$f(\mathcal{G},T_{\alpha\beta}T^{\alpha\beta})$ Theory and Complex Cosmological Structure

TL;DR

This paper investigates how a new modified gravity theory, involving the Gauss-Bonnet term and stress-energy tensor squared, affects the complexity and evolution of spherically symmetric cosmic structures, providing exact solutions and discussing their cosmological implications.

Contribution

It introduces a novel $f( ext{G}, T^2)$ gravity model and derives exact solutions under specific conditions, exploring their physical and cosmological relevance.

Findings

Some solutions describe thin shells satisfying Israel conditions.

Other solutions exhibit voids fulfilling Darmois constraints.

The solutions have potential applications in modern cosmology.

Abstract

The basic objective of this investigation is to explore the impact of a novel gravitational modification, specifically, the $f(\mathcal{G}, \mathbf{T}^2)$ (where $\mathbf{T}^2 \equiv T_{\alpha\beta}T^{\alpha\beta}$, $T^{\alpha\beta}$ denotes the stress-energy tensor) model of gravitation, upon the complexity of time-dependent dissipative as well as non-dissipative spherically symmetric celestial structures. To find the complexity factor $(\mathbb{C}_{\mathbf{F}})$ from the generic version of the structural variables, we performed Herrera's scheme for the orthogonal cracking of Riemann tensor. In this endeavor, we are mainly concerned with the issue of relativistic gravitational collapse of the dynamically relativistic spheres fulfilling the presumption of minimal $\mathbb{C}_{\mathbf{F}}$. The incorporation of a less restrictive condition termed as quasi-homologous $(\mathbb{Q}_{\mathbf{H}})$ condition together with the zero $\mathbb{C}_{\mathbf{F}}$, allows us to formulate a range of exact solutions for a particular choice of $f(\mathcal{G}, \mathbf{T}^2)$ model. We find that some of the given exact solutions relax the Darmois junction conditions and describe thin shells by satisfying the Israel conditions, while some exhibit voids by fulfilling the Darmois constraints on both boundary surfaces. Eventually, few expected applications of the provided solutions in the era of modern cosmology are debated.