AR_final file_2018-19

− 1 . 0 − 0 . 5 0 . 0 ln Ω m − 0 . 006 − 0 . 004 − 0 . 002 0 . 000 0 . 002 0 . 004 0 . 006 0 . 008 0 . 010 ( f nu − f an ) /f nu Ω ℓ = 0 . 025 Ω ℓ = 0 . 05 Ω ℓ = 0 . 1 Ω ℓ = 0 . 2 Ω ℓ = 0 . 5 Figure 4: Percentage error of the ansatz (3)–(4) is shown for different values of the brane parameter Ω ℓ , starting from the matter domination until the present epoch. Here, f nu and f an represent the numerical solution for f and the ansatz (3) respectively. Note that, during matter domination Ω m → 1 and, at the present epoch, Ω m = Ω m 0 = 0 . 28. scattering optical depth of the CMB photons, obser- vations of the Ly- α absorption spectra of the high- redshift quasars and the luminosity function and clustering properties of high-redshift Ly- α emit- ters. These observations suggest that this epoch extended over a broad redshift range 6 . z . 15. However, our understanding on most of the funda- mental issues associated with this epoch, such as the properties of ionizing sources, topology of neu- tral hydrogen and the morphology of ionized HII regions etc. at different stages of the reionization remains uncertain. Observations of the redshifted HI 21-cm signal which provides a direct window to the state of hy- drogen in the IGM have the potential to probe this complex epoch. There is considerable effort under- way to detect the EoR 21-cm signal using radio interferometry from HI surveys such as GMRT, LO- FAR, MWA, PAPER, SKA and HERA. The analyses of the redshifted 21-cm signal have so far been performed on the basis of traditional N -point correlation statistics. However, beyond the simplest two-point function (power spectrum), higher order correlations are difficult to calculate. By contrast, the Minkowski functionals (MFs) are extremely useful tools in quantitatively describing morphology because they contain information of all the higher order moments. The MFs have been ex- tensively employed to study the morphology of the large scale structure of the universe (the cosmic web) and the CMB. Since the reionization land- scape is similarly rich in geometrical properties, studying the morphology of reionization using MFs is both compelling and feasible. The physics un- derlying the reionization process is expected to be manifested in the geometry and morphology of HI and HII regions. Satadru Bag . Varun Sahni , (Rajesh Mondal, Tirthankar Roy Choudhury, Prakash Sarkar and Somnath Bharadwaj) have explored this vibrant reionization landscape using percolation analysis, the Minkowski functionals and the Shapefinders. In percolation analysis a key role is also played by the following quantities which can be defined, for a ( 61 )