Abstract
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.
Highlights
Inflation is one of the successful paradigms in modern cosmology that can address various cosmological issues [1,2,3] and generate primordial perturbations [4,5,6,7]
We show parameter spaces where the Hubble scale during the inflation can be as small as 10−4 GeV, 1 GeV, 104 GeV, and 108 GeV for the number of e-folds of 40, 45, 50, and 55, respectively, with other cosmological constraints being satisfied
A possibility to increase ns is the introduction of a linear term, which can be generated by a fermion condensation in VERY LOW SCALE COLEMAN-WEINBERG INFLATION
Summary
A small-field inflation generally leads to a rather low reheating temperature. The recently proposed relaxion mechanism [27], as a solution to the hierarchy problem of Higgs boson by utilizing a slowly rolling scalar field in the context of inflationary cosmology, requires a very long period and a very low energy scale of inflation for a phase transition by QCD(-like) strong dynamics to take place during inflation, in the minimal model [27,28,29] and in some extended models [30,31,32,33].
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