Superimposed oscillations in brane inflation

Santiago Ávila,Danièle A Steer,Jérôme Martin

doi:10.1088/1475-7516/2014/08/032

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. 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 cS 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, when cS is small, 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.

Highlights

It is a near certainty that the universe underwent a period of accelerated expansion — inflation — early in its history
Since ǫ2 is defined in terms of derivatives of ǫ1 which itself contains γ [see Eq (14)], the second horizon flow parameter ǫ2 is discontinuous. (This is true in the the Standard Single Field Inflation (SSFI)-Starobinsky model.) following from the definition in terms of γ, the parameter δ1 is discontinuous
We find that the scale invariant value of the power-spectrum on small scales is given by lim Pζ(k) =

Summary

Introduction

It is a near certainty that the universe underwent a period of accelerated expansion — inflation — early in its history. The spectacular Planck data [1, 2] is entirely compatible with Standard Single Field Inflation (SSFI) in the slow-roll regime, and with a canonical kinetic term [3,4,5]. In the process we will characterise how, for a given inflaton potential, the properties of the superimposed oscillations in Pζ(k) — amplitude and frequency for example — depend on non-standard kinetic terms in the Lagrangian for the inflaton. For arbitrary potentials V (φ) and T (φ), and working in a spatially flat Friedmann-Lemaıtre-Robertson-Walker (FLRW) background geometry with metric ds2 = −dt2 + a2(t)dx, the Friedmann and scalar field equations of motion following from Eq (3) are given, respectively, by H2 1 3MP2l [(γ 1)T ] (6) φ − γ3 2γ3 1 γ3

Objectives

Results

Conclusion