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

Abstract

The basic objective of this investigation is to explore the impact of a novel gravitational modification, specifically, the f (G, T 2 ) (where G := R 2 + R αβσς R αβσς − 4R αβ R αβ and T 2 := T αβ T αβ , T αβ 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 (CF) 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 CF. The incorporation of a less restrictive condition termed as quasi-homologous (QH) condition together with the zero CF, allows us to formulate a range of exact solutions for a particular choice of f (G, 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.

Dynamical analysis of logarithmic energy-momentum squared gravity

“…[12] (see also [13]). There is a rapidly growing literature considering EMSG, see [14][15][16][17][18][19][20][21] for some cosmological applications and [22][23][24][25][26] for some other applications. EMSG theories are a special family of a Lorentz invariant and covariant generalization of GR proposed in Ref.…”

Big Bang Nucleosynthesis constraints on $f(T,T_G)$ gravity

“…There is a rich literature on modified and extended theories of gravity. One may start from the Einstein-Hilbert Lagrangian and add extra terms, resulting in f (R) gravity [9][10][11], in f (G) gravity [12][13][14], in f (G, T ) theories [15], in f (P ) gravity [16][17][18] in Lovelock gravity [19,20], in Weyl gravity [21], in Horndeski/Galileon scalar-tensor theories [22,23] etc. Nevertheless, one can follow a different approach, and add new terms to the equivalent torsional formulation of gravity, resulting to f (T ) gravity [24,25], to f (T, T G ) gravity [26][27][28], to f (T, B) gravity [29,30], to scalar-torsion theories [31] etc.…”