# Observational constraints on generalized Proca theories

## TL;DR

This paper tests generalized Proca theories against cosmological data, finding they can address the Hubble tension and are favored over the standard model, with specific constraints on model parameters.

## Contribution

It provides observational constraints on generalized Proca theories, demonstrating their potential to alleviate the Hubble tension and remain consistent with cosmological data.

## Key findings

- Parameter s is constrained to about 0.16-0.25 at 95% CL.
- Model with s>0 reduces Hubble tension compared to ΛCDM.
- Generalized Proca theories remain compatible with observational data.

## Abstract

In a model of the late-time cosmic acceleration within the framework of generalized Proca theories, there exists a de Sitter attractor preceded by the dark energy equation of state $w_{\rm DE}=-1-s$, where $s$ is a positive constant. We run the Markov-Chain-Monte-Carlo code to confront the model with the observational data of Cosmic Microwave Background (CMB), baryon acoustic oscillations, supernovae type Ia, and local measurements of the Hubble expansion rate for the background cosmological solutions and obtain the bound $s=0.254^{{}+ 0.118}_{{}-0.097}$ at 95% confidence level (CL). Existence of the additional parameter $s$ to those in the $\Lambda$-Cold-Dark-Matter ($\Lambda$CDM) model allows to reduce tensions of the Hubble constant $H_0$ between the CMB and the low-redshift measurements. Including the cosmic growth data of redshift-space distortions in the galaxy power spectrum and taking into account no-ghost and stability conditions of cosmological perturbations, we find that the bound on $s$ is shifted to $s=0.16^{+0.08}_{-0.08}$ (95 % CL) and hence the model with $s>0$ is still favored over the $\Lambda$CDM model. Apart from the quantities $s, H_0$ and the today's matter density parameter $\Omega_{m0}$, the constraints on other model parameters associated with perturbations are less stringent, reflecting the fact that there are different sets of parameters that give rise to a similar cosmic expansion and growth history.