Gauge theory duals of cosmological backgrounds and their energy momentum tensors

Abstract

We revisit type IIB supergravity backgrounds with null and spacelike singularities with natural gauge theory duals proposed in [S. R. Das, J. Michelson, K. Narayan, and S. P. Trivedi, Phys. Rev. D 74, 026002 (2006)] and [S. R. Das, J. Michelson, K. Narayan, and S. P. Trivedi, Phys. Rev. D 75, 026002 (2007)]. We show that for these backgrounds there are always choices of the boundaries of these deformed ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ space-times, such that the dual gauge theories live on 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 ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ 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 nonzero for time dependent backgrounds.