Cosmology in generalized Proca theories

TL;DR

This paper explores generalized Proca theories with derivative interactions, analyzing their cosmological implications, stability conditions, and late-time acceleration solutions, including vector Galileons as a special case.

Contribution

It provides a comprehensive analysis of cosmological dynamics and stability in generalized Proca theories up to quintic order, extending previous models with new stability conditions and concrete examples.

Findings

Existence of stable de Sitter solutions for late-time acceleration

Conditions for absence of ghosts and Laplacian instabilities in perturbations

Vector Galileons are encompassed as a special case within the framework

Abstract

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.