Horizon Physics - Stanford Institute For Theoretical Physics

Horizon Physics& String TheoryPlan:I. Classical spacetime, particle motion, and horizonsII. 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 forstring theory in empirical science. (includingspinoffs: improved understanding of theory andobservational constraints).--Black hole physics*major puzzles for quantum gravity and a role forstring theory in their resolution.

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

Nothing moves faster than light does onthe spacetime geometry.Particles not subject to non-gravitationalforce take the shortest path.Let's start with flat spacetime (with nomatter or radiation to cause curvature).Actually, let's start just with flat space (notime). Pythagorean theorem:Can rotate orshift the picturewithout changingthis relation.

Now include time:Can boost orshift withoutchanging:

More on boost' (for those who likeequations):

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 (notembedded in larger system). Basically ameasure of how lengths change as wemove in the spacetime.space (two dimensional):spacetime: neighboring initially paralleltrajectories move apart or together

In flat spacetime, an observer has accessto light rays from all of space if they waitlong enough. Can send signals from anyfinite-energy massive trajectory to another.If the observer accelerates uniformly, theycan lose contact ( Rindler Horizon') butthis takes an infinite amount of energy.

Horizons:The Einstein equations havesolutions in which observers losecontact with each other (can'tcommunicate even with lightrays).The energetics of light and matterprobing such a geometry isstrongly affected by this.

For example, de Sitter(exponentially expanding)cosmology:

Black Hole horizonClassically, exterior geometry largelyindependent of formation matter, justdepending on mass, spin, charge. Thereis substantial evidence that this is just acoarse-grained description.

Energetics and horizons:Clock of an observer far outsideticks infinitely many times as aninfaller approaches the horizon.Escape velocity is thespeed of light at thehorizon.

The curvature is mild; a particle crossingthe horizon in classical GR is relativelyunperturbed.(curvaturesmall despitecirclesshrinking)

There is substantial observationalevidence for both kinds of horizonsblack holesSensitivity to EM andgravitational radiation closer in

Cosmological horizonsLateUniverseEarly U: As we will discuss, radiation fromthe time that atoms formed behaves asexpected if expansion was accelerated.Planck

Separation of energy scales and dangerous irrelevance'

How do we ever do physics with so muchthat is unknown?Wilsonian effective field theory (basicidea):Physical quantity, such as force betweentwo objects, or scattering probability, hasa leading contribution at low energies, andsubleading corrections that have to dowith unknown higher energy physics.infinite sequence of irrelevant' terms.

For many purposes, at long distances (lowenergies) we can ignore the infinitesequence of unknowns.But for a process that goes over sufficientlylong time periods, or over sufficiently largeranges of fields (and/or with sufficientamounts of data), sensitivity to higherenergy physics can develop.

An electromagnetic example:Consider a weak electric fieldpermeating space, with twocharges initially sitting at rest.The weak field acceleratescharges over a long time,producing a large invariant energy

A similar effect occurs in weaklycurved geometries with ahorizon: evolution of trajectoriesof (say) two probes sent in withmodest energy leads to a largenonlocal invariant energy in thenear horizon region.

In early universe cosmology, wefind dangerously irrelevant'features (spoiler alert):Substantial data, includingPlanckESA

I. Cosmology:*Expansion of the universe*Cosmic inflation*Quantum fluctuations and structure*New tests for degrees of freedom andinteractionsRole of Quantum Gravity (String Theory):--accounts for dangerously irrelevant effects,especially large-field' inflation with detectableprimordial gravitational waves--Major spinoffs: mechanisms for inflation andobservable signatures, incorporated into lowenergy description and data analysis

The probability to find the particle at someposition, in the ground state, is aGaussian function (normal distribution)This is (schematically) the answer if thefield fluctuation is non-interacting. It is agood approximation, but nowadays we aretesting for interaction effects on P( )

Horizon Physics& String TheoryPlan:I. Classical spacetime, particle motion, and horizonsII. Two important examples observed in nature:--Cosmological horizons and the origin of structure*Beautifully simple theory of seeds for structure,quantum uncertainty principle in expandinguniverse*Yet, sensitivity to quantum gravity and a role forstring theory in empirical science. (includingspinoffs: improved understanding of theory andobservational constraints).--Black hole physics*major puzzles for quantum gravity and a role forstring theory in their resolution.

Previously, on Horizon Physics.Nothing moves faster than light. Curvature Energy" equations lead tospacetimes with horizonsWe can systematically parameterize highenergy physics effects, often irrelevant butcan matter over long times, large fieldsIn early universe cosmology, exponentialexpansion plus exit introduces scalar fieldfluctuations that freeze out at Hubble scale.

Inflation plus quantum uncertainty principle:

The coefficient functions in our interval dsare dynamical, so just like they can'thelp but fluctuate according to theHeisenberg uncertainty principle.

Fluctuations of and of the geometryPrimordialgravitational waves!

