IR flow of stochastic power spectra for interacting spectator scalars in the inflationary de Sitter spacetime
Abstract
In this work we investigate the behaviour of early inflationary cosmic correlation functions under the flow of the infrared scale for interacting spectator scalar field theories. We start with the derivation of the one-loop effective potentials for ϕ4, ϕ4-Yukawa and broken phase O(N) model in the inflationary de Sitter spacetime, first using the local Schwinger-DeWitt expansion propagator, and next using the exact de Sitter propagator. The Schwinger-DeWitt expansion being valid in a sub-Hubble length scale, furnishes suitable framework to determine the leading curvature corrections to high energy phenomena having sub-Hubble Compton wavelengths. These effective potentials show spontaneous symmetry breaking pattern, and are next used as ultraviolet boundary conditions in the Wetterich equation generating the desired IR flow. The flow is shown to drive the theory towards symmetry restoration. Using these IR-improved effective potentials, we next compute the stochastic power spectra and spectral indices for the temporally coincident two point correlation function of the spectator scalar. We show that the results corresponding to the aforementioned two kind of propagators are roughly in qualitative agreement with each other, but may differ quantitatively significantly. Both of them show increase in the spectral index in the deep IR for ϕ4 and ϕ4-Yukawa. The effect of fermionic interaction has been emphasised. Also for the case of the O(N) scalar, we demonstrate that the effective potential's shape becomes more and more insensitive to the flow as N gets large. Implication of this on the correlation function has been discussed.
Related
- Dynamic Vacuum Energy in Weyl Integrable Spacetime Part I: Implications for Inflationary Cosmology
- Analytical primordial power spectra from a potential dominated pre-inflationary bounce in a closed universe
- Eigenvalue formulation of Stochastic Inflation and application to large perturbation generating inflationary features
- Geometric criticality and regular quasibound spectra of axial Proca fields in Schwarzschild spacetime
- Weakly interacting Bose-Einstein condensate with stochastic resetting
BibTeX
@misc{nath2026flow,
title = {{IR flow of stochastic power spectra for interacting spectator scalars in the inflationary de Sitter spacetime}},
author = {Vishal Nath and Sourav Bhattacharya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05957},
eprint = {2610.05957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05957},
}
RIS
TY - UNPB
TI - IR flow of stochastic power spectra for interacting spectator scalars in the inflationary de Sitter spacetime
AU - Vishal Nath
AU - Sourav Bhattacharya
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05957
UR - https://arxiv.org/abs/2610.05957
AB - In this work we investigate the behaviour of early inflationary cosmic correlation functions under the flow of the infrared scale for interacting spectator scalar field theories. We start with the derivation of the one-loop effective potentials for ϕ^4, ϕ^4-Yukawa and broken phase O(N) model in the inflationary de Sitter spacetime, first using the local Schwinger-DeWitt expansion propagator, and next using the exact de Sitter propagator. The Schwinger-DeWitt expansion being valid in a sub-Hubble length scale, furnishes suitable framework to determine the leading curvature corrections to high energy phenomena having sub-Hubble Compton wavelengths. These effective potentials show spontaneous symmetry breaking pattern, and are next used as ultraviolet boundary conditions in the Wetterich equation generating the desired IR flow. The flow is shown to drive the theory towards symmetry restoration. Using these IR-improved effective potentials, we next compute the stochastic power spectra and spectral indices for the temporally coincident two point correlation function of the spectator scalar. We show that the results corresponding to the aforementioned two kind of propagators are roughly in qualitative agreement with each other, but may differ quantitatively significantly. Both of them show increase in the spectral index in the deep IR for ϕ^4 and ϕ^4-Yukawa. The effect of fermionic interaction has been emphasised. Also for the case of the O(N) scalar, we demonstrate that the effective potential's shape becomes more and more insensitive to the flow as N gets large. Implication of this on the correlation function has been discussed.
ER -