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

TL;DR

The paper investigates whether an axion-like Early Dark Energy (EDE) cosmology can reproduce the rapid cosmic reionisation indicated by observations without requiring extreme Lyman continuum escape fractions or reliance on ultra-faint galaxies. It couples the EDE-induced changes in early structure formation to the reionisation photon budget via the equations $\tfrac{dQ}{dt}=\tfrac{\dot{n}_{ion}}{\langle n_{H}\rangle}-\tfrac{Q}{\bar{t}_{rec}}$ and $\dot{n}_{ion}=f_{esc}\xi_{ion}\rho_{UV}$, exploring their dependence on $f_{esc}$, $\xi_{ion}$, and $\rho_{UV}$ derived from the UV luminosity function down to $M_{UV,lim}$. The results show that EDE predicts higher high-redshift galaxy abundances (due to larger $\sigma_8$), yielding reionisation histories consistent with current constraints for moderate $f_{esc}\sim0.05-0.1$ and $M_{UV,lim}\sim-15$ to $-17$, with a higher $\xi_{ion}$ relaxing the photon-budget requirements further. This work suggests that reionisation history can serve as an independent probe of EDE cosmologies, providing a cross-check on high-z galaxy populations and the ionising photon budget, subject to improved constraints on $\xi_{ion}$ and the faint-end LF turnover.

Abstract

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.

Figures (4)

• Figure 1: The prediction of SMF at redshift $z\sim6-11$ under EDE model with the $M_h-M_\ast$ scaling relation from 2021ApJ...922...29S. The error shade represents the uncertainties of HMF and the scaling relation. The data points are from both JWST 2025AA...695A..20S2024MNRAS.533.1808W2025ApJ...978...89H and pre-JWST 2021ApJ...922...29S2016ApJ...825....5S2020ApJ...893...60K2019MNRAS.486.3805B. The EDE model predicts relatively higher galaxy abundance at each redshift due to its elevated $\sigma_{8}$ (Table \ref{['tab:ede_params']}), and shows consistency with the observations at $z\sim7-11$. In particular, the prediction is consistent with the low mass end at each redshift bin, which is of particular importance for the reionisation.
• Figure 2: The LF at $z\sim6-11$ under the EDE model with the scaling relation from 2021ApJ...922...29S. The error shade incorporates the uncertainty from the $M_\ast-M_{UV}$ relation, in addition to those from SMF in Figure \ref{['fig:smf']}. The predictions from EDE are well agreed with the data at $z\sim7, 8, 11$ as well as the bright and faint ends of other redshifts. The overestimation in the intermediate brightness range, on the other hand, might be the result of the instantaneous SFR and dust attenuation, which could be verified with future observations. We also plot the rescaled LF at $z\sim6-8$ by $1/3$ and $z\sim8-10$ by $1/4$ to match the data points with intermediate brightness (dashed line), in which case the reionisation would be greatly delayed due to the insufficiency of the faint galaxies. We plot the data points from 2023ApJ...948L..14C2022ApJ...940L..55F2023arXiv230406658H2023ApJS..265....5H2023ApJ...946L..35M2022ApJ...940L..14N2023ApJ...951L...1P2023MNRAS.518.6011D2023MNRAS.523.1009B2023MNRAS.523.1036B2022arXiv220512980B2021AJ....162...47B2022ApJ...928...52F2018ApJ...867..150M2018ApJ...855..105O2020MNRAS.493.2059B2019ApJ...883...99S2023arXiv231104279F2024MNRAS.527.5004M2024ApJ...965...98C2017ApJ...835..113L2025arXiv250924881C. The black data points are collected from pre-JWST observations, and the red data points are from JWST.
• Figure 3: The comparison between reionisation history observations and EDE-based predictions with various parameter combinations. (Left) When adopting $f_{esc}=0.05$ and $\lg [\xi_{ion}/Hz \ erg^{-1}]=25.8$, a conservative choice of $M_{\text{UV,lim}}\leq-15$ provides a good fit to the data. (Right) With $M_{\text{UV,lim}}=-17$, a low value of $f_{esc}\sim0.1$ is sufficient for predicting a coherent evolution of the neutral fraction. In case the completion time of EoR is prioritised, the requirements of both parameters can be reduced to $f_{esc}\sim 0.05$ and $M_{UV, lim}\sim -17$. The data points are from various probes, i.e., Lyman-$\alpha$ Emitter 2018ApJ...856....2M2019MNRAS.485.3947M2019ApJ...878...12H2020MNRAS.495.3602W2022MNRAS.517.3263B2023ApJ...949L..40B2023ApJ...947L..24M2024ApJ...967...28N2025MNRAS.536.2355J2024ApJ...975..208T2025arXiv250105834K2025MNRAS.538L..16Q, CMB 2020AA...641A...6P, Lyman-$\alpha$ and Lyman-$\beta$ forest dark fraction 2015MNRAS.447..499M2023ApJ...942...59J, Quasars 2018Natur.553..473B2018ApJ...864..142D2020ApJ...896...23W2020ApJ...897L..14Y2022MNRAS.512.5390G2024ApJ...969..162D, Lyman-break galaxy 2023NatAs...7..622C2024ApJ...973....8H2024ApJ...971..124U, Lyman-$\alpha$ Emitter clustering 2015MNRAS.453.1843S2018PASJ...70S..13O, and Lyman-$\alpha$ LF 2010ApJ...723..869O2014ApJ...797...16K2018PASJ...70S..16K2017ApJ...842L..22Z2018PASJ...70...55I2021ApJ...923..229G2021ApJ...919..120M2022ApJ...926..230N.
• Figure 4: The reionisation history with two values of $\xi_{ion}$. Given a higher $\xi_{ion}$, EDE predicts a fast rate of reionisation and reconstructs a consistent reionisation history with a less stringent parameter set ($(f_{esc}, \rm \lg{\xi_{ion}/Hz \ erg^{-1}}, M_{UV,lim})=(0.05, 25.8, -15)$). Alternatively, when $\rm \lg[\xi_{ion}/Hz \ erg^{-1}]$ is reduced to $25.3$ as is suggested by 2024MNRAS.535.2998S, generating a similar result requires an escalated $f_{esc}=0.15$ that marks the upper limit of $f_{esc}$ for EDE model, which is still lower than the previous assumption of $0.2$. On the other hand, given that the theoretical LFs are rescaled to match the data points with intermediate brightness, as in Figure \ref{['fig:lf']}, the insufficiency of the faint galaxies would greatly delay the entire reionisation process (dotted line).