Cosmological perturbations in Energy-Momentum Squared Gravity

TL;DR

This paper develops a covariant, gauge-invariant framework for analyzing linear cosmological perturbations in Energy-Momentum Squared Gravity, revealing distinctive signatures that can be tested with cosmological observations.

Contribution

It provides the first comprehensive derivation of perturbation equations in Energy-Momentum Squared Gravity, including scalar, vector, and tensor modes, with detailed analysis of their behavior.

Findings

Scalar perturbations can be enhanced or suppressed relative to GR.

Vector modes exhibit non-trivial vorticity at early times.

Tensor modes are damped waves with effective masses that vary slowly.

Abstract

We present a fully covariant and gauge-invariant analysis of linear cosmological perturbations in Energy-Momentum Squared Gravity. Working within the 1+3 formalism, we derive the exact propagation equations for scalar, vector, and tensor modes on FLRW backgrounds, in the case of radiation and dust. Two representative subclasses are examined in detail, in which non-linearity enters through $\mathcal{O}(\eta\rho^2)$ corrections or modifications in the equation-of-state parameter and the sound speed. For scalar perturbations, the density contrast can be enhanced or reduced relative to General Relativity, depending on the coupling parameter and the wavelength regime. A similar behaviour occurs for vector modes, allowing for a non-trivial vorticity at early-times. Tensor modes, described by the magnetic part of the Weyl tensor and the shear tensor propagate as damped waves with slowly varying effective masses. All sectors reduce continuously to their GR limits as $\eta\!\to\!0$. The framework isolates robust signatures - early-time scalar tilts, tensor damping shifts, and altered vorticity decay - that can be confronted with CMB and large-scale-structure observations to constrain these theories of gravity.