometry is strongly affected by this.

For example, de Sitter (exponentially expanding) cosmology:

Black Hole horizon

Classically, exterior geometry largely independent of formation matter, just depending on mass, spin, charge. There is substantial evidence that this is just a coarse-grained description.

Energetics and horizons:

Clock of an observer far outside ticks infinitely many times as an infaller approaches the horizon.

Escape velocity is the speed of light at the horizon.

The curvature is mild; a particle crossing the horizon in classical GR is relatively unperturbed.

(curvaturesmall despitecircles shrinking)

There is substantial observational evidence for both kinds of horizons

Sensitivity to EM and gravitational radiation closer in

black holes

Cosmological horizons

Late Universe

Early U: As we will discuss, radiation from the time that atoms formed behaves as expected if expansion was accelerated.

Planck

Separation of energy scales and `dangerous irrelevance'

How do we ever do physics with so much that is unknown? Wilsonian effective field theory (basic idea):

Physical quantity, such as force between two objects, or scattering probability, has a leading contribution at low energies, and subleading corrections that have to do with unknown higher energy physics.

infinite sequence of `irrelevant' terms.

For many purposes, at long distances (low energies) we can ignore the infinite sequence of unknowns. But for a process that goes over sufficiently long time periods, or over sufficiently large ranges of fields (and/or with sufficient amounts of data), sensitivity to higher energy physics can develop.

An electromagnetic example: Consider a weak electric field permeating space, with two charges initially sitting at rest.

The weak field accelerates charges over a long time, producing a large invariant energy

A similar effect occurs in weakly curved geometries with a horizon: evolution of trajectories of (say) two probes sent in with modest energy leads to a large nonlocal invariant energy in the near horizon region.

In early universe cosmology, we find `dangerously irrelevant' features (spoiler alert):

Substantial data, including

Planck ESA

I. Cosmology:

*Expansion of the universe*Cosmic inflation*Quantum fluctuations and structure*New tests for degrees of freedom and interactions

Role of Quantum Gravity (String Theory):--accounts for dangerously irrelevant effects, especially `large-field' inflation with detectable primordial gravitational waves--Major spinoffs: mechanisms for inflation and observable signatures, incorporated into low energy description and data analysis

The probability to find the particle at some position, in the ground state, is a Gaussian function (normal distribution)

This is (schematically) the answer if the field fluctuation is non-interacting. It is a good approximation, but nowadays we are testing for interaction effects on P()

Horizon Physics & String TheoryPlan:

I. Classical spacetime, particle motion, and horizons

II. Two important examples observed in nature:

--Cosmological horizons and the origin of structure *Beautifully simple theory of seeds for structure, quantum uncertainty principle in expanding universe

*Yet, sensitivity to quantum gravity and a role for string theory in empirical science. (including spinoffs: improved understanding of theory and observational constraints).

--Black hole physics *major puzzles for quantum gravity and a role for string theory in their resolution.

Previously, on Horizon Physics...Nothing moves faster than light...

``Curvature = Energy" equations lead to spacetimes with horizons

In early universe cosmology, exponential expansion plus exit introduces scalar field fluctuations that freeze out at Hubble scale.

We can systematically parameterize high energy physics effects, often irrelevant but can matter over long times, large fields

Inflation plus quantum uncertainty principle:

The coefficient functions in our interval ds are dynamical, so just like they can't help but fluctuate according to the Heisenberg uncertainty principle.

Fluctuations of and of the geometry

Primordial gravitational waves!

Springel, Frenk, White

Observations

Simulations

Measurements of the frequency dependence (black body) and tiny spatial fluctuations of the light, including its polarization, have helped precisely constrain the model of the expanding universe, requiring so far only 6 parameters

Planck ESA (cf COBE,...,WMAP...)

Superhorizon perturbations:

*Fluctuations correlated on scales longer than the size of the horizon at the time when atoms formed. **The polarized light created at this time, no further inside-horizon sources that could mimic its structure. (Spergel/Zaldarriaga, cf Turok)

Alternative(s?):I. Cosmic strings: well-defined theory, ruled out as leading seeds of structure.

II. Bounce? Clever idea (super-horizon for different reason), but much more difficult to control. Existing examples either don't bounce, or do using exotic energy sources incompatible with black hole thermodynamics (see below).Regardless, spacetime singularity resolution is a great problem.

Pen, Seljak, Turok '97.

Primordial gravitational wave search:

The next round will test field range between ~10 Mp and ~ 1 Mp. This is extraordinary reach. (Instant gratification for a string theorist!)

