$f(T,\mathcal{T})$ gravity and cosmology

TL;DR

This paper introduces a new modified gravity theory, $f(T, ext{T})$, which couples torsion and matter trace, providing a unified cosmological model that explains inflation, matter dominance, and late-time acceleration with stable perturbations.

Contribution

The paper develops the $f(T, ext{T})$ gravity theory, extending $f(T)$ gravity by coupling torsion with matter, and explores its cosmological implications and stability properties.

Findings

Unified description of inflation, matter dominance, and late acceleration.

Dark energy can be quintessence, phantom, or crossing the phantom divide.

Cosmology remains stable with no ghosts or instabilities for many models.

Abstract

We present an extension of $f(T)$ gravity, allowing for a general coupling of the torsion scalar $T$ with the trace of the matter energy-momentum tensor $\mathcal{T}$. The resulting $f(T,\mathcal{T})$ theory is a new modified gravity, since it is different from all the existing torsion or curvature based constructions. Applied to a cosmological framework, it leads to interesting phenomenology. In particular, one can obtain a unified description of the initial inflationary phase, the subsequent non-accelerating, matter-dominated expansion, and then the transition to a late-time accelerating phase. Additionally, the effective dark energy sector can be quintessence or phantom-like, or exhibit the phantom-divide crossing during the evolution. Moreover, in the far future the universe results either to a de Sitter exponential expansion, or to eternal power-law accelerated expansions. Finally, a detailed study of the scalar perturbations at the linear level reveals that $f(T,\mathcal{T})$ cosmology can be free of ghosts and instabilities for a wide class of ansatzes and model parameters.