Cosmic reionization holds the key to understand structure formation in the Universe, and can inform us about the properties of the first sources, as their star formation efficiency and escape fraction of ionizing photons. By combining the recent release of Planck electron scattering optical depth data with observations of high-redshift quasar absorption spectra, we obtain strong constraints on viable reionization histories. We show that inclusion of Planck data favors a reionization scenario with a single stellar population. The mean x HI drops from ∼ 0.8 at z = 10.6 to ∼ 10 −4 at z = 5.8 and reionization is completed around 5.8 z 8.5 (2-σ), thus indicating a significant reduction in contributions to reionization from high redshift sources. We can put independent constraints on the escape fraction f esc of ionizing photons by incorporating the high-redshift galaxy luminosity function data into our analysis. We find a non-evolving f esc of ∼ 10% in the redshift range z = 6 − 9.

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The escape fraction, fesc, of ionizing photons from high-redshift galaxies is a key parameter to understand cosmic reionization and star formation history. Yet, in spite of many efforts, it remains largely uncertain. We propose a novel, semi-empirical approach based on a simultaneous match of the most recently determined luminosity functions of galaxies in the redshift range 6 ≤ z ≤ 10 with reionization models constrained by a large variety of experimental data. From this procedure, we obtain the evolution of the best-fitting values of fesc along with their 2σ limits. We find that, averaged over the galaxy population, (i) the escape fraction increases from fesc = 0.068+ 0.054− 0.047 at z = 6 to fesc = 0.179+ 0.331− 0.132 at z = 8 and (ii) at z = 10 we can only put a lower limit of fesc > 0.146. Thus, although errors are large, there is an indication of a 2.6 times increase of the average escape fraction from z = 6 to 8, which might partially release the ‘starving reionization’ problem.

In the absence of complex astrophysical processes that characterize the reionization era, the 21‐cm emission from neutral hydrogen (H i) in the post‐reionization epoch is believed to be an excellent tracer of the underlying dark matter distribution. Assuming a background cosmology, it is modelled through (i) a bias function b(k, z), which relates H i to the dark matter distribution and (ii) a mean neutral fraction () which sets its amplitude. In this paper, we investigate the nature of large‐scale H i bias. The post‐reionization H i is modelled using gravity only N‐body simulations and a suitable prescription for assigning gas to the dark matter haloes. Using the simulated bias as the fiducial model for H i distribution at z≤ 4, we have generated a hypothetical data set for the 21‐cm angular power spectrum (Cℓ) using a noise model based on parameters of an extended version of the Giant Metrewave Radio Telescope (GMRT). The binned Cℓ is assumed to be measured with S/N ≳ 4 in the range 400 ≤ℓ≤ 8000 at a fiducial redshift z= 2.5. We explore the possibility of constraining b(k) using the principal component analysis on these simulated data. Our analysis shows that in the range 0.2 < k < 2 Mpc−1, the simulated data set cannot distinguish between models exhibiting different k‐dependences, provided 1 ≲b(k) ≲ 2 which sets the 2σ limits. This justifies the use of linear bias model on large scales. The largely uncertain is treated as a free parameter resulting in degradation of the bias reconstruction. The given simulated data are found to constrain the fiducial with an accuracy of ∼4 per cent (2σ error). The method outlined here could be successfully implemented on future observational data sets to constrain b(k, z) and and thereby enhance our understanding of the low‐redshift Universe.