Primordial perturbations and inflation in holographic cosmology

TL;DR

This paper explores how holographic braneworld models influence inflationary cosmology, specifically affecting scalar perturbations through the inflaton's speed of sound, while tensor perturbations remain unchanged, leading to second-order spectral index modifications.

Contribution

It introduces a holographic braneworld inflation model with a boundary conformal field, deriving modified Einstein equations and analyzing their impact on cosmological perturbations.

Findings

Scalar power spectrum depends on the inflaton's speed of sound.

Tensor power spectrum remains unaffected by the braneworld scenario.

Spectral indices are modified at second order in slow-roll parameters.

Abstract

We consider an inflationary scenario in the holographic braneworld with a cosmological fluid occupying the 3+1 dimensional brane located at the holographic boundary of an asymptotic ADS$_5$ bulk. The contribution of the boundary conformal field can be represented as a modification of Einstein's equations on the boundary. Using these effective Einstein equations we calculate the cosmological perturbations and derive the corresponding power spectra assuming a general $k$-essence type of inflaton. We find that the braneworld scenario affects the scalar power spectrum only in the speed of sound dependence on the slow-roll parameters whereas there is no change in the tensor power spectrum. This implies that the changes in the spectral indices appear at the second order in the slow-roll parameter expansion.