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

Abstract

We consider a massless, minimally coupled quantum scalar field theory with an asymmetric self interaction, $V(\varphi )=\lambda {\varphi }^4/4!+\beta {\varphi }^3/3!$ ($\lambda >0$) 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 $V(\varphi )$ as well of $\varphi$, leading to some dynamical screening of the inflationary cosmological constant $\Lambda$, at late times, with the initial conditions, $⟨\varphi ⟩=0=⟨V(\varphi )⟩$. In this work we first compute the vacuum expectation values of $\varphi ,{\varphi }^2$ and $V(\varphi )$, 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 $⟨{\varphi }^2⟩$. We next compute $⟨{\varphi }^2⟩$ 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 $⟨{\varphi }^2⟩$. 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.

arXiv commentv3, 38pp, 11 figures, 1 table; Added figure, references, discussions and clarifications; Improved presentation; Accepted in JCAP

References in corpus (53)

• Quantum Contributions to Cosmological Correlations
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Super-Acceleration from Massless, Minimally Coupled ${\varphi }^4$
• Stochastic Quantum Gravitational Inflation
• Correlation Functions in Stochastic Inflation
• Super-Hubble de Sitter Fluctuations and the Dynamical RG
• Stochastic Inflationary Scalar Electrodynamics
• Two Loop Scalar Self-Mass during Inflation
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Leading Log Solution for Inflationary Yukawa
• Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
• The "in-in" Formalism and Cosmological Perturbations
• Infrared Correlations in de Sitter Space: Field Theoretic vs. Stochastic Approach
• On "dynamical mass" generation in Euclidean de Sitter space
• Production of Massless Fermions during Inflation
• Nonperturbative resummation of de Sitter infrared logarithms in the large-N limit
• De Sitter Diagrammar and the Resummation of Time
• Scalar field correlator in de Sitter space at next-to-leading order in a 1/N expansion
• Renormalization group flow and symmetry restoration in de Sitter space
• A Completely Regular Quantum Stress Tensor with $w<-1$
• Photon mass generation during inflation: de Sitter invariant case
• CosMIn: The Solution to the Cosmological Constant Problem
• Infrared resummation for derivative interactions in de Sitter space
• Scalar correlation functions in de Sitter space from the stochastic spectral expansion
• Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Dark energy from primordial inflationary quantum fluctuations
• The Well-Tempered Cosmological Constant
• Relaxing the Cosmological Constant: a Proof of Concept
• Stability of de Sitter spacetime against infrared quantum scalar field fluctuations
• Review on stochastic approach to inflation
• Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: the ladder-rainbow approximation
• A novel way to determine the scale of inflation
• Summing Inflationary Logarithms in Nonlinear Sigma Models
• Backreaction of superhorizon scalar field fluctuations on a de Sitter geometry : a renormalisation group perspective
• Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach
• Nonperturbative infrared enhancement of nonGaussian correlators in de Sitter space
• Secular effects on inflation from one-loop quantum gravity
• Scalar correlation functions for a double-well potential in de Sitter space
• Cosmological Coleman-Weinberg Potentials and Inflation
• On the measure of spacetime and gravity
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter II: kinetic-conformal cross terms
• Patient Observers and Non-perturbative Infrared Dynamics in Inflation
• Renormalization group inspired autonomous equations for secular effects in de Sitter space
• Quantum Effects of Mass on Scalar Field Correlations and Fluctuations during Inflation
• A Graceful Exit for the Cosmological Constant Damping Scenario
• One-loop electromagnetic correlators of SQED in power-law inflation
• A minimal self tuning model to solve the cosmological constant problem
• Late time solution for interacting scalar in accelerating spaces
• Bose-Fermi Cancellation of Cosmological Coleman-Weinberg Potentials
• Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime
• Stochastic Dynamics of Infrared Fluctuations in Accelerating Universe
• Quantum Fluctuations of a Self-interacting Inflaton

Cited by in corpus (4)

• IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation
• Resummation of local and non-local scalar self energies via the Schwinger-Dyson equation in de Sitter spacetime
• From the Fokker-Planck equation to perturbative QFT's results in de Sitter space
• Self-interacting scalar field in (2+1) dimensions Einstein gravity with torsion