BICEP/Keck(+Planck), SPIDER, SPT, ABS, PolarBear, Simons Observatory, CMBS4, LiteBird, CLASS,...

This is just the beginning. The large amount of data collected also enables us to distinguish qualitatively distinct inflation mechanisms. Also test for more subtle effects of particles and fields operating during inflation (nearly 14 billion years ago). These are subleading to the essential features of inflation already tested. Inflation and its observables -- especially those testable with the gravitational wave search -- are sensitive to quantum gravity.___________________________________We lack a complete theory of cosmology as a whole, related to puzzling features of horizons as well as strongly-curved `singularities'.

Many tests of the interactions of primordial fields. One current example (data analysis in progress) concerns massive particles which could source highly nonlinear perturbations

Not just a bell curve, more structure. An example of `non-Gaussianity'.

Many early and ongoing works on effects of additional massless fields, e.g. Bond et al.

CMB Data reach:

Statistical noise from the quantum fluctuations themselves. More data => more independent tests => smaller error bars. Roughly:

Data increasing (+large-scale structure)

Results will be either concrete bounds on masses/couplings of particles propagating ~14 billion years ago, or discovery of parameter consistent with their existence. (Standard scientific methodology.)Flauger, Mirbabayi, Senatore, ES, Munchmeyer/ Planck, Smith, Wenren, cf Peiris, Easther, Komatsu/Spergel/Wandelt,...

Position space features

Similar picture for strings, could test them as well as different particle properties.__________________________________

Search well underway, but I can't give results yet. Hopefully this gives you an idea of the powerful reach of modern cosmological data for high energy physics.

Note that the possibility of, and tests for, substructure in the CMB fluctuations does not detract from the scientific status of inflation.

The leading effects are as predicted in inflation. Subleading corrections could be there or not, depending on the details.

We are interested in them because of the rich window it provides into dynamics in the very early universe. This includes observables sensitive to quantum gravity corrections:

`Dangerous irrelevance' and String Theory

Recall idea of a series of correction terms

For V(this is

Irrelevance versus `dangerous irrelevance' of high energy physics:

For many purposes, at long distances (low energies) we can ignore the infinite sequence of unknowns when we parameterize our ignorance of high energy physics. But for a process that goes over sufficiently long time periods, or over sufficiently large ranges of fields (and/or with sufficient amounts of data), sensitivity to higher energy physics can develop.

This applies in inflation:

Timescales disambiguation

3 basic ways of measuring duration:

This is a lot of extra degrees of freedom, way beyond those observed. Various versions (for example, different D) are connected dynamically: one theory, many solutions. *Almost all have positive potential energy (and not low energy supersymmetry). *Enough to plausibly find ones with realistic features like the small late-time accelerated expansion (no other explanation yet forthcoming...).

The theory has passed stringent thought-experimental tests internal consistency checks.

For example, black holes have a course-grained description in terms of general relativity. In certain cases, string theory provides a fine-grained account of the many microstates of the system. (More later...)

Inflation needs V nearly constant

But quantum gravity at its natural scale can affect V strongly, ruining inflation

Turning this around, inflation &observations are sensitive to quantum gravity/string-theory effects! (not enough to fix the theory of QG...)

Therefore inflation models strictly speaking require control of quantum gravity (QG) effects. So we model this using string theory as a framework for QG. (Kachru, Kallosh, Linde, Maldacena, McAllister, Trivedi '03; Alishahiha, ES, Tong '03-4, ...)

This has led to substantially new ideas for inflation, a more complete understanding of the range of inflation and its observational signatures, and as a result, concrete empirical constraints on early universe physics (ongoing).

Parameterized Ignorance ofQuantum Gravity Effects:

A simple effect:

Without string theory:

With string theory, we find additional heavy degrees of freedom that adjust, producing a flatter potential. (General point made in 2010 paper with Dong et al following many early examples, all well before Planck data...) This can also destabilize the system in some directions, so research aimed at balance of forces to avoid runaway instabilities.

*String theory mechanisms exemplifying range of inflationary dynamics (and signatures), lead to much more systematic understanding of the paradigm

The greatest sensitivity to QG occurs in the simplest (most symmetric) case of large-field inflation, with detectable primordial gravitational waves:

Gravitational waves

Parameterizedignorance of quantum grav.

String Theory `axion' fields

From ubiquitous Axion-Flux couplings

New degrees of freedom eachMp

ES, Westphal, McAllister, Flauger; Kaloper, Sorbo, Lawrence,...

underlying periodicity =>additional testable structures (data: Flauger, Easther, Peiris/Planck, ...)

