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≥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≈−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.Comment: 23 pages, oversight in perturbations calculation corrected,
conclusions for expanding models modifie