# Screening $\Lambda$ in a new modified gravity model

## TL;DR

This paper introduces a new modified gravity model, EMLG, which extends $ ext{Lambda}$CDM by including a logarithmic term in the energy-momentum tensor, providing a potential mechanism to screen the cosmological constant and alleviate observational tensions.

## Contribution

The paper proposes a novel Energy-Momentum Log Gravity model with an explicit exact solution, and constrains its parameters using observational data, showing it can screen $ ext{Lambda}$ and relax $H_0$ tension.

## Key findings

- Model prefers slightly negative $ ext{alpha}$, leading to $ ext{Lambda}$ screening.
- The model's $ ext{alpha}$ parameter is consistent with zero within uncertainties.
- EMLG can relax the $H_0$ tension in cosmological measurements.

## 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 ($\alpha'= -0.032\pm 0.043$), 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.