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 vertical bar Phi vertical bar can easily be generated via the spatial modulation of vertical bar Phi vertical bar across the horizon, with Delta vertical bar Phi vertical bar/vertical bar Phi vertical bar > 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.