The Dynamics of Multi-Scalar Field Cosmological Models and Assisted Inflation

TL;DR

This paper analyzes the late-time dynamics of multi-scalar field cosmological models with exponential potentials, showing conditions under which assisted inflation or curvature scaling solutions dominate, and revealing persistent scalar field effects.

Contribution

It demonstrates that assisted inflation is the global attractor for certain parameters and that all scalar fields remain significant at late times, challenging previous assumptions.

Findings

Assisted inflation is the late-time attractor for inflationary parameters.

Multi-field curvature scaling solutions dominate for other parameter values.

Scalar fields remain non-negligible at late times, contrary to prior beliefs.

Abstract

We investigate the dynamical properties of a class of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials. We show that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions asymptotically the curvature is not dynamically negligible). Consequently, we find that in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behaviour, contrary to what is commonly believed. The early-time and intermediate behaviour of the models is also studied. In particular, n-scalar field models are investigated and the structure of the saddle equilibrium points corresponding to inflationary m-field scaling solutions and non-inflationary m-field matter scaling solutions are also studied (where m<n), leading to interesting transient dynamical behaviour with new physical scenarios of potential importance.