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

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.

10 pages, LaTeX; V2: version submitted to PRD. References added, minor error in text corrected

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• Bimetric varying speed of light theories and primordial fluctuations
• Bispectrum signatures of a modified vacuum in single field inflation with a small speed of sound
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• Keeping an Eye on DBI: Power-counting for small-$c_s$ Cosmology
• Assessing the foundation and applicability of some dark energy fluid models in the Dirac-Born-Infeld framework
• Consistency of Tachyacoustic Cosmology with de Sitter Swampland Conjectures
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• Horizon-preserving dualities and perturbations in non-canonical scalar field cosmologies
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