de Sitter Holography
andEntanglement Entropy
Based on:*ArXiv 1804.08623 with Xi Dong & Gonzalo
Torroba*dS/dS and FRW/FRW dualities:
2004-2011
with Alishahiha, Dong, Horn, Karch,
Matsuura, Tong, Torroba*Somewhat related refs: Miyaji,Takayanagi,
Sato, Narayan, Mozaffar/Mollabashi,
Nomura/Rath/Salzetta,...

Accelerated expansion dominates
Observationally:
LateUniverse

Early Universe: inflation fits wellPlanckPositive potential V(scalars)
dominates String-Theoretically,
with controlled negative sources(orientifolds & cousins) plausibly
producing metastable dips inotherwise steep directions+othersources tofullystabilize
Various mechanisms:
Supercritical (ES 2001+...), GKP '01/KKLT'03,
LARGE Volume, Riemann Surfaces,...

Explicit example (2+1 bulk dimensions):
Dong, ES, Torroba 2010.

Thought-experimentally:
Gibbons/Hawking dS entropy
demands QG interpretation

dSd+1

SGH = Vd-1/4GN

More generally, we need a more
complete QG framework for theV>0 landscape.

AdS/CFT leads to emergent
spacetime from gauge theory
description. Many aspects to its
dictionary. One recent focus is QI

TFD state of twoCFTs (entangled atthermal scale) dual tojoined spacetime
Find analogous
statement for dS, withconcrete holographic
interpretation of SG-H .
Entangled state of 2 interacting
cut-off CFTs (at cut-off scale).

dSd+1 = Two coupled cutoff ddimensional CFTs, constrainedby residual d-dimensional gravity(on approximate dSd geometry)
This follows from 2+1
independent arguments,
macroscopic and microscopic.
They agree because of the metastability (no hard cosmologicalconstant in string theory).

Macroscopic:

AdS/dSdS/dS (each pointis (d-1)-sphere)

2 IR regions, each ~IR region of AdS/dS

Microscopic: Uplifting AdS/CFT

Versus AdS brane construction(branes probing tip of cone).

The dS/CFT conjecture gives athird indication of this structure
Strominger; Anninos, Hartman...

ZCFT = g)2 CFTsSymmetries manifest, but bulk unitarity not;restriction on irrelevant operators Shenker.
Maldacena; Harlow/Stanford,...

dS not obtained by analytic
continuation of AdS in string
theory (would yield complex
fluxes). Decays infect future
infinity.

dSd+1 = Two coupled cutoff ddimensional CFTs, constrainedby residual d-dimensional gravity(on approximate dSd geometry)

This follows from 2+1
independent arguments,macroscopic and microscopic.
They agree because of the metastability (no hard cosmologicalconstant in string theory).
puredS holography<<speculation<<exactsolution

This agreement (despite someremaining ambiguity) seems
unlikely to be a coincidence.

Many prior calculations:*Transmission between the IR regions:M', m' related to bulk and d-dim'l`glueball' masses*Holographic RG: moduli stabilization bothfor AdS (=> CFT, single-trace=0) and dS.
Single-trace couplings also don't flow in
dS/dS holographic RG.

*Quasilocal stress tensor => ctotal = 0 (GRd)*...

This talk: entanglement structureof the matter sector state,interpretation of dS entropyRole of GRd: e.g. d=2 LiouvilleHartle/Hawking...Polchinski '89 ... Martinec et al ...

Negative matter ground state (Casimir)
energy => Wheeler-deWitt describes global
Connection to TT and JT gravity? cf Dubovsky,Gorbenko, Mirbabayi,...

Cutoff => finite-dimensional
matter Hilbert space

Cutoff scale: sinh(w/L)=1. This is thescale of the Hawking-Page transition tolarge black holes.

dS3/dS2:

Interactions between the CFTs=> ground state (i.e.long-liveddS state) may be highly mixed.

Would predict Von Neumann andRenyi entropies are all the same,and equal to SGibbons-Hawking

Holographic calculation of Von
Neumann and Renyi entropies:

SVN : Extremal surface at , anchored on UV
slice. Volume law (tracing over second matter
sector, internal d.o.f.)

dS3/dS2:

Holographic Renyi entropies:
Lewkowycz & Maldacena '13, Dong '16.

=
Area of `cosmic brane' on Euclidean gravity-sidegeometry, anchored on UV slice, with deficit angle:=>
Our Euclidean geometry: (d+1)-sphere/ZN:
EdSd+1=3=> Sn=SVN
at large c

So indeed we have a flat
entanglement spectrum (c>>1)

So the finite Hilbert space wederived earlier, combined withthis ~ maximally mixed state,
gives the dS entropy as theentanglement entropy between
the 2 matter sectors (includingthe coefficient).

Interpretation of SGibbons-Hawking :RT Surface

Observer O cannot interact with
2nd matter sector, traces over it.

Late times  >0 in dS
Hubeny/Rangamani/Takayanagi (HRT)

dS3/dS2: extremal surface is a geodesic at
UV slice.

The geodesic becomes complex at latetimes, when its peak hits future infinity.
S = c/6 for each such Hubble patch.

FRW decay

Again 2-throated warped metricPreviously found (Dong, Horn, ES,Matsuura, Torroba '12) entropy boundand d.o.f. count grows like . GRdalso decouples at late times.
Geodesic => SRT ~  .

Future/ongoing Directions:*At least naively, get volume law
for smaller entangling regions.
cf Balasubramanian/McDermott/Van Raamsdonk,
Karch/Uhlemann Mollabashi/Shiba/Takayanagi

One Hubble
patch has ~cd.o.f. (`inside thematrix' cf Susskind/Witten '98).
*Entropies in FRW decay*Calculations of dSd+1 correlators
generalizing HKLL
*Analyze interaction Hamiltonianand in simple/toy models (e.g.
(integrating out internal d.o.f.)

SYK x SYK with irrelevant couplings, cfMaldacena Qi) and in D1D5 system.