Time-dependent AdS/CFT duality II: holographic reconstruction of bulk metric and possible resolution of singularity

Chu, Chong‐Sun; Ho, Pei-Ming

doi:10.1088/1126-6708/2008/02/058

Cited by 30 publications

(12 citation statements)

References 43 publications

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“…Once again one is able to independently tune the background temperature of the field theory away from the de Sitter temperature and study the resultant dynamics. Genuinely time dependent cosmologies have also attracted some attention in the holographic context: [208][209][210] examine duals to big crunches in gravity in terms of quantum dynamics, while [211][212][213][214][215][216] study quantum fields in time-dependent singular backgrounds.…”

Section: Discussionmentioning

confidence: 99%

Holographic thermal field theory on curved spacetimes

Marolf

Rangamani

Wiseman

2014

Class. Quantum Grav.

122

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The AdS/CFT correspondence relates certain strongly coupled CFTs with large effective central charge c eff to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in understanding gravity duals for CFTs on non-trivial spacetimes at finite temperature, both in and out of equilibrium. Such gravity methods provide powerful new tools to access the physics of these strongly coupled theories, which often differs qualitatively from that found at weak coupling.Our discussion begins with basic aspects of AdS/CFT and progresses through thermal CFTs on the Einstein Static Universe and on periodically identified Minkowski spacetime. In the latter context we focus on states describing so-called plasma balls, which become stable at large c eff . We then proceed to out-of-equilibrium situations associated with dynamical bulk black holes. In particular, the non-compact nature of these bulk black holes allows stationary solutions with non-Killing horizons that describe time-independent flows of CFT plasma. As final a topic we consider CFTs on black hole spacetimes. This discussion provides insight into how the CFT transports heat between general heat sources and sinks of finite size. In certain phases the coupling to small sources can be strongly suppressed, resulting in negligible heat transport despite the presence of a deconfined plasma with sizeable thermal conductivity. We also present a new result, explaining how this so-called droplet behaviour is related to confinement via a change of conformal frame. arXiv:1312.0612v3 [hep-th] 22 Feb 2014 7 One may alternatively express T µν in terms of the intrinsic geometry and extrinsic curvature K µν of B d [23] which gives a more covariant and universal expression

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Section: Discussionmentioning

confidence: 99%

Holographic thermal field theory on curved spacetimes

Marolf

Rangamani

Wiseman

2014

Class. Quantum Grav.

122

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“…Time-dependent deformations of this background were considered in [3,4,[22][23][24][25]. Specifically, we shall consider a background of the form [24] obtained by introducing a time-dependent dilaton background and adjusting the metric ofg µν such that the Einstein equation (7) and the Klein-Gordon equation (8) remain satisfied.…”

Section: Time-dependent Ads Background and Cft Dualmentioning

confidence: 99%

“…In the works of [3,4,[22][23][24] a bulk dilaton field φ had a time dependent (or a null coordinate dependent) boundary condition so that e φ becomes small at some time (or null time), while Einstein frame curvatures become large in the bulk, signifying a singularity. When the singularity is null, the dual theory appears to predict a smooth time evolution, and because of the absence of particle production one expects that the spacetime is smooth in the future.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations in a cosmology with a spacelike singularity and their gauge theory dual description

et al. 2016

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We consider a time-dependent deformation of anti-de-Sitter (AdS) space-time which contains a spacelike "singularity" -a space-like region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled region near the boundary, we reconstruct the bulk fluctuations after the singularity crossing making use of generic properties of boundary-to-bulk propagators. Finally, we extract the spectrum of the fluctuations at late times given some initial spectrum. We find that the spectral index is unchanged, but the amplitude increases due to the squeezing of the fluctuations during the course of the evolution. This investigation can teach us important lessons on how the spectrum of cosmological perturbations passes through a bounce which is singular from the bulk point of view but which is resolved using an ultraviolet complete theory of quantum gravity.

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“…In the case when the initial bulk scalar field has a scale invariant power spectrum, δφ ∝ k −3/2 , the gauge field at t = −t b , the time of matching onto the boundary in the past, has A in k (t) = A k (−t b ) ∼ k −9/4 . Assuming this scaling for the gauge Fourier modes, it can easily be seen that Region R 2 gives gives a contribution comparable to (30). With the initial conditions given by (29) and the growth of the gauge modes given by (27) we can write the boundary data in the future, encoded in the operator:…”

Section: Holographic Curvature Perturbation At Late Timesmentioning

confidence: 99%

“…We here consider a time-dependent deformation of AdS [25][26][27][28] (see also [29,30]) which yields a contracting phase with increasing curvature leading to a bulk singularity at a time which we call t = 0. The evolution for t > 0 is the mirror inverse of what happens for t < 0.…”

Section: Introductionmentioning

confidence: 99%

Holographic curvature perturbations in a cosmology with a space-like singularity

Ferreira

Brandenberger

2016

J. Cosmol. Astropart. Phys.

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We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call t = 0, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in the bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.

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Time-dependent AdS/CFT duality II: holographic reconstruction of bulk metric and possible resolution of singularity

Cited by 30 publications

References 43 publications

Holographic thermal field theory on curved spacetimes

Holographic thermal field theory on curved spacetimes

Fluctuations in a cosmology with a spacelike singularity and their gauge theory dual description

Holographic curvature perturbations in a cosmology with a space-like singularity

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