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 μ ν T μ ν ) = α ln ( λ T μ ν T μ ν ) , 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 Λ in the past for α < 0 , suggested for alleviating some cosmological tensions. We show that the second law of thermodynamics requires α ≤ 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 → ( Λ + 2 α ) / 3 as a → ∞ , where the new term is due to the constant effective inertial mass density that arises from EMLG contribution of dust, whereas H → Λ / 3 as a → ∞ in the Λ CDM model. We also show the existence of new interesting features and trajectories that are absent in Λ CDM with or without spatial curvature.