Leading all-loop quantum contribution to the effective potential in the inflationary cosmology

Abstract

In this paper, we have constructed quantum effective potentials and used them to study slow-roll inflationary cosmology. We derived the generalised RG equation for the effective potential in the leading logarithmic approximation and applied it to evaluate the potentials of the T 2 and T 4-models, which are often used in modern models of slow-roll inflation. We found that while the one-loop correction strongly affects the potential, breaking its original symmetry, the contribution of higher loops smoothes the behaviour of the potential. However, unlike the ϕ 4-case, we found that the effective potentials preserve spontaneous symmetry breaking when summing all the leading corrections.We calculated the spectral indices ns and r for the effective potentials of both models and found that they are consistent with the observational data for a wide range of parameters of the models.