Dynamical renormalization and universality in classical multifield cosmological models

TL;DR

This paper introduces a dynamical renormalization group framework for classical multifield cosmological models, revealing universal IR behavior and interpolations between geodesic and gradient flows on scalar manifolds.

Contribution

It develops a novel RG approach linking UV and IR limits in multifield cosmology, demonstrating universality for models with constant Gaussian curvature scalar manifolds.

Findings

RG flow interpolates between geodesic and gradient flows.

Two-field models with constant Gaussian curvature are IR universal.

Universal IR approximants describe cosmological orbits across models.

Abstract

We study the scaling behavior of classical multifield cosmological models with complete scalar manifold $({\cal M},{\cal G})$ and positive smooth scalar potential $\Phi$, introducing a dynamical renormalization group action which relates their UV and IR limits. We show that the RG flow of such models interpolates between a modification of the geodesic flow of $({\cal M},{\cal G})$ (obtained in the UV limit) and the gradient flow of $({\cal M},{\cal G},V)$ (obtained in the IR limit), where the classical effective potential $V$ is proportional to $\sqrt{2\Phi}$. Using this fact, we show that two-field models whose scalar manifold has constant Gaussian curvature equal to $-1$, $0$ or $1$ are infrared universal in the sense that they suffice to describe the first order IR approximants of cosmological orbits for all two-field models with positive smooth scalar potential.