Screening anisotropy via energy-momentum squared gravity: $\Lambda$CDM model with hidden anisotropy

TL;DR

This paper proposes a generalized $ ext{Λ}$CDM model incorporating anisotropy and energy-momentum squared gravity, which can cancel out anisotropic effects, reproduce standard cosmology, and potentially address the H₀ tension.

Contribution

It introduces a novel anisotropic $ ext{Λ}$CDM model with energy-momentum squared gravity that cancels shear effects, evades BBN limits, and impacts early and late Universe phenomena.

Findings

Shear scalar can be completely screened in the model.

The model reproduces the standard Friedmann equation of $ ext{Λ}$CDM.

Potential implications for the H₀ tension and CMB quadrupole.

Abstract

We construct a generalization of the standard $\Lambda$CDM model, wherein we simultaneously replace the spatially flat Robertson-Walker metric with its simplest anisotropic generalization (LRS Bianchi I metric), and couple the cold dark matter to the gravity in accordance with the energy-momentum squared gravity (EMSG) of the form $f(T_{\mu\nu}T^{\mu\nu})\propto T_{\mu\nu}T^{\mu\nu}$. These two modifications -- namely, two new stiff fluid-like terms of different nature -- can mutually cancel out, i.e., the shear scalar can be screened completely, and reproduce mathematically exactly the same Friedmann equation of the standard $\Lambda$CDM model. This evades the BBN limits on the anisotropy, and thereby provides an opportunity to manipulate the cosmic microwave background quadrupole temperature fluctuation at the desired amount. We further discuss the consequences of the model on the very early times and far future of the Universe. This study presents also an example of that the EMSG of the form $f(T_{\mu\nu}T^{\mu\nu})\propto T_{\mu\nu}T^{\mu\nu}$, as well as similar type other constructions, is not necessarily relevant only to very early Universe but may even be considered in the context of a major problem of the current cosmology related to the present-day Universe, the so-called $H_0$ problem.