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