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 wDE=-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 the 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=0.254-0.097+0.118 at 95% confidence level (C.L.). Existence of the additional parameter s to those in the Λ-cold-dark-matter (ΛCDM) model allows to reduce tensions of the Hubble constant H0 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% C.L.) and hence the model with s>0 is still favored over the ΛCDM model. Apart from the quantities s,H0 and the today's matter density parameter Ωm0, 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.
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