Coupling the inflationary sector to matter

We describe the coupling of matter fields to an inflationary sector of supergravity, the inflaton φ and a stabilizer s, in models where the kähler potential has a flat inflaton direction. such models include, in particular, advanced versions of the hyperbolic α-attractor models with a flat inflaton direction kähler potential, providing a good fit to the observational data. if the superpotential is at least quadratic in the matter fields u i , with restricted couplings to the inflaton sector, we prove that under certain conditions: i) the presence of the matter fields does not affect a successful inflationary evolution. ii) there are no tachyons in the matter sector during and after inflation. iii) the matter masses squared are higher than 3h 2 during inflation. the simplest class of theories satisfying all required conditions is provided by models with a flat direction kähler potential, and with the inflaton φ and a stabilizer s belonging to a hidden sector, so that matter fields have no direct coupling to the inflationary sector in the kähler potential and in the superpotential.