Holographic methods for cosmology. Gonzalo Torroba Stanford University

Transcription

1 Holographic methods for cosmology Gonzalo Torroba Stanford University Observations and Theoretical Challenges in Primordial Cosmology KITP, UCSB, April 2013

2 Members of the collaboration Matt Dodelson Shunji Matsuura Xi Dong Bart Horn Eva Silverstein

3 During the last century, Cosmology has seen some of the most spectacular discoveries in the history of Physics big bang inflation Dark energy Accelerated expansion Accelerating universe, both in the far past and future Simplest example: de Sitter universe, a / exp(ht) de Sitter (1917)

4 Fascinating properties of accelerating cosmologies: Event horizons Thermodynamic laws Hawking, Bekenstein, Gibbons,... (70 s) event horizon T = H 1, S = Area 4G N Lead to deep questions in theoretical cosmology: microscopic origin of thermodynamic properties? UV complete framework for calculating observables? Formulate quantum gravity on cosmological spacetimes?!

5 Our approach: formulate cosmology holographically and determine the degrees of freedom that build up cosmological spacetimes Strategy: generalize AdS/CFT to cosmology V FRW ds 1/R AdS

6 Organization of the talk A. Macroscopic holography B. Uplifting AdS/CFT to cosmology C. General features of QFT duals

7 A. Macroscopic holography Why a holographic formulation of cosmology? Gibbons-Hawking entropy for de Sitter more general idea of holographic principle t Hooft, Susskind - relates spacetime geometry to number of quantum states covariant entropy bound N apple e A(B)/4 Bousso basic mechanism responsible for AdS/CFT also in ds string theory constructions provide ds and FRW holographic duals

8 Observables in ds I + correlators at future infinity causal patch measurements (limited precision) I Structure of correlators at I + metaobservers (useful for inflation) ds symmetries ) conformal transf. of boundary Suggests ds d+1, euclidean CFT d Z Strominger;Witten; Maldacena hf (f)i = Df F(f) (f) 2

9 Causal patch holography Alishahiha, Karch, Silverstein, Tong ds d+1 /ds d ds 2 d+1 = dr 2 +sin 2 ( r R )ds2 ds d E loc r R E pr! 0 ds d Compare to AdS/dS ds d two AdS throats deformed and glued near central slice Causal patch of ds d+1, Two coupled QFTs on with dynamical gravity ds d

10 B. Uplifting AdS/CFT to cosmology AdS/CFT duality Dong, Horn, Silverstein, GT R B R > 0 X AdS N color branes r V B (dr/dr) 2 R 2 =+ 1 R 2 g 2 s N R n 2 R > 0 1/R R > 0 color flux AdS color flux

11 Uplifting AdS/CFT V R < 0 orientifold color flux no hard c.c.! ds 1/R R > 0 AdS Internal space of negative curvature obtained by adding magnetic flavor branes Orientifolds provide negative tension for the intermediate term in the potential With other ingredients in place to stabilize all light fields... can lead to metastable de Sitter solutions Concrete brane construction given in Dong, Horn, Silverstein, GT arxiv:

12 Brane construction Background internal geometry: (dr/dr) 2 R < 0 R 2 = 1 R 2 + const R d? orientifold R < 0 The cone of AdS/CFT now becomes compact N color branes B N color antibranes Two tips; place color branes at one and antibranes at the other Agrees w/ macroscopics! ds d+1 B Two large N QFTs on dsd plus Gravityd ds/ds

13 Properties of the duality Two large N gauge theories with dyonic flavors living on ds Framework for calculating Z observables in causal patch hf ( )i $ D Z (1) [ ]Z (2) [ ]F ( ) Semiholographic: lower dimensional dynamical gravity. But screened by large N matter sector Microscopic explanation of thermodynamic properties Area of ds horizon = Thermal entropy of large N matter sector FRW decays Dong, Horn, Matsuura Silverstein, GT arxiv: arxiv: Dual to two t-dep QFTs Precise duality at late times! S!1, GR d decouples

14 C. RG structure of ds dual arxiv: Dong, Horn, Silverstein, GT Conditions on a QFT so that it can describe holographically an observer patch of de Sitter? From gravity side, both AdS and ds look very special... n maximal symmetry ) ds 2 d+1 = dr 2 + a(r) 2 ds 2 ds d a(r) = sin(h)(r) for (A)dS moduli stabilization V 0 ( )=0 metastable stable For AdS, properties should be equivalent to having a CFT Features of ds dual that encode max. sym. and stabilization?

15 n n n de Boer, Verlinde, Verlinde; Henningson, Skenderis... Holographic RG Energy-Radius relation: ds 2 = dr 2 + a(r) 2 ĝ µ dx µ dx ) E loc = a(r)e proper E UV QFT RG scale a(r) E L E =0 r =0 r = L r = L UV Z Z QFT = DM e S QF T = Z Z DM E<EL DM E>EL e S QF T = Z bulk = Z Z D Z D e S = Z D r<l e S r<l D r>l e S r>l Heemskerk Polchinski e S eff(e L ) IR(L, ) Z DM E<EL e S 0(M)+ R d d x p g O Z e S eff(e L ) = e S 0 D e R d d x p g O UV (L, ) Postulate: IR(L, ) = UV (L, )

16 Consequences of moduli stabilization Bulk scalar sitting at (local) minimum: V 0 ( )=0 S = Z, d d+1 x p g (@ ) 2 + V ( )+... V ( )=V V 00 ( ) UV dominated by classical trajectory (L UV )=! (L) = ) log UV has no linear term in Wilson action S e = S 0 (M)+g 1 O g 2(L)O Single trace couplings do not L g 1 =0 2. Iterative structure of L g n only depends on g mapplen Strong simplification of RG evolution Suggests new way of organizing the QFT path integral

17 Partial moduli stabilization work in progress Dodelson et al Apply lessons from holographic RG to construct dual QFTs single trace =0 for each metastabilized scalar Explicit UV complete model for uplifting? Simpler construction that uplifts AdS/CFT but doesn t stabilize all moduli D3 gauge theory flavors + orbifold V uplift : N f N c 1 3/ h changes VEV and dimension of tr (F 4 µ ) May also be useful for holographic dual of inflation

18 D. Summary and future directions ds and FRW dual to two large N gauge theories plus gravity with enough magnetic flavors for uplifting. Explains thermodynamic properties and provides a framework for calculating observables Nontrivial agreement between micro and macroscopic results indicates a consistent framework for holographic cosmology Develop more string theory constructions of ds, FRW and models of inflation Explicit description of matter content and couplings of dual QFTs. Flesh out more explicitly holographic dictionary Is uplifting the only mechanism for obtaining a ds dual? Relation to global ds/cft description?