Dynamical renormalization and universality in classical multifield cosmological models

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.