Cosmological spacetimes with spatially constant sign-changing curvature

TL;DR

The paper challenges the standard FLRW-imposed restrictions of the Cosmological Principle by constructing globally hyperbolic spacetimes with a time function $t$ whose spatial slices have constant curvature $k(t)$ that can change sign and even topology over time, forming explicit counterexamples to traditional FLRW cosmologies. It presents three concrete $k(t)$-dependent geometries—the $k(t)$-warped model, the $k(t)$-conformal model, and the $k(t)$-radial model—each realized as smooth metrics with $g^{(4)}=-dt^2+g^{(3)}_t$ and a curvature function $k(t)$ guiding the geometry. The authors classify the admissible $k(t)$ for which global hyperbolicity holds and show the associated matter content corresponds to a radially anisotropic fluid, with potential connections to inflationary scenarios. These constructions open new cosmological possibilities, including matching a finite Big-Bang to observed flatness and exploring accelerated expansion toward a Euclidean phase, with observational implications to be investigated.

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. García-Moreno, B. Janssen, A. Jiménez-Cano, M. Mars and R. Vera