Bispectrum from five-dimensional inflation

TL;DR

This work extends single-field inflation to five dimensions and analyzes the resulting primordial non-Gaussianity observed on a 3-brane. Using the Schwinger-Keldysh in-in formalism with a full cubic action, the authors derive the bulk and brane power spectra and bispectra, uncovering that special conformal invariance is broken at late times, which shapes the bispectrum compared to 4D inflation. They find that the brane-observed bispectrum depends on two momentum ratios and exhibits a pronounced enhancement in the squeezed limit, offering a distinct observational signature of higher-dimensional inflation. The results connect the 5D slow-roll parameters to observable quantities like $n_s$ and $r$, and provide concrete predictions for the momentum-dependent $f_{\mathrm{NL}}$ that could help distinguish 5D from 4D scenarios in future cosmological data.

Abstract

It was proposed that five-dimensional (5D) inflation can blow up the size of a compact dimension from the 5D Planck length to the micron size, as required by the dark dimension proposal, relating the weakness of the actual gravitational force to the size of the observable universe. Moreover, it was shown that 5D inflation can generate the (approximate) flat power spectrum of primordial density fluctuations consistent with present observations. Here we compute the bispectrum of primordial scalar perturbations and show that unlike the power spectrum, it differs from the four-dimensional case at all angular distances, due to the fact that in contrast to global dilatations, invariance under special conformal transformations is not restored at late times. Moreover there is an additional enhancement in the squeezed limit.

Figures (2)

• Figure 1: $\tau'$ complex plane
• Figure 2: $x$ complex plane