Constraints from growth-rate data on some coupled dark energy models mimicking a ΛCDM expansion

The CDM expansion can be mimicked by dark energy coupled to matter. In this case, the equation of state w and coupling Q of this coupled dark energy cannot be constrained by observations of the Hubble function alone. In this article, we determine the constraints on two such coupled dark energy models, considering some current and forecast Euclid-like growth-rate data and assuming the prior on the CDM dark matter density parameter today, m0 = 0.295 0.04. The first model is defined by a constant equation of state. We find that, at 2 , w = -1.02 +0.06 -0.22 and the coupling function Q0 today is Q0 H -3 0 = 0.057 +0.353 -0.148 , with H 0 the Hubble constant. The second model is defined by a varying equation of state w = wawb ln(1 + z), with z the redshift and ( wa , wb ) two constants. We find that, at 2 , wa = -0.99 +0.17 -0.90 , wb = -0.04 +0.31 -1.17 and Q0 H -3 0 = 0.0002 +1.35 -0.18 . These constraints on coupled dark energy agree with a CDM model but are too poor to discard with confidence coupled dark energy different from a vacuum but mimicking a CDM expansion.