The Big Trip and Wheeler-DeWitt equation

TL;DR

This paper refines the Wheeler-DeWitt equation to better model universe behavior post-big trip, introducing a more general form and a solution method, predicting a specific state with maximal emergence probability.

Contribution

It presents a generalized Wheeler-DeWitt equation and a novel solution method based on the Moutard transformation, improving modeling of universe evolution after a big trip.

Findings

Standard formulation allows efficient solution generation

Generalized equation predicts maximal emergence at w=-1/3

New formulation broadens applicability of the Wheeler-DeWitt approach

Abstract

Of all the possible ways to describe the behavior of the universe that has undergone a big trip the Wheeler-DeWitt equation should be the most accurate -- provided, of course, that we employ the correct formulation. In this article we start by discussing the standard formulation introduced by Gonz\'alez-D\'iaz and Jimenez-Madrid, and show that it allows for a simple yet efficient method of the solution's generation, which is based on the Moutard transformation. Next, by shedding the unnecessary restrictions, imposed on aforementioned standard formulation we introduce a more general form of the Wheeler-DeWitt equation. One immediate prediction of this new formula is that for the universe the probability to emerge right after the big trip in a state with $w=w_0$ will be maximal if and only if $w_0=-1/3$.