Cosmic acceleration in dust only Universe via energy-momentum powered gravity

TL;DR

This paper introduces a modified gravity theory called energy-momentum powered gravity (EMPG) that explains late-time cosmic acceleration using pressureless matter alone, differing from standard models by non-conservation of matter energy.

Contribution

The paper proposes a novel gravity model adding a term dependent on the energy-momentum tensor, providing a new explanation for cosmic acceleration without dark energy.

Findings

EMPG can produce late-time acceleration with pressureless matter.

Parameter constraints show EMPG mimics ΛCDM evolution.

Energy in EMPG is not conserved and does not dilute as in standard cosmology.

Abstract

We propose a modified theory of gravitation constructed by the addition of the term $f(T_{\mu\nu}T^{\mu\nu})$ to the Einstein-Hilbert action, and elaborate a particular case $f(T_{\mu\nu}T^{\mu\nu})=\alpha(T_{\mu\nu}T^{\mu\nu})^{\eta}$, where $\alpha$ and $\eta$ are real constants, dubbed as energy-momentum powered gravity (EMPG). We search for viable cosmologies arising from EMPG especially in the context of the late-time accelerated expansion of the Universe. We investigate the ranges of the EMPG parameters $(\alpha,\eta)$ on theoretical as well as observational grounds leading to the late-time acceleration of the Universe with pressureless matter only, while keeping the successes of standard general relativity at early times. We find that $\eta=0$ corresponds to the $\Lambda$CDM model, whereas $\eta\neq 0$ leads to a $w$CDM-type model. However, the underlying physics of the EMPG model is entirely different in the sense that the energy in the EMPG Universe is sourced by pressureless matter only. Moreover, the energy of the pressureless matter is not conserved, namely, in general it does not dilute as $\rho\propto a^{-3}$ with the expansion of the Universe. Finally, we constrain the parameters of an EMPG-based cosmology with a recent compilation of 28 Hubble parameter measurements, and find that this model describes an evolution of the Universe similar to that in the $\Lambda$CDM model. We briefly discuss that EMPG can be unified with Starobinsky gravity to describe the complete history of the Universe including the inflationary era.