Superimposed Oscillations in Brane Inflation

TL;DR

This paper extends the analysis of superimposed oscillations in the primordial power spectrum from the Starobinsky model to Dirac Born Infeld (DBI) inflation, revealing significant differences in spectral features due to non-linear kinetic terms and exploring potential fits to Planck CMB data.

Contribution

It introduces a detailed analysis of oscillatory features in the power spectrum within DBI inflation, highlighting how non-linear kinetic terms alter spectral shapes and amplitudes compared to the Starobinsky model.

Findings

Power spectrum shows similar scale invariance on large and small scales.

Intermediate scales exhibit larger amplitude and higher frequency oscillations.

Calculating non-Gaussianities involves all terms in the cubic action.

Abstract

In canonical scalar field inflation, the Starobinsky model (with a linear potential but discontinuous slope) is remarkable in that though slow-roll is violated, both the power-spectrum and bi-spectrum can be calculated exactly analytically. The two-point function is characterised by different power on large and small scales, and a burst of small amplitude superimposed oscillations in between. Motivated by string-theory models with stuck branes, we extend this analysis to Dirac Born Infeld (DBI) inflation, for which generalised slow-roll is violated at the discontinuity and a rapid variation in the speed of sound c_s occurs. In an attempt to characterise the effect of non-linear kinetic terms on the oscillatory features of the primordial power-spectrum, we show that the resulting power spectrum has a shape and features which differ significantly from those of the standard Starobinsky model. In particular, the power-spectrum now takes very similar scale invariant values on large and small scales, while on intermediate scales it is characterised by much larger amplitude and higher frequency superimposed oscillations. We also show that calculating non-Gaussianities in this model is a complicated but interesting task since all terms in the cubic action now contribute. Investigating whether the superimposed oscillations could fit to the Planck Cosmic Microwave Background (CMB) data (for instance by explaining the large scale Planck anomalies) with, at the same time, small non-Gaussianities remains an intriguing and open possibility.