Induced Multi-phase Inflation with Reheating: Leptogenesis and Dark Matter Production in Metric versus Palatini

Abstract

We study non-minimally coupled scalar-induced multi-phase inflation in metric and Palatini gravity, considering linear, Brans-Dicke-like, and Higgs-like sectors. The scalar spectral index lies in the range \( n_s \simeq 0.93 \ \text{--} \ 0.98 \), consistent with \textit{Planck} and combined \textit{Planck}+ACT data. The tensor-to-scalar ratio can reach \( r \sim 0.03 \) in metric, whereas Palatini models generically predict \( r \lesssim 10^{-5} \). In the Palatini case, field excursions remain sub-Planckian, and the perturbative unitarity cutoff is raised. Reheating proceeds via perturbative inflaton decays into Higgs bosons and fermionic dark matter (DM) through the portal coupling \( \lambda_{12} \) and Yukawa coupling \( y_\chi \). Radiative stability of the inflationary plateau constrains the couplings to \( y_\chi, \lambda_{12} \sim 10^{-7} \ \text{--} \ 10^{-3} \), implying \( 4\,\mathrm{MeV} \lesssim T_{\rm rh} \lesssim 10^{15}\,\mathrm{GeV} \). Palatini realizations require smaller couplings and thus a narrower reheating window. Non-thermal DM production $\chi$ from inflaton decays is viable for DM mass \( m_\chi \sim \mathrm{keV} \ \text{--} \ \mathrm{PeV} \) with \( y_\chi \lesssim 10^{-6} \) over large parameter regions. We estimate the inflaton-right-handed neutrino (RHN) Yukawa coupling \( y_N \) required for successful baryogenesis via non-thermal leptogenesis within a Type-I seesaw framework, for the lightest RHN mass \( M_{N_1} \sim 10^{9} \ \text{--} \ 10^{14}\,\mathrm{GeV} \), provided \( M_{N_1} > T_{\rm max} \), where \( T_{\rm max} \) follows from radiatively consistent reheating. In Palatini scenarios, the lower maximal temperature and tighter stability bounds further restrict the leptogenesis parameter space.