Primordial perturbations from inflation with a hyperbolic field-space

TL;DR

This paper investigates hyperinflation driven by a hyperbolic field-space, analyzing primordial perturbations, and finds that certain potentials are consistent with observations while others are excluded.

Contribution

It extends previous work by confirming and elaborating on the perturbation analysis of hyperinflation using standard cosmological perturbation methods.

Findings

Power spectrum and spectral tilt derived in terms of slow-varying parameters.

Power-law potentials are excluded by Planck data.

Exponential potentials can be consistent with observations.

Abstract

We study primordial perturbations from hyperinflation, proposed recently and based on a hyperbolic field-space. In the previous work, it was shown that the field-space angular momentum supported by the negative curvature modifies the background dynamics and enhances fluctuations of the scalar fields qualitatively, assuming that the inflationary background is almost de Sitter. In this work, we confirm and extend the analysis based on the standard approach of cosmological perturbation in multi-field inflation. At the background level, to quantify the deviation from de Sitter, we introduce the slow-varying parameters and show that steep potentials, which usually can not drive inflation, can drive inflation. At the linear perturbation level, we obtain the power spectrum of primordial curvature perturbation and express the spectral tilt and running in terms of the slow-varying parameters. We show that hyperinflation with power-law type potentials has already been excluded by the recent Planck observations, while exponential-type potential with the exponent of order unity can be made consistent with observations as far as the power spectrum is concerned. We also argue that, in the context of a simple $D$-brane inflation, the hyperinflation requires exponentially large hyperbolic extra dimensions but that masses of Kaluza-Klein gravitons can be kept relatively heavy.