Scale-invariance in expanding and contracting universes from two-field models

TL;DR

This paper investigates how two-field cosmological models with general actions can produce scale-invariant perturbations in both expanding and contracting universes, highlighting the importance of field space geometry.

Contribution

It demonstrates the conditions under which scale-invariant spectra arise in two-field models, emphasizing the role of field space metric and stability of solutions.

Findings

Scale-invariant perturbations in contracting universes occur for any $w \, \geq 0$ but are associated with unstable backgrounds.

Nearly scale-invariant spectra in expanding universes are only achieved near $w \approx -1$, with stable attractor solutions.

The field space metric plays a crucial role in enabling these scale-invariant solutions.

Abstract

We study cosmological perturbations produced by the most general two-derivative actions involving two scalar fields, coupled to Einstein gravity, with an arbitrary field space metric, that admit scaling solutions. For contracting universes, we show that scale-invariant adiabatic perturbations can be produced continuously as modes leave the horizon for any equation of state parameter $w \ge 0$. The corresponding background solutions are unstable, which we argue is a universal feature of contracting models that yield scale-invariant spectra. For expanding universes, we find that nearly scale-invariant adiabatic perturbation spectra can only be produced for $w \approx -1$, and that the corresponding scaling solutions are attractors. The presence of a nontrivial metric on field space is a crucial ingredient in our results.