Abstract
We study a new model of Energy-Momentum Squared Gravity (EMSG), called Energy-Momentum Log Gravity (EMLG), constructed by the addition of the term f(T_{mu nu }T^{mu nu })=alpha ln (lambda ,T_{mu nu }T^{mu nu }), envisaged as a correction, to the Einstein–Hilbert action with cosmological constant Lambda . The choice of this modification 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, importantly, leading to an explicit exact solution of the matter energy density in terms of redshift. We look for viable cosmologies, in particular, an extension of the standard Lambda CDM model. EMLG provides an effective dynamical dark energy passing below zero at large redshifts, accommodating a mechanism for screening Lambda in this region, in line with suggestions for alleviating some of the tensions that arise between observational data sets within the standard Lambda CDM model. We present a detailed theoretical investigation of the model and then constrain the free parameter alpha ', a normalisation of alpha , using the latest observational data. The data does not rule out the Lambda CDM limit of our model (alpha '= 0), but prefers slightly negative values of the EMLG model parameter (alpha '= -0.032pm 0.043), which leads to the screening of Lambda . We also discuss how EMLG relaxes the persistent tension that appears in the measurements of H_0 within the standard Lambda CDM model.
Highlights
CDM model is 3.4 σ lower than the model-independent local value reported from supernovae by Riess et al [17]; secondly, the Lyman-α forest measurements of the baryon acoustic oscillations (BAO) by the Baryon Oscillation Spectroscopic Survey (BOSS) prefer a smaller value of the pressureless matter density parameter than is preferred by the cosmic microwave background (CMB) data within CDM [18]
As a new example of such zero-crossing models, we study a particular theory of modified gravity: Energy-Momentum Squared Gravity (EMSG)
We have introduced a new model of Energy-Momentum Squared Gravity, which we call Energy-Momentum Log Gravity (EMLG)
Summary
CDM model is 3.4 σ lower than the model-independent local value reported from supernovae by Riess et al [17]; secondly, the Lyman-α forest measurements of the baryon acoustic oscillations (BAO) by the Baryon Oscillation Spectroscopic Survey (BOSS) prefer a smaller value of the pressureless matter density parameter than is preferred by the CMB data within CDM [18]. The particular case η = 1/2, dubbed, ‘Scale Independent EMSG’, is one of the exceptions, along with the case η = 1 (EMSG with f (T 2) = αT 2), which provides explicit exact solutions for H (z) required for a detailed observational test In this model, the new terms in the field equations enter with the same power as the usual terms in GR, yet the standard energy is not conserved, and this leads to u(z) = (1+z)3α −1 and v(z) = ρm,0(1+z)3+3α, which could provide the desired features in the α < 0 case. We discuss the fact that the EMLG model relaxes, at some level, the persistent tension that appears between different measurements of H0 within the standard CDM model
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