Cosmological Scaling Solutions and Cross-coupling Exponential Potential

TL;DR

This paper analyzes the dynamics of multiple scalar fields with exponential potentials in cosmology, identifying stable solutions and their implications for inflation and matter interactions.

Contribution

It provides a phase-space analysis revealing the stability and attractor properties of scaling solutions with cross-coupling exponential potentials.

Findings

Power-law scaling solutions exist for flat positive or steep negative potentials.

The positive potential scaling solution is the unique late-time attractor.

Negative potential solutions are unstable in an expanding universe.

Abstract

We present a phase-space analysis of cosmology containing multiple scalar fields with a positive or negative cross-coupling exponential potential. We show that there exist power-law kinetic-potential-scaling solutions for a sufficiently flat positive potential or for a steep negative potential. The former is the unique late-time attractor, but it is difficult to yield assisted inflation. The later is never stable in an expanding universe. Moreover, for a steep negative potential there exists a kinetic-dominated regime in which each solution is a late-time attractor. In the presence of ordinary matter these scaling solutions with a negative cross-coupling potential are found unstable. We briefly discuss the physical consequences of these results.