Primordial perturbations from inflation with a hyperbolic field-space
  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.
