The Earliest Epoch of Reionisation in the Standard $\Lambda$CDM Model

Abstract

We show that the earliest possible reionisation of the Universe is approximately at $z\simeq 13.5$ and the optical depth is $\tau\simeq 0.17$ in the conventionally accepted $\Lambda$ cold dark matter ($\Lambda$CDM) model with adiabatic fluctuations of a flat spectrum normalised to the cosmic microwave background. This is consistent with the reionisation found by WMAP (the apparently earlier reionisation epoch of the WMAP is ascribed to the adoption of the instantaneous reionisation approximation), i.e., the WMAP result is realised only if reionisation of the universe takes place nearly at the maximal efficiency in the $\Lambda$CDM model.