The GAPS Programme at the TNG: LXXII. TOI-5734b: A hot sub-Neptune orbiting a relatively young K dwarf with an Earth-like density

Context. Increasing interest in young exoplanets is leading to a growing effort to understand the formation and evolutionary processes responsible for their different architectures. One interesting target is TOI-5734, a relatively young K3-K4 dwarf star (500(-150)(+300) Myr) showing a transiting candidate in photometric observations followed up with high-resolution spectroscopic data.Aims. Using both Transiting Exoplanet Survey Satellite (TESS) photometry and High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) radial-velocity (RV) data, we aim to validate the presence of the companion TOI-5734b, measure its planetary mass, size, and its orbital parameters after having characterised its host star. We then aim to study its possible planetary composition and atmospheric evolution.Methods. By simultaneously modelling photometry and high-cadence RVs, we measured the radius, mass, and density of TOI-5734b precisely, which were needed in order to reconstruct the evolution of its atmosphere under the high-energy irradiation of its young host. In particular, we employed Gaussian processes (GPs) with a flexible kernel to discriminate between the stellar activity of the young host and planetary signals.Results. We confirmed the planetary nature of TOI-5734b and measured its orbital period (P-b similar to 6.18 d), radius (R-b = 2.10(-0.12)(+0.12) R-circle plus), and mass (M-b = 9.1(-2.6)(+2.6) M-circle plus). By measuring its density (rho(b) = 0.98(-0.30)(+0.36) rho(circle plus)) and running atmospheric evolution modelling, we infer that TOI-5734b is close to having a rocky composition and an almost completely depleted primary envelope. We also modelled stellar activity, which points to a rotational period of the star of P-rot = 11.09(-0.08)(+0.07) d; this is compatible with its young age. Our results point toward the possibility of considering the target for atmospheric studies with present and future ground- and space-based facilities.