${\mathbb{T}}^2$- inflation: Sourced by energy-momentum squared gravity

Abstract

In this paper, we examine chaotic inflation within the context of the energy-momentum squared gravity (EMSG) focusing on the energy-momentum powered gravity (EMPG) that incorporates the functional $f({\mathbb{T}}^2)\propto ({\mathbb{T}}^2{)}^{\beta }$ in the Einstein-Hilbert action, in which $\beta$ is a constant and ${\mathbb{T}}^2\equiv T_{\mu \nu }{T}^{\mu \nu }$ where $T_{\mu \nu }$ is the energy-momentum tensor, which we consider to represent a single scalar field with a power-law potential. We demonstrate that the presence of EMSG terms allows the single-field monomial chaotic inflationary models to fall within current observational constraints, which are otherwise disfavored by Planck and BICEP/Keck findings. We show that the use of a non-canonical Lagrangian with chaotic potential in EMSG can lead to significantly larger values of the non-Gaussianity parameter, $f_{\mathrm{Nl}}^{\mathrm{equi}}$ whereas EMSG framework with canonical Lagrangian gives rise to results similar to those of the standard single-field model.

25 pages, 4 figures, and 2 tables, added discussion, accepted by Physics of the Dark Universe