Did the Pseudo-Sphere Universe have a Beginning?

TL;DR

This paper investigates the no-boundary wave-function in negatively curved spacetime, finding solutions with singularities that challenge the assumption of a boundaryless universe.

Contribution

It provides a semi-classical analysis of the no-boundary proposal in negative curvature scenarios, revealing singularities that question its validity.

Findings

Identified Lorentzian and tunneling solutions in negative curvature spacetime

Found conical singularities at the origin, contradicting no-boundary conditions

Analyzed regularity in 2+1 and 3+1 dimensions

Abstract

A calculation of the no-boundary wave-function of the universe is put forward for a spacetime with negative curvature. A semi-classical Robertson-Walker approximation is attempted and two solutions to the field equations, one Lorentzian and the other a tunneling one are found. The regularity of those solutions are analysed explicitly, both in 2+1 and 3+1 dimensions and a conical singularity is found at the origin of the time axis, contradicting the no-boundary assumption.