Wave Function of a Brane-like Universe

TL;DR

This paper explores the wave function of a brane-like universe within a mini-superspace model, highlighting its dependence on embedding time and its unique boundary conditions, contrasting with canonical quantum gravity.

Contribution

It introduces a novel approach to quantum cosmology by analyzing the wave function's dependence on embedding time and classically disconnected epochs.

Findings

Wave function depends on embedding time $ au$

Wave function vanishes at the Big Bang

Different boundary conditions lead to discrete energy levels

Abstract

Within the mini-superspace model, brane-like cosmology means performing the variation with respect to the embedding (Minkowski) time $\tau$ before fixing the cosmic (Einstein) time $t$. The departure from Einstein limit is parameterized by the 'energy' conjugate to $\tau$, and characterized by a classically disconnected Embryonic epoch. In contrast with canonical quantum gravity, the wave-function of the brane-like Universe is (i) $\tau$-dependent, and (ii) vanishes at the Big Bang. Hartle-Hawking and Linde proposals dictate discrete 'energy' levels, whereas Vilenkin proposal resembles $\alpha$-particle disintegration.