Quantum modes in DBI inflation: exact solutions and constraints from vacuum selection

TL;DR

This work addresses inflation models with a variable sound speed within the DBI/k-inflation framework and derives exact background solutions alongside exact curvature-perturbation spectra. It introduces a two-parameter family of backgrounds governed by the first slow-roll parameter epsilon and a sound-speed parameter s, solving the mode equations exactly for constant parameters and extending to slow-roll to second order. A key result is the exact scalar spectral index for constant parameters and a robust second-order slow-roll expression in terms of flow parameters, revealing how vacuum selection and bulk-string physics can imprint on the primordial spectrum. The analysis shows that in certain DBI regimes the Bunch-Davies vacuum may be ill-defined or sensitive to bulk physics, which could yield observable signatures and place constraints via non-Gaussianity on the total inflationary duration.

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.