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

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 $\mathit{\text{Planck}}$ and combined $\mathit{\text{Planck}}$+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 $4\mathrm{M}\mathrm{e}\mathrm{V}\lesssim T_{\mathrm{r}\mathrm{h}}\lesssim {10}^{15}\mathrm{G}\mathrm{e}\mathrm{V}$. Palatini realizations require smaller couplings and thus a narrower reheating window. Non-thermal DM production $\chi$ from inflaton decays is viable for DM mass $m_{\chi }\sim \mathrm{k}\mathrm{e}\mathrm{V}\text{ – }\mathrm{P}\mathrm{e}\mathrm{V}$ 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 $M_{N_1}\sim {10}^9\text{ – }{10}^{14}\mathrm{G}\mathrm{e}\mathrm{V}$, provided $M_{N_1}>T_{\mathrm{m}\mathrm{a}\mathrm{x}}$, where $T_{\mathrm{m}\mathrm{a}\mathrm{x}}$ follows from radiatively consistent reheating. In Palatini scenarios, the lower maximal temperature and tighter stability bounds further restrict the leptogenesis parameter space.