Integrable Cosmological Models with an Arbitrary Number of Scalar Fields

TL;DR

The paper addresses the challenge of finding integrable cosmological models with multiple non-minimally coupled scalar fields. It proposes a construction where the Ricci scalar $R$ becomes an integral of motion by choosing a particular non-minimal coupling $U(oldsymbol{ amephi})$ and potential $V(oldsymbol{ amephi})$, yielding a constant $R=R_0$. In the spatially flat FLRW context, the authors reformulate the system in conformal time and show that with quartic potentials the dynamics decouple into $N$ independent first integrals, leading to solutions expressible through elliptic and hyperbolic functions. The work extends known one-field integrable models to arbitrary $N$, connects to chiral cosmological models, and outlines pathways to generalize to other metrics such as open/closed FLRW or Bianchi I, thereby enriching the set of exactly solvable multi-field cosmologies with potential physical applications.

Abstract

We consider cosmological models with an arbitrary number of scalar fields nonminimally coupled to gravity and construct new integrable cosmological models. In the constructed models, the Ricci scalar is an integral of motion irrespectively of the type of metric. The general solutions of evolution equations in the spatially flat FLRW metric have been found for models with the quartic potentials.