Impact of the primordial fluctuation power spectrum on the reionization history

Abstract

We argue that observations of the reionization history can be used as a probe of primordial density fluctuations, particularly on small scales. Although the primordial curvature perturbations are well constrained from measurements of cosmic microwave background (CMB) anisotropies and large-scale structure, these observational data probe the curvature perturbations only on large scales, and hence its information on smaller scales will give us further insight on primordial fluctuations. Since the formation of early galaxies is sensitive to the amplitude of small-scale perturbations, and then, in turn, gives an impact on the reionization history, one can probe the primordial power spectrum on small scales through observations of reionization. In this work, we focus on the running spectral indices of the primordial power spectrum to characterize the small-scale perturbations, and investigate their impact on the reionization history using the numerical code \texttt{21cmFAST}, which adopts a simple but commonly used reionization model. We also derive the constraints on the running spectral indices from observations of the reionization history indicated by the luminosity function of the Lyman-$\alpha$ emitters. We show that the reionization history, in combination with large-scale observations such as CMB, would be a useful tool to investigate primordial density fluctuations.