Free scalar correlators in de Sitter via the stochastic approach beyond slow roll

Abstract

The stochastic approach to calculating scalar correlation functions in de Sitter spacetime is extended beyond the overdamped "slow roll" approximation. We show that with the correct noise term, it reproduces the exact asymptotic long-distance behaviour of field correlators in free field theory, thereby demonstrating the viability of the technique. However, we also show that the naïve way of calculating the noise term by introducing a cut-off at the horizon does not give the correct answer unless the cut-off is chosen specifically to give the required result. We discuss the implications of this for interacting theories.

Accepted for publication to Physical Review D

References in corpus (8)

• Cosmological implications of the Higgs mass measurement
• Spacetime curvature and the Higgs stability during inflation
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Spectator Dark Matter
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Unequal time correlators of stochastic scalar fields in de Sitter space

Cited by in corpus (5)

• Numerical stochastic inflation constrained by frozen noise
• Computing First-Passage Times with the Functional Renormalisation Group
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude
• Scalar field effective potentials in de Sitter spacetime