Cosmologies in Horndeski's second-order vector-tensor theory

TL;DR

This paper explores the cosmological implications of Horndeski's second-order vector-tensor theory, focusing on the effects of a free parameter that influences the universe's evolution and observational constraints.

Contribution

It provides a detailed analysis of the cosmological consequences of Horndeski's gauge-invariant vector-tensor theory, including singularity conditions and observational viability.

Findings

Negative coupling leads to finite-time singularities.

Viable cosmological models exist for positive coupling.

Observational constraints on the coupling are weak due to higher-order curvature interactions.

Abstract

Horndeski derived a most general vector-tensor theory in which the vector field respects the gauge symmetry and the resulting dynamical equations are of second order. The action contains only one free parameter, $\lambda$, that determines the strength of the non-minimal coupling between the gauge field and gravity. We investigate the cosmological consequences of this action and discuss observational constraints. For $\lambda<0$ we identify singularities where the deceleration parameter diverges within a finite proper time. This effectively rules out any sensible cosmological application of the theory for a negative non-minimal coupling. We also find a range of parameter that gives a viable cosmology and study the phenomenology for this case. Observational constraints on the value of the coupling are rather weak since the interaction is higher-order in space-time curvature.