A Portrait of the Cosmic Reionisation History in the Context of the Early Dark Energy Model

Recent JWST observations of Lyman-$α$ emission at $z \sim 11-6$ indicate a rapid reionization of the intergalactic medium within the first $\sim700$ Myr. The required Lyman continuum (LyC) photon budget may naturally arise from the unexpectedly high galaxy number densities revealed by JWST, reducing the need for scenarios invoking very high LyC escape fractions ($f_{\rm esc}\gtrsim0.2$) or dominant contributions from ultra-faint galaxies ($M_{\rm UV}>-15$) in the standard $Λ$CDM framework. In this work, we model the reionization history under the Early Dark Energy (EDE) paradigm -- originally proposed to ease the Hubble tension -- which also explains the observed over-abundance of high-$z$ galaxies without extreme star formation efficiencies. The EDE model yields reionization histories consistent with current constraints while requiring only moderate LyC escape fractions and UV luminosity densities ($f_{\rm esc}\sim 0.05-0.1$, $M_{\rm UV}\lesssim -17$ to $-15$). Our results suggest that, once key astrophysical parameters are better constrained, the reionization history could serve as an independent and complementary probe of EDE cosmologies.