Revisiting the energy-momentum squared gravity

TL;DR

This paper revisits energy-momentum squared gravity by incorporating second derivatives of the matter Lagrangian, deriving a scalar tensor form, and analyzing stability, showing compatibility with cosmic expansion and late-time acceleration.

Contribution

It introduces new corrections to energy-momentum squared gravity and analyzes their physical implications using stability theory.

Findings

Cosmological models compatible with universe expansion.

Emergence of matter domination era.

Approach to late-time accelerated expansion near de-Sitter.

Abstract

In this paper we have revisited the energy-momentum squared gravity theory, by taking into account the second derivative of the matter Lagrangian with respect to the metric, encapsulating relations originated from thermodynamical grounds. After obtaining the scalar tensor representation of the energy-momentum squared gravity with the new corrections, we have analyzed the physical implications by relying on the linear stability theory. The results show that the current cosmological system is compatible with the expansion of the Universe for some specific matter Lagrangians, explaining the emergence of matter domination era, approaching the late time accelerated expansion era close to the de-Sitter phenomenology.