Isocurvature and Curvaton Perturbations with Red Power Spectrum and
  Large Hemispherical Asymmetry
  We calculate the power spectrum and hemispherical asymmetry of isocurvature
and curvaton perturbations due to a complex field \Phi which is evolving along
the tachyonic part of its potential. Using a semi-classical evolution of
initially sub-horizon quantum fluctuations, we compute the power spectrum, mean
field and hemispherical asymmetry as a function of the number of e-foldings of
tachyonic growth \Delta N and the tachyonic mass term cH^2. We find that a
large hemispherical asymmetry due to the modulation of |\Phi| can easily be
generated via the spatial modulation of |\Phi| across the horizon, with Delta
|\Phi|/|\Phi| > 0.5 when the observed Universe exits the horizon within 10-40
e-foldings of the beginning of tachyonic evolution and c is in the range 0.1-1.
The spectral index of the isocurvature and curvaton perturbations is generally
negative, corresponding to a red power spectrum. Dark matter isocurvature
perturbations due to an axion-like curvaton with a large hemispherical
asymmetry may be able to explain the hemispherical asymmetry observed by WMAP
and Planck. In this case, the red spectrum can additionally suppress the
hemispherical asymmetry at small scales, which should make it easier to satisfy
scale-dependence requirements on the asymmetry from quasar number counts.
