Gauge Theory Duals of Cosmological Backgrounds and their Energy Momentum Tensors

We revisit Type IIB supergravity backgrounds with null and spacelike singularities with natural gauge theory duals proposed in {\tt hep-th/0602107} and {\tt hep-th/0610053}. We show that for these backgrounds there are always choices of the boundaries of these deformed $AdS_5 \times S^5$ space-times, such that the dual gauge theories live on {\it flat} metrics and have space-time dependent couplings. We present a new time dependent solution of this kind where the effective string coupling is always bounded and vanishes at a spacelike singularity in the bulk, and the space-time becomes $AdS_5 \times S^5$ at early and late times. The holographic energy momentum tensor calculated with a choice of flat boundary is shown to vanish for null backgrounds and to be generically non-zero for time dependent backgrounds.