Holographic Signatures of Cosmological Singularities

To gain insight into the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge-gravity duality. The dual description of the bulk evolution towards the singularity involves $\mathcal{N}=4$ super Yang-Mills theory on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. More generally, the boundary evolution exhibits a process of particle creation similar to that in inflation. This leads us to conjecture that information on the quantum nature of cosmological singularities is encoded in long-wavelength features of the boundary wave function.

Figure 1

The proper boundary separation ${\mathcal{L}}_{\mathrm{bdy}}$ as a function of the real part of $c$ for $p=-1/4$. The solid curve corresponds to real $c$, whereas the dashed curves correspond to complex conjugate pairs of $c$. Note that there are five possible geodesics for each ${\mathcal{L}}_{\mathrm{bdy}}$.

Figure 2

A conformal diagram of the anisotropic de Sitter boundary geometry shows that two points separated by the horizon size can be connected by a null geodesic that bounces off ${\mathcal{I}}^{-}$.

Figure 3

$\mathrm{Re}(e^{-{\mathcal{L}}_{\mathrm{reg}}})$ as a function of the boundary separation for $p=-1/4$, computed from the bulk spacelike geodesics with $\mathrm{Re}(c)<0$. The colors correspond to those in Fig. 1; e.g., the red dashed line is the contribution from each of the two complex conjugate geodesics.