Large Field Polynomial Inflation: Parameter Space, Predictions and (Double) Eternal Nature

TL;DR

This paper explores a polynomial inflation model with a concave saddle point, analyzing its parameter space, predictions for tensor-to-scalar ratio, and the possibility of multiple eternal inflation phases, consistent with recent observational data.

Contribution

It provides the first comprehensive scan of parameter space for a quartic polynomial inflation model with a concave saddle point, including the novel prediction of two phases of eternal inflation.

Findings

Tensor-to-scalar ratio can be as low as 10^{-8} or saturate current bounds.

Radiative stability does not strongly constrain model parameters.

The model predicts the possibility of two distinct eternal inflation phases.

Abstract

Simple monomial inflationary scenarios have been ruled out by recent observations. In this work we revisit the next simplest scenario, a single--field model where the scalar potential is a polynomial of degree four which features a concave ``almost'' saddle point. We focus on trans--Planckian field values. We reparametrize the potential, which greatly simplifies the procedure for finding acceptbale model parameters. This allows for the first comprehensive scan of parameter space consistent with recent Planck and BICEP/Keck 2018 measurements. Even for trans--Planckian field values the tensor--to--scalar ratio $r$ can be as small as $\mathcal{O}(10^{-8})$, but the model can also saturate the current upper bound. In contrast to the small--field version of this model, radiative stability does not lead to strong constraints on the parameters of the inflaton potential. For very large field values the potential can be approximated by the quartic term; as well known, this allows eternal inflation even for field energy well below the reduced Planck mass $M_{\rm Pl}$, with Hubble parameter $H \sim 10^{-2} M_{\rm Pl}$. More interestingly, we find a region of parameter space that even supports {\em two phases of eternal inflation}. The second epoch only occurs if the slope at the would--be saddle point is very small, and has $H \sim 10^{-5} M_{\rm Pl}$; it can only be realized if $r \sim 10^{-2}$, within the sensitivity range of next--generation CMB observations.