Abstract
We apply the functional renormalization group to Starobinsky's stochastic equation describing the local dynamics of a light scalar field in de Sitter. After elaborating on the over-damped regime of stochastic dynamics, we introduce an effective average action for the stochastic field, resulting by progressively integrating out frequencies, and study its flow equation in the local potential approximation (LPA). This effective action determines the approach to equilibrium and allows for the computation of unequal time correlators 〈φ(t)φ(t+Δ t)〉 for large values of Δ t. The stochastic RG flow in the LPA can be formulated in two ways, one that preserves the stochastic supersymmetry and one that breaks it. We show that both predict a characteristic decay time very close to that determined by the dynamical mass for a massless self-interacting scalar in de Sitter m2∼ λH2. Furthermore, the temporal supersymmetric formulation remarkably recovers the flow for the effective potential found using Quantum Field Theory methods and a smoothing over spatial wavelengths. We also discuss how the stochastic framework generically predicts an infrared mass which is a few percent smaller than the dynamical mass obtained in the LPA. Our results further support the notion that stochastic inflation captures the correct IR dynamics of light scalar fields in inflation.
Original language | English |
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Article number | 013 |
Journal | Journal of Cosmology and Astroparticle Physics |
Volume | 2018 |
Issue number | 8 |
DOIs | |
Publication status | Published - 13 Aug 2018 |
Funding
GR would like to thank Ian Moss for useful conversations and Julien Serreau for sharing his knowledge on the applications of the Functional Renormalization Group to scalars in de Sitter and extensive discussions on the work presented in this paper. The authors would also like to thank the anonymous referee whose substantial input has allowed us to improve this paper significantly. GR is partially supported by STFC grant ST/P000371/1 — Particles, Fields and Spacetime.
Keywords
- ination
- physics of the early universe
- quantum field theory on curved space