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

TL;DR

This paper constructs quantum effective potentials for inflationary cosmology, deriving a generalised RG equation and summing all leading loop corrections, which preserves symmetry breaking and aligns with observational data.

Contribution

It introduces a method to sum all leading loop corrections to the effective potential in inflationary models, maintaining symmetry breaking and improving model accuracy.

Findings

Higher loops smooth the potential's behavior.

Effective potentials remain symmetry-breaking after all leading corrections.

Results are consistent with observational data across parameter ranges.

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 $\phi^4$-case, we found that the effective potentials preserve spontaneous symmetry breaking when summing all the leading corrections. We calculated the spectral indices $n_s$ 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.