Abstract
We study a two-parameter family of exactly solvable inflation models with
variable sound speed, and derive a corresponding exact expression for the
spectrum of curvature perturbations. We generalize this expression to the slow
roll case, and derive an approximate expression for the scalar spectral index
valid to second order in slow roll. We apply the result to the case of DBI
inflation, and show that for certain choices of slow roll parameters, the
Bunch-Davies limit (a) does not exist, or (b) is sensitive to stringy physics
in the bulk, which in principle can have observable signatures in the
primordial power spectrum.
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