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In this work, we study inflation with the non-minimally coupled quadratic,Standard Model (SM) Higgs and hilltop potentials through $\xi \phi^2R$ term inthe Palatini gravity. We first analyze observational parameters of Palatiniquadratic potential as functions of $\xi$ for high-$N$ scenario and low-$N$scenario. In addition to this, taking into account inflaton $\phi$ has anon-zero vacuum expectation value $v$ afterwards inflation, we displayobservational parameters of well-known symmetry-breaking potentials type ofHiggs potential and its generalizations which are hilltop potentials in thePalatini formalism for high-$N$ scenario and low-$N$ scenario. We calculateinflationary parameters of Palatini Higgs potential as functions of $v$ fordifferent $\xi$ values where inflaton values both $\phi>v$ and $\phi<v$ duringinflation as well as we show that observational parameters of Palatini Higgspotential in the induced gravity limit for high-$N$ scenario. On the otherhand, we illustrate different from the Higgs potential the effect of $\xi$ onhilltop potentials which can agree with the observations for inflaton valuesolely $\phi<v$ and $\xi$, $v\ll1$ for both two scenarios, which we mentionedabove. For each considered potentials, we also display $n_s-r$ values fit thecurrent data given by the Keck Array/BICEP2 and Planck collaborations.

Quadratic, Higgs and hilltop potentials in the Palatini gravity