Holographic Description of AdS Cosmologies

TL;DR

The paper uses AdS/CFT to study cosmologies with big bang/crunch singularities by mapping to a dual 2+1D CFT deformed by multi-trace operators. A controlled regularization of the unbounded dual potential converts singular bulk evolution into hairy black holes, enabling a finite-temperature effective potential to be computed and linking cosmological singularities to thermal states in the dual theory. The authors find no evidence for a bounce: in the full theory, the big bang appears as a rare fluctuation from an equilibrium quantum gravity state, while the approach to a big crunch corresponds to large black hole formation. This work connects semiclassical spacetime emergence to thermal dynamics in the dual field theory and introduces a framework for exploring entropy and probability in cosmological transitions.

Abstract

To gain insight in the quantum nature of the big bang, we study the dual field theory description of asymptotically anti-de Sitter solutions of supergravity that have cosmological singularities. The dual theories do not appear to have a stable ground state. One regularization of the theory causes the cosmological singularities in the bulk to turn into giant black holes with scalar hair. We interpret these hairy black holes in the dual field theory and use them to compute a finite temperature effective potential. In our study of the field theory evolution, we find no evidence for a "bounce" from a big crunch to a big bang. Instead, it appears that the big bang is a rare fluctuation from a generic equilibrium quantum gravity state.

Figures (8)

• Figure 1: The function $\beta_i$ obtained from the instantons.
• Figure 2: Anti-de Sitter cosmologies.
• Figure 3: The functions $\beta(\alpha)$ obtained from the solitons and from hairy black holes of two different sizes. The full line shows the soliton curve $\beta_{s}(\alpha)$, the dot-dashed line shows the $\beta_{R_e}(\alpha)$ curve for $R_e=.2$ black holes and the dashed line is the $R_e=1$ curve.
• Figure 4: The boundary condition curve $\beta_{k,\epsilon}(\alpha) = -k\alpha^2 +\epsilon\alpha^3$ with $k=1$ and $\epsilon=.22$.
• Figure 5: The mass of the hairy black holes that obey the boundary conditions $\beta_{k,\epsilon}(\alpha)$ with $k=1$ and $\epsilon =.22$.. The full line gives the masses of the second branch of solutions, which are associated with the second intersection point of the curves $\beta_{k,\epsilon}(\alpha)$ and $\beta_{R_e}(\alpha)$, and hence have more hair. This branch disappears in the limit $\epsilon \rightarrow 0$.