ObservationsSpringel, Frenk, WhiteSimulations

Measurements of the frequencydependence (black body) and tinyspatial fluctuations of the light,including its polarization, havehelped precisely constrain themodel of the expanding universe,requiring so far only 6 parametersPlanck ESA (cf COBE,.,WMAP.)

Superhorizon perturbations:*Fluctuations correlated on scales longerthan the size of the horizon at the timewhen atoms formed.**The polarized light created at this time, nofurther inside-horizon sources that couldmimic its structure.(Spergel/Zaldarriaga, cf Turok)

Alternative(s?):I. Cosmic strings: well-defined theory, ruledout as leading seeds of structure.Pen, Seljak,Turok '97.II. Bounce? Clever idea (super-horizon for different reason),but much more difficult to control. Existing examples eitherdon't bounce, or do using exotic energy sourcesincompatible with black hole thermodynamics (see below).Regardless, spacetime singularity resolution is a greatproblem.

Primordial gravitational wavesearch:BICEP/Keck( Planck), SPIDER, SPT, ABS,PolarBear, Simons Observatory, CMBS4, LiteBird,CLASS,.The next round will test field range between 10 Mp and 1 Mp. This isextraordinary reach.(Instant gratification for a string theorist!)

This is just the beginning.The large amount of data collected alsoenables us to distinguish qualitativelydistinct inflation mechanisms. Also test formore subtle effects of particles and fieldsoperating during inflation (nearly 14 billionyears ago). These are subleading to theessential features of inflation already tested.Inflation and its observables -- especiallythose testable with the gravitational wavesearch -- are sensitive to quantum gravity.We lack a complete theory of cosmology asa whole, related to puzzling features ofhorizons as well as strongly-curved singularities'.

Many tests of the interactions ofprimordial fields. One currentexample (data analysis inprogress) concerns massiveparticles which could sourcehighly nonlinear perturbationsNot just a bellcurve, morestructure. Anexample of nonGaussianity'.Many early and ongoing works on effects of additional massless fields, e.g.Bond et al.

CMB Data reach:Statistical noise from the quantumfluctuations themselves.More data more independent tests smaller error bars. Roughly:Data increasing ( large-scale structure)

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

Position space featuresSimilar picture for strings, could test themas well as different particle properties.Search well underway, but I can't giveresults yet. Hopefully this gives you anidea of the powerful reach of moderncosmological data for high energy physics.

Note that the possibility of, andtests for, substructure in the CMBfluctuations does not detract fromthe scientific status of inflation.The leading effects are aspredicted in inflation. Subleadingcorrections could be there or not,depending on the details.We are interested in thembecause of the rich window itprovides into dynamics in the veryearly universe. This includesobservables sensitive to quantumgravity corrections:

Dangerous irrelevance' andString Theory

Recall idea of a series of correction termsFor V( this is

Irrelevance versus dangerous irrelevance'of high energy physics:For many purposes, at long distances (lowenergies) we can ignore the infinitesequence of unknowns when weparameterize our ignorance of high energyphysics.But for a process that goes over sufficientlylong time periods, or over sufficiently largeranges of fields (and/or with sufficientamounts of data), sensitivity to higherenergy physics can develop.

This applies in inflation:

Timescales disambiguation3 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 realisticfeatures like the small late-time acceleratedexpansion (no other explanation yetforthcoming.).The theory has passed stringent thoughtexperimental tests internal consistencychecks.For example, black holes have a coursegrained description in terms of generalrelativity. In certain cases, string theoryprovides a fine-grained account of the manymicrostates of the system. (More later.)

Inflation needs V nearly constantBut quantum gravityat its natural scalecan affect V strongly,ruining inflationTurning this around, inflation &observations are sensitive toquantum gravity/string-theoryeffects! (not enough to fix thetheory of QG.)

Parameterized Ignorance ofQuantum Gravity Effects:Therefore inflation models strictly speakingrequire control of quantum gravity (QG)effects. So we model this using stringtheory as a framework for QG. (Kachru, Kallosh,Linde, Maldacena, McAllister, Trivedi '03; Alishahiha, ES, Tong '03-4,.)This has led to substantially new ideas forinflation, a more complete understanding ofthe range of inflation and its observationalsignatures, and as a result, concreteempirical constraints on early universephysics (ongoing).

A simple effect:Without string theory:With string theory, we find additional heavydegrees of freedom that adjust, producing aflatter potential. (General point made in 2010paper with Dong et al following many earlyexamples, all well before Planck data.)This can also destabilize the system insome directions, so research aimed atbalance of forces to avoid runawayinstabilities.

*String theory mechanisms exemplifyingrange of inflationary dynamics (andsignatures), lead to much more systematicunderstanding of the paradigm

The greatest sensitivity to QGoccurs in the simplest (mostsymmetric) case of large-fieldinflation, with detectableprimordial gravitational waves:Gravitational waves