# Cosmology in beyond-generalized Proca theories

## TL;DR

This paper explores beyond-generalized Proca theories, extending vector-tensor models to explain late-time cosmic acceleration, analyzing stability, perturbation speeds, and growth of structures, with implications for dark energy and observational tests.

## Contribution

It introduces and analyzes the cosmological implications of beyond-generalized Proca theories, including stability conditions, perturbation dynamics, and observational signatures distinct from previous models.

## Key findings

- Stable on isotropic backgrounds without Ostrogradski instabilities.
- Modified propagation speeds of perturbations compared to generalized Proca theories.
- Growth rate of matter perturbations can match redshift-space distortion data.

## Abstract

The beyond-generalized Proca theories are the extension of second-order massive vector-tensor theories (dubbed generalized Proca theories) with two transverse vector modes and one longitudinal scalar besides two tensor polarizations. Even with this extension, the propagating degrees of freedom remain unchanged on the isotropic cosmological background without an Ostrogradski instability. We study the cosmology in beyond-generalized Proca theories by paying particular attention to the dynamics of late-time cosmic acceleration and resulting observational consequences. We derive conditions for avoiding ghosts and instabilities of tensor, vector, and scalar perturbations and discuss viable parameter spaces in concrete models allowing the dark energy equation of state smaller than $-1$. The propagation speeds of those perturbations are subject to modifications beyond the domain of generalized Proca theories. There is a mixing between scalar and matter sound speeds, but such a mixing is suppressed during most of the cosmic expansion history without causing a new instability. On the other hand, we find that derivative interactions arising in beyond-generalized Proca theories give rise to important modifications to the cosmic growth history. The growth rate of matter perturbations can be compatible with the redshift-space distortion data due to the realization of gravitational interaction weaker than that in generalized Proca theories. Thus, it is possible to distinguish the dark energy model in beyond-generalized Proca theories from the counterpart in generalized Proca theories as well as from the $\Lambda$CDM model.