An improved model of HII bubbles during the epoch of reionization

The size distribution of ionized regions during the epoch of reionization -- a key ingredient in understanding the HI power spectrum observable by 21cm experiments -- can be modelled analytically using the excursion set formalism of random walks in the smoothed initial density field. To date, such calculations have been based on simplifying assumptions carried forward from the earliest excursion set models of two decades ago. In particular, these models assume that the random walks have uncorrelated steps and that haloes can form at arbitrary locations in the initial density field. We extend these calculations by incorporating recent technical developments that allow us to (a) include the effect of correlations in the steps of the walks induced by a realistic smoothing filter and (b) more importantly, account for the fact that dark matter haloes preferentially form near peaks in the initial density. A comparison with previous calculations shows that including these features, particularly the peaks constraint on halo locations, has large effects on the size distribution of the HII bubbles surrounding these haloes. For example, when comparing models at the same value of the globally averaged ionized volume fraction, the typical bubble sizes predicted by our model are more than a factor 2 larger than earlier calculations. Our results can potentially have a significant impact on estimates of the observable HI power spectrum.Comment: 13 pages, 6 figures; v2 - added clarifications and fixed typos. Accepted in MNRA

The Averaging Problem in Cosmology

This thesis deals with the averaging problem in cosmology, which has gained considerable interest in recent years, and is concerned with correction terms (after averaging inhomogeneities) that appear in the Einstein equations when working on the large scales appropriate for cosmology. It has been claimed in the literature that these terms may account for the phenomenon of dark energy which causes the late time universe to accelerate. We investigate the nature of these terms by using averaging schemes available in the literature and further developed to be applicable to the problem at hand. We show that the effect of these terms when calculated carefully, remains negligible and cannot explain the late time acceleration.Comment: 126 pages, PhD thesis; some typos fixed, one reference adde