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The $\Lambda CDM$ expansion could be mimicked by a dark energy coupled tomatter. Then, the equation of state $\bar w$ and coupling $\bar Q$ of thiscoupled dark energy could not be constrained by observations of the Hubblefunction alone. Also, in this paper, we determine the constraints on two suchcoupled dark energy models considering some current and forecast Euclid-likegrowth-rate data and assuming the prior on the $\Lambda CDM$ dark matterdensity parameter today $\Omega_{m0}=0.295\pm 0.04$. The first model is definedby a constant equation of state. We find that at $2\sigma$, $\barw=-1.02_{-0.22}^{+0.06}$ and the coupling function $\bar Q_0$ today is $\barQ_0H_0^{-3}=0.057_{-0.148}^{+0.353}$ with $H_0$ the Hubble constant. The secondmodel is defined by a varying equation of state $\bar w=\bar w_a-\barw_b\ln(1+z)$, with $z$ the redshift and $(\bar w_a,\bar w_b)$, two constants.We find that at $2\sigma$, $\bar w_a=-0.99_{-0.90}^{+0.17}$, $\barw_b=-0.04_{-1.17}^{+0.31}$ and $\bar Q_0H_0^{-3}=0.0002_{-0.18}^{+1.35}$. Theseconstraints on coupled dark energy agreed with a $\Lambda CDM$ model but aretoo poor to discard confidently a coupled dark energy different from vacuum butmimicking a $\Lambda CDM$ expansion.

Constraints from growth-rate data on some coupled dark energy models mimicking a $\Lambda CDM$ expansion