Renormalisation group improvement in the stochastic formalism

Abstract

We investigate compatibility between the stochastic infrared (IR) resummation of light test fields on inflationary spacetimes and renormalisation group running of the ultra-violet (UV) physics. Using the Wilsonian approach, we derive improved stochastic Langevin and Fokker-Planck equations which consistently include the renormalisation group effects. With the exception of stationary solutions, these differ from the naive approach of simply replacing the classical potential in the standard stochastic equations with the renormalisation group improved potential. Using this new formalism, we exemplify the IR dynamics with the Yukawa theory during inflation, illustrating the differences between the consistent implementation of the UV running and the naive approach.

arXiv comment18 pages, 1 figure, 1 appendix, matches accepted version in JCAP

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• Spectator dark matter in non-standard cosmologies
• Novel mechanism for CMB modulation in the Standard Model
• Gravitational waves from a curvature-induced phase transition of a Higgs-portal dark matter sector
• Early universe dynamics of PQ field with very small self-coupling and its implications for axion dark matter
• The effective Higgs potential and vacuum decay in Starobinsky inflation