Viability of bouncing cosmology in energy-momentum-squared gravity

TL;DR

This paper critically examines energy-momentum-squared gravity (EMSG), revealing that its bouncing solutions are not physically viable or regular, and explores conditions under which modified theories can produce acceptable bouncing cosmologies.

Contribution

It demonstrates that EMSG does not produce a regular bounce for our universe and identifies specific conditions and modifications that can yield viable bouncing solutions.

Findings

EMSG's bounce solutions are not representative of our universe.

Only the case with n=5/8 in generalized theories yields a viable bounce.

Most solutions are geodesically incomplete or singular.

Abstract

We analyze the early-time isotropic cosmology in the so-called energy-momentum-squared gravity (EMSG). In this theory, a $T_{\mu\nu}T^{\mu\nu}$ term is added to the Einstein-Hilbert action, which has been shown to replace the initial singularity by a regular bounce. We show that this is not the case, and the bouncing solution obtained does not describe our Universe since it belongs to a different solution branch. The solution branch that corresponds to our Universe, while nonsingular, is geodesically incomplete. We analyze the conditions for having viable regular-bouncing solutions in a general class of theories that modify gravity by adding higher order matter terms. Applying these conditions on generalizations of EMSG that add a $\left(T_{\mu\nu}T^{\mu\nu}\right)^{n}$ term to the action, we show that the case of $n=5/8$ is the only one that can give a viable bouncing solution, while the $n>5/8$ cases suffer from the same problem as EMSG, i.e. they give nonsingular, geodesically incomplete solutions. Furthermore, we show that the $1/2<n<5/8$ cases can provide a nonsingular initially de Sitter solution. Finally, the expanding, geodesically incomplete branch of EMSG or its generalizations can be combined with its contracting counterpart using junction conditions to provide a (weakly) singular bouncing solution. We outline the junction conditions needed for this extension and provide the extended solution explicitly for EMSG. In this sense, EMSG replaces the standard early-time singularity by a singular bounce instead of a regular one.