Quantum Probabilities for Inflation from Holography

TL;DR

The paper shows that for a universe with nonzero $\Lambda$, the Wheeler-DeWitt equation yields large-volume solutions with two real domains: Euclidean AdS and Lorentzian dS. A universal complex semiclassical structure links the probabilities of de Sitter histories to the action of asymptotically AdS configurations, establishing a holographic connection via AdS/CFT within a single wave function. This leads to a holographic method to compute inflationary probabilities, with slow-roll inflation naturally arising from the asymptotic expansion and a Starobinsky-like regime. The framework unifies quantum cosmology and holography, suggesting that classical distinctions between signs of $\Lambda$ may be emergent at the quantum level and opening paths to include inhomogeneities and fundamental theory embeddings.

Abstract

The evolution of the universe is determined by its quantum state. The wave function of the universe obeys the constraints of general relativity and in particular the Wheeler-DeWitt equation (WDWE). For non-zero Λ, we show that solutions of the WDWE at large volume have two domains in which geometries and fields are asymptotically real. In one the histories are Euclidean asymptotically anti-de Sitter, in the other they are Lorentzian asymptotically classical de Sitter. Further, the universal complex semiclassical asymptotic structure of solutions of the WDWE implies that the leading order in \hbar quantum probabilities for classical, asymptotically de Sitter histories can be obtained from the action of asymptotically anti-de Sitter configurations. This leads to a promising, universal connection between quantum cosmology and holography.

Figures (1)

• Figure 1: A solution of \ref{['c3']} for the leading, universal coefficient function $k_3$ that specifies the asymptotic wave function. The approximately linear behavior for large $\chi$ is characteristic of field driven, slow roll inflation.