Some new cosmological applications of the energy-momentum squared gravity

Abstract

We investigate two specific forms of a new-type of modified gravity called Energy Momentum Squared Gravity (EMSG) constructed by the addition of the term f(TµνT µν) to the Einstein-Hilbert action with a cosmological constant (Λ). First, we propose a new model of EMSG, called Energy-Momentum Log Gravity (EMLG) described by f(TµνT µν) = α ln(λ TµνT µν). This choice is made as a specific way of including new terms in the right-hand side of the Einstein field equations, resulting in constant effective inertial mass density and leading to an explicit exact solution of the dust energy density in terms of redshift. We look for viable cosmologies, in particular, an extension of standard ΛCDM model. The EMLG provides an effective dynamical dark energy passing below zero at large redshifts, accommodating a mech anism for screening Λ, in line with suggestions for alleviating some of the tensions between observational data sets prevailing within the ΛCDM model. We present a theoretical investigation and then constrain the free parameters of the model using the latest observational data, and discuss the results. Second, we simultaneously replace the spatially flat Robertson-Walker metric with its simplest anisotropic extension, and couple the CDM to the gravity via the EMSG of the form f(TµνT µν) ∝ TµνT µν. These two modifications can mutually cancel out, namely, the shear scalar can be screened completely, and reproduce mathematically the same Friedmann equation of the ΛCDM model. This evades the BBN limits on the anisotropy, and thereby provides an op portunity to manipulate the CMB quadrupole temperature fluctuation at the desired amount. We also discuss the consequences of the model on the very early times and far future of the Universe.