Heavy fields adjust to produce flatter (hence viable!) potential energy V()

String theoretic version of two classic, now disfavored models remains so far viable as a result of unwinding and flattening V.

Dong, Horn, ES, Westphal '10

Planck ESA

Planck

This scenario led us to a much more comprehensive understanding of inflationary dynamics: the nearly constant V() could arise from interactions slowing the field. Range of observational signatures much broader, now tested much more systematically and model-independently. This is now a pattern, there are several key examples where string theory exhibited new phenomena and exposed hidden assumptions in our thinking about inflation and observational constraints on its parameters. Provides input into elegant and systematic low energy field theory parameterizations of observables. cf Maldacena,...,Senatore et al.

+ many new effects for multiple fields

II. Black Holes:

*Thermodynamics, Hawking radiation, Statistical Mechanics*Holography and information *Puzzles

Role of String Theory:--Accounts for dangerously irrelevant effects, large non-local energy in near horizon region

--New test of long range non-local (perfectly causal!) interactions in string theory

n.b. Thought-experimental constraint that stress-energy sources respect these laws excludes some Alt-cosmo.

Black holes in GR and Thermodynamics

S > 0, entropy increases in Thermodynamics

Energy = T Sin Thermodynamics

Hawking Radiation: As in cosmology, a forming black hole is time-dependent, so excites fields away from the vacuum.

On the face of it, lost information about what formed black hole. Would violate quantum mechanics if true.

HolographySusskind, ...

Hawking evaporation calculation gave thermal (information-losing) result => Since AdS/CFT says otherwise, something is off.

Must be careful to keep track of what observers can actually see. Still, some can see enoughof the problem to still give a potential paradox. Almheiri et al '12. Various approaches.

This assumed that high energy physics is truly irrelevant in this problem, because of the weak curvature. But recall the evolution of trajectories of infallers => dangerous irrelevance. Must calculate its effect to see if there's really a paradox.

Weakly curved geometries with a horizon: evolution of trajectories of (say) two probes sent in with modest energy leads to a large nonlocal invariant energy in the near horizon region.

This could lead to a breakdown of effective field theory (GR) at long range, as a result of non-localities (perfectly causal!)

String Theory is a good candidate for the theory of quantum gravity, consider the question in that framework.

Embedding in spacetime fluctuates: formally infinite mean square size < XX > infinite because of high-frequency modes. Need high energy probe to detect. (Susskind

'94)

The late infaller is such a

Quantum uncertainty principle again!(Applied to each wave on the string)

The calculation makes a dramatic prediction (using certain coordinates)

This long-range interaction testable (requires detailed, subtle analysis) in a coordinate-independent way, via flat spacetime scattering:

Passes very nontrivial test, exhibiting predicted long range of interaction and revealing new features. Also happens in field theories with an AdS/CFT dual string theory description.

Dodelson, Torroba, ES

Even at low input energies and weak curvature, the black hole horizon has `dangerously irrelevant' features,i.e. sensitivity to microphysics.Given this, we should revisit black hole apparent paradox. (cf other near horizon probes: Shenker/Stanford,...)

Regardless, interesting just as a piece of physics going beyond General Relativity, not suppressed as naively expected from series of `irrelevant' terms

Remark (BHs => Cosmo):

There is evidence that holography is more general than black holes (or anti de Sitter spacetime). Major direction of research is to upgrade the AdS/CFT correspondence to the generic and realistic case of positive potential (de Sitter, inflation, and `dark energy'). Some similar issues with horizon infallers there, although not the same information problem.

Summary:

Horizons arise in cosmology and black hole spacetime geometries. Their physics involves a genuine intersection between real observations and thought experiments. Classical physics plus essential quantum fluctuations leads to a beautiful theory of the origin of structure, and to puzzling aspects of black holes. Quantum gravity (string theory) plays a subtle but important role, even contributing to our understanding of empirical measurements of early universe dynamics.

Much more to come!

Final Comment:

Many have contributed to this field. It is a truly international effort. My own collaborators include scientists originally from Argentina, Canada, China, Germany, Greece, Iran, Israel, Italy, Russia, UK,... as well as the United States, and I regularly interact with researchers from many additional countries (France, India, Japan, New Zealand, Sri Lanka, ...). This is not unusual, and our commitment to the best science and scientists from anywhere in the world is one of the major strengths of academic science in the US. Let's keep it that way!