Gravitational Wave Constraints on DBI Inflation

TL;DR

The paper derives a model-independent upper bound on the primordial gravitational wave amplitude for UV DBI inflation, finding r_* < 10^{−7}, and a lower bound r_* > ~0.002 for red spectra with detectable non-Gaussianity, which cannot be satisfied simultaneously under standard UV DBI assumptions. It shows that reconciling with data requires relaxing the BM bound or adopting generalized DBI actions, notably IR inflation with multiple coincident branes, which can potentially satisfy the bounds for certain throat geometries and flux topologies. A generalized kinetic framework P = −f1(φ)√(1−f2(φ)X) − f3(φ) demonstrates how the BM bound can be weakened if f1f2 ≫ 1 on observable scales, while IR models show that throat geometry (AdS_5 vs KS) and global string constraints crucially impact viability. Overall, the study uses gravitational-wave constraints alongside density perturbation data to discriminate among DBI inflation variants and guide viable generalizations.

Abstract

An upper bound on the amplitude of the primordial gravitational wave spectrum generated during ultra-violet DBI inflation is derived. The bound is insensitive to the form of the inflaton potential and the warp factor of the compactified dimensions and can be expressed entirely in terms of observational parameters once the volume of the five-dimensional sub-manifold of the throat has been specified. For standard type IIB compactification schemes, the bound predicts undetectably small tensor perturbations with a tensor-scalar ratio $r < 10^{-7}$. This is incompatible with a corresponding lower limit of $r > 0.1 (1-n_s)$, which applies to any model that generates a red spectral index $n_s <1$ and a potentially detectable non-Gaussianity in the curvature perturbation. Possible ways of evading these bounds in more general DBI-type scenarios are discussed and a multiple-brane model is investigated as a specific example.