Non-perturbative analysis for a massless minimal quantum scalar with $V(\phi)=\lambda \phi^4/4!+\beta \phi^3/3!$ in the inflationary de Sitter spacetime

TL;DR

This paper investigates a massless scalar field with a hybrid potential in de Sitter space, analyzing its quantum and non-perturbative effects, backreaction on inflation, and mass generation using stochastic and quantum field theory methods.

Contribution

It provides a non-perturbative analysis of a hybrid scalar potential in de Sitter space, comparing stochastic and quantum field theory approaches, and explores dynamical mass generation and backreaction effects.

Findings

Non-perturbative secular logarithms grow with time.

Stochastic and quantum results differ numerically but show similar qualitative behavior.

Partial resummation of local self-energy contributions was achieved.

Abstract

We consider a massless, minimally coupled quantum scalar field theory with an asymmetric self interaction, $V (\phi) = \lambda\phi^4/4!+\beta\phi^3/3!$ ($\lambda >0$) in the inflationary de Sitter spacetime. The potential is bounded from below. While the $\beta=0$ case has been much well studied, the motivation behind taking such a hybrid potential corresponds to the fact that it might generate finite negative vacuum expectation values of $V(\phi)$ as well of $\phi$, leading to some dynamical screening of the inflationary cosmological constant $\Lambda$, at late times, with the initial conditions, $\langle \phi \rangle=0=\langle V(\phi) \rangle $. In this work we first compute the vacuum expectation values of $\phi,\, \phi^2$ and $V(\phi)$, using the late time, non-perturbative and infrared effective stochastic formalism. The backreactions to the inflationary $\Lambda$ are estimated. We also compute the dynamically generated mass of the scalar field using $\langle \phi^2 \rangle$. We next compute $\langle\phi^2\rangle$ using quantum field theory with respect to the initial Bunch-Davies vacuum at one and two loops, using the Schwinger-Keldysh formalism. These results show non-perturbative secular logarithms, growing with the cosmological time. Using next a recently proposed renormalisation group inspired formalism, we attempt to find out a resummed $\langle\phi^2\rangle$. We have been able to resum some part of the same which contains contributions only from the local self energy. The corresponding dynamically generated mass is computed. Comparison of the stochastic and the quantum field theory results shows that they differ numerically, although they have similar qualitative behaviour. Possible reasons for such quantitative mismatch is discussed. The manifestation of strong non-classical effects in the results found via both the formalisms has been emphasised.