$f(T,\mathcal{T})$ gravity and cosmology (1405.0519v3)

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.

Overview of Modified Gravity and Cosmology in $f(T, \mathcal{T})$ Theory

The paper under consideration provides an extension to $f(T)$ gravity by allowing a general coupling of the torsion scalar $T$ with the trace of the matter energy-momentum tensor $\mathcal{T}$. This results in the formulation of the $f(T, \mathcal{T})$ gravitational theory, which is a novel modification utilizing different principles compared to existing torsion-based or curvature-based theories. The application of this theory within a cosmological context leads to intriguing phenomena and potential explanations for the universe's evolution.

The main focus of the paper is to describe how $f(T, \mathcal{T})$ gravity can offer a unified framework encapsulating the inflationary phase, matter-dominated expansion, and late-time acceleration of the universe. The effective dark energy sector described by the theory can oscillate between quintessence or phantom-like behavior, and may exhibit phantom-divide crossing during the cosmic evolution. These features represent the flexibility and depth of this modified gravity model in creating diverse cosmological scenarios that conform to observational data.

Key Claims and Findings

1. Unified Cosmic Evolution: The $f(T, \mathcal{T})$ framework can potentially unify descriptions of different evolutionary phases of the universe, including the initial inflationary period, subsequent matter-dominated phase, and eventual transition to accelerated expansion.
2. Dark Energy Phenomenology: The theory allows for a dark energy sector possessing characteristics of quintessence or phantom cosmologies. Moreover, the phantom-divide crossing further enriches the theory's ability to describe varying cosmological states.
3. Future Expansion Scenarios: In the long-term evolution, the cosmological model under $f(T, \mathcal{T})$ gravity may lead to outcomes such as de Sitter exponential expansion or eternal power-law accelerated expansion.
4. Stability and Perturbations: A comprehensive analysis of scalar perturbations at the linear level verifies that a wide class of models within the $f(T, \mathcal{T})$ framework is free from ghosts and instabilities, which is crucial for theoretical viability.

Implications

The formulation of $f(T, \mathcal{T})$ gravity represents a significant step forward in attempts to reconcile observations of cosmic acceleration and modified gravity theories. Practical implications include further cosmological model applications aimed at elucidating the connection between dark energy characteristics and gravitational couplings at the universal scale.

Theoretically, the ability to encompass various cosmic evolutionary paths under a single framework enriches the scope of modified gravity theories in explaining the universe beyond the standard model. Consequently, the paper provides a platform for future research into gravitational theories with non-minimal couplings and their implications for cosmological phenomena.

Future Developments

The paper opens pathways for more advanced models incorporating and testing different function forms of $f(T, \mathcal{T})$. Prospective research should aim at deeper observational constraints using data from type Ia supernovae, baryon acoustic oscillations, and cosmic microwave background, among others. Additional investigation into spherically symmetric solutions, scalar-vector-tensor perturbations, and inflationary consequences could enrich the theoretical foundation and observational capabilities of $f(T, \mathcal{T})$ gravity.

In summary, this work serves as a catalyst for exploring non-conventional gravitational theories that positively redefine our understanding of cosmic evolution, specifically the mechanisms driving dark energy influence within the universe.