Cosmology in energy-momentum squared symmetric teleparallel gravity

TL;DR

This paper introduces a new gravity theory combining non-metricity and energy-momentum squared terms, derives analytical solutions for cosmology, and constrains model parameters using observational data, indicating a quintessence-like universe.

Contribution

It proposes a novel $f(Q,T_{ ext{μν}}T^{ ext{μν}})$ gravity model, derives analytical solutions for barotropic fluids, and constrains parameters with observational data.

Findings

Model favors quintessence regime according to Om diagnostic

Parameters constrained using CC, BAO, Pantheon+SH0ES data

Analytical solution for $f(Q, T_{μν}T^{μν}) = Q + η T_{μν}T^{μν}$

Abstract

In this letter, we explore the $f(Q,T_{\mu\nu}T^{\mu \nu})$ gravity theory, building upon the foundations laid by the $f(Q)$ and $f(Q,T)$ gravity theories. Here, $Q$ represents non-metricity and $T_{\mu\nu}$ stands for the energy-momentum tensor. The proposed action encompasses an arbitrary function of both non-metricity $Q$ and the square of the energy-momentum tensor, specifically $T^2=T_{\mu\nu}T^{\mu \nu}$. We find the analytical solution for the barotropic fluid case $p=\omega \rho$ for the model $f(Q, T_{\mu \nu}T^{\mu \nu}) = Q + \eta(T_{\mu \nu}T^{\mu \nu}) $. We constrain parameters of the solution $H(z)$ utilizing CC, BAO, and latest Pantheon+SH0ES samples with the help of Monte Carlo Markov Chain sampling technique along with Bayesian statistical analysis. Further, from the Om diagnostic test, we find that the assumed cosmological model favors the quintessence regime.