Rapidly-Varying Speed of Sound, Scale Invariance and Non-Gaussian Signatures

Abstract

We show that curvature perturbations acquire a scale invariant spectrum for any constant equation of state, provided the fluid has a suitably time-dependent sound speed. In order for modes to exit the physical horizon, and in order to solve the usual problems of standard big bang cosmology, we argue that the only allowed possibilities are inflationary (albeit not necessarily slow-roll) expansion or ekpyrotic contraction. Non-Gaussianities offer many distinguish features. As usual with a small sound speed, non-Gaussianity can be relatively large, around current sensitivity levels. For DBI-like lagrangians, the amplitude is negative in the inflationary branch, and can be either negative or positive in the ekpyrotic branch. Unlike the power spectrum, the three-point amplitude displays a large tilt that, in the expanding case, peaks on smallest scales. While the shape is predominantly of the equilateral type in the inflationary branch, as in DBI inflation, it is of the local form in the ekpyrotic branch. The tensor spectrum is also generically far from scale invariant. In the contracting case, for instance, tensors are strongly blue tilted, resulting in an unmeasurably small gravity wave amplitude on cosmic microwave background scales.

41 pages, 12 figures. v4: Few typos in equations (7.39) corrected

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