Isocurvature and Curvaton Perturbations with Red Power Spectrum and Large Hemispherical Asymmetry

TL;DR

This paper investigates how a complex field undergoing tachyonic growth can produce large hemispherical asymmetry and red power spectra in isocurvature and curvaton perturbations, potentially explaining observed cosmic asymmetries.

Contribution

It introduces a semi-classical method to compute perturbations from a tachyonic complex field and links these to observable hemispherical asymmetry and spectral tilt.

Findings

Large hemispherical asymmetry can be generated during early tachyonic growth.

The spectral index of perturbations is generally negative, indicating a red spectrum.

Red spectra can suppress asymmetry at small scales, aligning with observations.

Abstract

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.