Primordial perturbations from inflation with a hyperbolic field-space

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.

18 pages, 10 figures, minor corrections, references added, version accepted for publication in PRD

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• The rapid-turn inflationary attractor
• Hyperinflation generalised: from its attractor mechanism to its tension with the `swampland conjectures'
• On the inflationary massive field with a curved field manifold
• Spectra and entropy of multi-field warm inflation
• Geometric structure of multi-form-field isotropic inflation and primordial fluctuations
• New Anisotropic Exact Solution in Multifield Cosmology
• Hyperbolic inflation in the Jordan frame
• Anisotropic Spacetimes in Chiral Scalar Field Cosmology