Dynamical analysis of logarithmic energy-momentum squared gravity

Abstract

We perform the dynamical system analysis of a cosmological model in the energy-momentum squared gravity (EMSG) of the form $f(T_{\mu \nu }{T}^{\mu \nu })=\alpha \ln (\lambda T_{\mu \nu }{T}^{\mu \nu })$, which is known as energy-momentum log gravity (EMLG). In particular, we show that the analytical cosmological solution of EMLG presented by Akarsu {\it et al.} (Eur. Phys. J. C 79:846, 2019) is a future attractor. It includes new terms in the right-hand side of the Einstein field equations, which yield constant inertial mass density and provide a dynamical dark energy with a density passing below zero at large redshifts, accommodating a mechanism for screening $\Lambda$ in the past for $\alpha <0$, suggested for alleviating some cosmological tensions. We show that the second law of thermodynamics requires $\alpha \le 0$ that allows the screening mechanism to take place. We also show that the model gives rise to an entire class of new stable late-time solutions with $H\to \sqrt{(\Lambda +2\alpha )/3}$ as $a\to \infty$, where the new term is due to the constant effective inertial mass density that arises from EMLG contribution of dust, whereas $H\to \sqrt{\Lambda /3}$ as $a\to \infty$ in the $\Lambda$CDM model. We also show the existence of new interesting features and trajectories that are absent in $\Lambda$CDM with or without spatial curvature.

13 pages, 4 figures, 1 table

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