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