Non-Gaussianity in braneworld and tachyon inflation

TL;DR

This paper develops the bispectrum for single-field braneworld and tachyon inflation using a gradient expansion in a stochastic-inflation framework. It demonstrates that, at leading slow-roll order, the non-Gaussianity parameter satisfies $4 f_{ m NL} \approx n_{ m s}-1$, identical to four-dimensional inflation, with potential momentum-dependent corrections that remain subdominant. Bulk Weyl terms and non-commutative spacetime extensions do not qualitatively modify this leading result, though bulk physics could enhance post-inflationary non-Gaussianity in some regimes. The work provides a generalized, non-linear Mukhanov equation on the brane and highlights the conditions under which inflationary non-Gaussianity remains a small contributor to the observed signal, pointing to areas where stronger signatures might arise from bulk effects or sub-horizon dynamics.

Abstract

We calculate the bispectrum of single-field braneworld inflation, triggered by either an ordinary scalar field or a cosmological tachyon, by means of a gradient expansion of large-scale non-linear perturbations coupled to stochastic dynamics. The resulting effect is identical to that for single-field 4D standard inflation, the non-linearity parameter being proportional to the scalar spectral index in the limit of collapsing momentum. If the slow-roll approximation is assumed, braneworld and tachyon non-Gaussianities are subdominant with respect to the post-inflationary contribution. However, bulk physics may considerably strengthen the non-linear signatures. These features do not change significantly when considered in a non-commutative framework.