All-loop effective potential for arbitrary scalar models in curved space-time

Abstract

In this paper we calculate the leading divergences of the effective potential for an arbitrary scalar theory on a curved spacetime background. Based on the recurrence relation between the leading poles following from the locality condition, we obtain a system of generalised renormalisation-group equations that can be studied numerically or analytically in some special cases. We study the simplest effective potentials for power-like models and give a comparison of them in the framework of cosmological phenomenology.

19 pages, 8 figures

References in corpus (16)

• Planck 2018 results. X. Constraints on inflation
• Encyclopaedia Inflationaris
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Higgs inflation: consistency and generalisations
• On the possible running of the cosmological "constant"
• Superconformal Generalization of the Chaotic Inflation Model λϕ^4/4 - ξ/ 2 ϕ^2 R
• Effective Potential in Curved Space and Cut-Off Regularizations
• Inflationary Parameters in Renormalization Group Improved ${\varphi }^4$ Theory
• Slow-Roll Inflation in the Jordan Frame
• Consistency Relations for Large Field Inflation: Non-minimal Coupling
• Leading all-loop quantum contribution to the effective potential in general scalar field theory
• Kinematically Dependent Renormalization
• More accurate slow-roll approximations for inflation in scalar-tensor theories
• The Renormalization Group and the Effective Action
• Effective potential in leading logarithmic approximation in non-renormalisable $SO(N)$ scalar field theories
• Non-renormalizable theories and finite formulation of QFT