Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach

Abstract

We examine long-wavelength correlation functions of massive scalar fields in de Sitter spacetime. For the theory with a quartic self-interaction, the two-point function is calculated up to two loops. Comparing our results with the Hartree-Fock approximation and with the stochastic approach shows that the former resums only the cactus type diagrams, whereas the latter contains the sunset diagram as well and produces the correct result. We also demonstrate that the long-wavelength expectation value of the commutator of two fields is equal to zero both for spacelike and timelike separated points.

Presentation expanded, matches published version

References in corpus (8)

• Stochastic Inflationary Scalar Electrodynamics
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• The quantum Fokker-Planck equation of stochastic inflation
• $\lambda {\varphi }^4$ in dS
• Renormalization group inspired autonomous equations for secular effects in de Sitter space
• Unequal time correlators of stochastic scalar fields in de Sitter space

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• Thermodynamics and decay of de Sitter vacuum
• On the global temperature of the Schwarzschild-de Sitter spacetime
• Explaining Large Electromagnetic Logarithms from Loops of Inflationary Gravitons
• 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
• IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation
• Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime
• Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude
• 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
• Separate universe in multifield inflation: a phase-space approach
• Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators