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tokens: to match the observed LFs at redshifts z = 6 − 10. Although not shown in the present paper, we find that a roughly constant (; best-fitting value) ε * is needed for all the flat and non-flat models considered here (see fig. 2 of Paper I ). We can then get limits for f esc at different redshifts from equation ( 12 ) using the MCMC constraints already obtained on the evolution of N ion ( z ). Note that we take the value of N γ as ≈3200 which is appropriate for the PopII Salpeter IMF assumed here. The redshift evolution of f esc for different models is shown in Fig. 4 . The corresponding 2-σ uncertainties, indicated by shaded regions in the plot, have been computed using the quadrature method (Mitra et al. 2013 ). We find that the best-fitting f esc remains almost constant at for the whole redshift range in all the flat models ( l eft panel). On the other hand, a strong redshift evolution of this quantity is required for the non-flat models (right panel) – it can increase by a factor of ∼7 from redshift 6 to 10. Moreover, if we consider their 2-σ ranges, these non-flat models can lead to an impractically high f esc (≳1) at redshifts z ≳ 8. The sole reason behind such trends is that the values of N ion for non-flat models can become as high as ∼1000 around z ≈ 8 − 9, considering their 2-σ limits (see panel (a) of Fig. 3 ), in order to produce very high optical depths required for those models. On the other hand, the upper limits (2-σ) of escape fraction for the flat models having relatively lower τ el can become at most for all the redshift ranges considered here. Such one-to-one correspondence between strong redshift evolution of f esc ( z ) and higher reionization optical depths has also been reported earlier in many studies (see e.g. Haardt Madau 2012 ; Kuhlen Faucher-Giguère 2012 ; Mitra et al. 2013 ). Figure 4. Redshift evolution of the escape fraction f esc ( z ) along with its 2-σ errors for all the flat (left panel) and non-flat (right panel) models considered in this work. The red solid lines in both panels correspond to an escape fraction of unity. 4 CONCLUDING REMARKS We have presented detailed statistical analysis of reionization in tilted flat and untilted non-flat ΛCDM, XCDM and φCDM inflation models. The cosmological parameters for these models are constrained by Planck 2015 TT + lowP + lensing CMB anisotropy and SNIa, BAO, H ( z ), and growth rate data, using physically motivated inflation power spectra for energy density inhomogeneities (Park Ratra 2018a , c ). For the non-flat models, these data prefer mildly closed models with Ω k ∼ −0.006 to −0.008. Although such models provide better fits to the observed low-l temperature anisotropy C l ’s and weak-lensing σ 8 estimates, they provide worse fits to the observed higher-l temperature anisotropy C l ’s and primordial deuterium abundances (Penton et al. 2018 ). These closed models also predict relatively higher reionization optical depth values (τ el ≈ 0.11–0.12) compared to