Dynamical analysis of logarithmic energy-momentum squared gravity

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 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 <= 0 that allows the screening mechanism to take H -> root(Lambda + 2 alpha )/3 as a -> infinity, where the new term is due to the constant effective inertial mass place. We also show that the model gives rise to an entire class of new stable late-time solutions with density that arises from EMLG contribution of dust, whereas H -> root Lambda/3 as a -> infinity 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.(c) 2022 Elsevier B.V. All rights reserved.