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 Ui, 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 3H2 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.
Supergravity Models Cosmology of Theories beyond the SM
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