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 ${\mathrm{ADS}}_5$ 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.

• Received 14 July 2020
• Accepted 16 October 2020

DOI:https://doi.org/10.1103/PhysRevD.102.123505