Stationary Phase Approximation and Instanton-like States for Cosmological In-In Path Integrals

Abstract

The path integral, which generates in-in correlation functions of a scalar field in a cosmological spacetime, is shown to admit nontrivial classical solutions as stationary phases. Although the solutions exist for Lorentzian signature, their contribution to the path integral is reminiscent that of the instantons in Euclidean field theories. When the scalar potential has more than one locally stable vacua, the correlation functions receive contributions from all of them via these instanton-like configurations, which is similar to tunneling. We present some explicit solutions for toy models and discuss possible implications of our results.

15 pages, 2 figures, revtex4-1, v2: title changed, references added, typos corrected, minor modifications, to appear in Phys. Rev. D

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Cited by in corpus (8)

• The Quantum Corrected Mode Function and Power Spectrum for a Scalar Field during Inflation
• The Gauss-Bonnet Coupling Constant in Classically Scale-Invariant Gravity
• On $i\epsilon$ Prescription in Cosmology
• The Functional Measure for the In-In Path Integral
• In-in formalism, pseudo-instantons and rethinking quantum cosmology
• Entropy mode loops and cosmological correlations during perturbative reheating
• Adiabatic regularization of functional determinants in cosmology and radiative corrections during inflation
• Complex time route to quantum backreaction