Holographic Cosmology Workshop - 2009

The holographic duality gives a one-to-one mapping between consistent theories of gravity with AdS_d ground state, and conformal field theories in d-1 dimensions. Since the latter are unambiguously well-defined, we can use their defining properties to prove rigorous, model-independent theorems covering all quantum gravity theories with negative cosmological constant. Taking d=3, I will prove in this talk that every two-dimensional CFT contains a primary perator of weight less than C /12 + 0.473695, where C is the sum of right- and left-moving central charges. Using the AdS/CFT dictionary, this establishes that every theory of quantum gravity in asymptotically AdS space contains some state of mass less than 1 / (4 G), above and beyond the universal sector of boundary metric excitations.

I discuss the basic model of Higgs inflation, with a large non-minimal curvature coupling, from the point of view of effective field theory. It is pointed out that the effective cutoff scale is uncomfortably low compared to the inflation scale, thus rendering these models extremely sensitive to the details of the ultraviolet completion.

It has been shown by Hertog and Horowitz that certain AdS boundary conditions allow non-singular initial conditions to evolve into a Big Crunch. To study this kind of cosmological singularities, one can use the dual quantum field theory, where the singularity is manifested by the presence of a multi-trace potential unbounded below. Recently, Craps, Hertog and Turok have proposed two specific models of this type to study the possibility of a Big Crunch/Big Bang transition. For both models, I will provide a D-brane interpretation of the unbounded potential. In particular, I will show that the AdS boundary conditions of interest cause spherical D-branes to be pushed to the boundary of AdS, and that the corresponding potential agrees with the multi-trace deformation of the boundary field theory

Certain classes of cosmological backgrounds in asymptotically anti-de-Sitter space-times have hologropically dual descriptions in terms of gauge theories. We analyse such backgrounds with smooth initial conditions, where curvatures become strong in a finite time and the gravity equations break down. We will show how the dual gauge theory can be used to continue time evolution in this singular region and speculate on the nature of space-time at late times.

An update is given on AdS/CFT models of cosmological singularities, in particular on models in which a big crunch instability of the bulk theory is induced by an unstable multi-trace deformation of the dual field theory.