Very low scale Coleman-Weinberg inflation with non-minimal coupling

We study viable small-field Coleman-Weinberg (CW) inflation models with the help of non-minimal coupling to gravity. The simplest small-field CW inflation model (with a low-scale potential minimum) is incompatible with the cosmological constraint on the scalar spectral index. However, there are possibilities to make the model realistic. First, we revisit the CW inflation model supplemented with a linear potential term. We next consider the CW inflation model with a logarithmic non-minimal coupling and illustrate that the model can open a new viable parameter space that includes the model with a linear potential term. We also show parameter spaces where the Hubble scale during the inflation can be as small as $10^{-4} $ GeV, $1$ GeV, $10^4 $ GeV, and $10^8$ GeV for the number of $e$-folds of $40,~45,~50$, and $55$, respectively, with other cosmological constraints being satisfied.