Constraining cosmological dynamics of scalar-tensor models of dark energy in teleparallel gravity

TL;DR

This paper investigates scalar-tensor models of dark energy within teleparallel gravity, deriving conditions for cosmological evolution that align with observed radiation and matter eras, using phase space analysis.

Contribution

It introduces a detailed dynamical analysis of scalar-tensor teleparallel gravity models, identifying specific conditions on coupling and potential functions for realistic cosmological evolution.

Findings

Quadratic form f(phi) supports radiation and matter eras.

Small coupling sigma ensures proper dominance of radiation and matter.

Lambda > 1 is necessary for realistic cosmic history.

Abstract

We consider a scalar-tensor theory in teleparallel gravity where a general function of the scalar field, f(phi), is non-minimally coupled to the torsion scalar T. First, we derive the field equations in this framework. Then, we study the cosmological evolution in a spatially flat, homogeneous, and isotropic universe described by the FRW metric, containing radiation and non-relativistic matter with energy densities rho_r and rho_m, respectively. We analyze the system as an autonomous dynamical model of dark energy. The cosmological behavior depends on the coupling function sigma = f'(phi)/sqrt(f(phi)) and the potential parameter lambda = [V'(phi) * f(phi)] / [V(phi) * f'(phi)]. A constant coupling sigma leads to a quadratic form f(phi) proportional to (phi + c)^2, while a constant lambda results in a power-law potential V(phi) proportional to f(phi)^lambda. These forms are supported by mathematical and physical considerations. We perform phase space analysis and show that lambda much greater than 1 is a necessary condition to obtain a radiation-dominated era with effective equation of state w_eff approximately 1/3 and a matter-dominated era with w_eff approximately 0. Moreover, small sigma^2 ensures radiation and matter dominance in the respective eras. Finally, we derive the necessary conditions for a viable cosmological trajectory in this setting.