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

We study cosmological perturbations produced by the most general twoderivative actions involving two scalar fields, coupled to Einstein gravity, with an arbitrary field space metric, that admit scaling solutions. For expanding universes, we find that scaleinvariant adiabatic perturbation spectra can be produced for any equation of state parameter w that satisfies −1 ≤ w < −1/3, and that all the scaling solutions are attractors. For contracting universes, we show that scale-invariant adiabatic perturbations can be produced continuously as modes leave the horizon for any w > −1/3. The corresponding background solutions are unstable, which we argue is a universal feature of contracting models that yield scale-invariant spectra. At no point do we assume slow-roll. The presence of a nontrivial metric on field space is a crucial ingredient in our results.