Cosmological Density Fluctuations in Stochastic Gravity -- Formalism and Linear Analysis --

Abstract

We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon crossing time is smaller than some critical value ($\sim |$slow-roll parameter ${|}^{-1}$), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.

14 pages

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Cited by in corpus (6)

• Infrared effects in inflationary correlation functions
• Stochastic Gravity: Theory and Applications
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Loops in inflationary correlation functions
• One-loop Corrections to Scalar and Tensor Perturbations during Inflation in Stochastic Gravity
• Cosmological perturbations from stochastic gravity