Cosmological spacetimes with spatially constant sign-changing curvature

TL;DR

This paper explores the construction of globally hyperbolic cosmological spacetimes with slices of constant curvature that change sign and topology over time, challenging traditional assumptions of the Cosmological Principle.

Contribution

It introduces new models of cosmological spacetimes with variable curvature sign and topology, expanding the scope of possible cosmological geometries.

Findings

Construction of spacetimes with sign-changing curvature slices.

Demonstration of models contradicting classical Cosmological Principle.

Collaboration with multiple researchers to develop these models.

Abstract

Globally hyperbolic spacetimes endowed with a time function $t$ whose spacelike slices $t=t_0$ have constant curvature $k(t_0)$ and where the sign of $k(t_0)$ (as well as the topology of the slice) varies with $t_0$, can be constructed despite some common claims about the implications of the classical Cosmological Principle. Here, we stress the possibilities of these cosmologies and announce the development of new models obtained in collaboration with G. Garc\'{\i}a-Moreno, B. Janssen, A. Jim\'enez-Cano, M. Mars and R. Vera