Quadratic, Higgs and hilltop potentials in the Palatini gravity

TL;DR

This paper investigates inflationary models with quadratic, Higgs, and hilltop potentials within Palatini gravity, analyzing observational parameters and their dependence on model variables across different scenarios.

Contribution

It provides a comprehensive analysis of inflation with various potentials in Palatini gravity, including effects of non-zero vacuum expectation values and comparisons with observational data.

Findings

Palatini quadratic potential's observational parameters depend on $\xi$ for different $N$ scenarios.

Palatini Higgs potential's parameters vary with $v$ and $\xi$, matching observations in certain limits.

Hilltop potentials can align with data for specific $\xi$ and $v$ values, differing from Higgs potential behavior.

Abstract

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.