Nonvacuum AdS cosmology and comments on gauge theory correlator

Several time dependent backgrounds, with perfect fluid matter, can be used to construct solutions of Einstein equations in the presence of a negative cosmological constant along with some matter sources. In this work we focus on the non-vacuum Kasner-AdS geometry and its solitonic generalization. To characterize these space-times, we provide ways to embed them in higher dimensional flat space-times. General space-like geodesics are then studied and used to compute the two point boundary correlators within the geodesic approximation.

Figure 1

Plot of $e^{-L_{\text{reg}}}$ as a function of $t_0$ for $p_1=p_2=\frac{1}{2}$, $p_3=0$ nonvacuum AdS-Kasner solution. As the spacelike surface at $t_0$ is pushed toward $t=0$, the correlator vanishes.

Figure 2

Plot of $e^{-L_{reg}}$ as a function $t_0$ for the soliton solution.