The Branch-cut Cosmology: A topological canonical quantum approach

TL;DR

This paper introduces a novel quantum cosmology model using a branch-cut approach to the Wheeler-DeWitt equation, based on Hořava-Lifshitz gravity, revealing a quantum transition between contraction and expansion phases.

Contribution

It presents a new topological quantum formulation of the universe's evolution using complex analysis and Hořava-Lifshitz gravity, with solutions indicating a quantum leap in cosmic phases.

Findings

Quantum leap between contraction and expansion phases.

Agreement with Bekenstein criterion.

Solutions for various potential parameterizations.

Abstract

In this contribution we sketch a branch-cut quantum formulation of the Wheeler-DeWitt equation analytically continued to the complex plane. As a starting point, we base our approach on the Ho\v{r}ava-Lifshitz formulation of gravity, which employs higher spatial-derivative terms of the spacetime curvature for renormalisation reasons. Following standard procedures, the quantization of the Lagrangian density is achieved by raising the Hamiltonian, the dynamical variable which represents the branch-cut complex scale factor and the conjugate momentum to the category of operators. We arrive at an Schr\"odinger-type equation with a non-linear potential. Solutions are then obtained and discussed for different potential parameterizations. The results reinforce the conception of a quantum leap between the contraction and expansion phases of the branch-cut universe, in good agreement with the Bekenstein criterion.