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

TL;DR

The paper investigates how two-field, two-derivative actions with a nontrivial field-space metric can produce scale-invariant adiabatic perturbations in both contracting and expanding cosmologies, within the framework of scaling solutions characterized by parameters c and Δ, where Δ = f1^2 − f2 − (1 − 6/c^2) h2. It finds that contracting backgrounds with w ≥ 0 can continuously generate a scale-invariant adiabatic spectrum at horizon exit, but the background is generically unstable, while expanding backgrounds yield nearly scale-invariant adiabatic spectra only for w ≈ −1 and are stable; the spectral indices depend only on c and Δ. In the contracting case the tensor spectrum is blue, with n_T = 6(1+w)/(1+3w), and the curvature/isocurvature coupling on super-horizon scales is driven by a nontrivial field-space metric. The work highlights the crucial role of curved field-space geometry in enabling adiabatic/isocurvature coupling and provides a compact two-parameter framework for classifying two-field scaling models.

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.