AR_final file_2018-19

Sahni have shown that for a suitable choice of Ω DE ( x ) ≡ ρ DE ( x ) /ρ cr, 0 , braneworld expansion h ( x ) = p Ω m 0 x 3 + Ω DE ( x ) + Ω ℓ − p Ω ℓ , x = 1+ z (1) can easily mimic the ΛCDM model h Λ CDM ( x ) = p Ω m 0 x 3 + Ω Λ . (2) It is interesting that there is a precise form of the Quintessence potential, V ( φ ), which gives rise to ΛCDM-like expansion on the brane. Consequently Ω DE ( z ) in (1) is replaced by Ω ϕ . Remarkably the reconstructed potential has precisely the same late- time form as V = V 0 coth 2 ( λϕ ). Figure shows that the expansion rate on the Braneworld containing a scalar field with a coth- like potential coincides with the expansion rate of the ΛCDM model. However it is important to em- phasize that perturbation growth in the two mod- els is quite different, and therefore these two mod- els: (i) Braneworld with a coth-like potential, (ii) the ΛCDM model, can easily be distinguished even though their expansion history is virtually identi- cal. Global analysis of luminosity- and colour-dependent galaxy clustering in the Sloan Digital Sky Survey Halo model is a statistical tool to describe the popu- lation and distribution of various types of galaxies inside dark-matter halos. The free parameters of the model are constrained by matching with the ob- served abundance and clustering data of the galax- ies. A key ingredient to compute the two-point correlation function (2PCF) of galaxies in the halo model framework is to compute the 2PCF of dark- matter halos and then take a weighted average. However, the correlation of dark-matter halos cal- culated from the simplest flavour of halo model suf- fers from several issues, like scale-dependent bias, halo-exclusion, etc., which are difficult to be mod- elled in a purely analytical framework. So an accu- rate technique would be to measure the 2PCF of ha- los directly from N-body simulations and then use the halo model framework to model the clustering of galaxies. To accurately model the galaxies of a range of luminosity, colour and HI mass, one needs to resolve halos of small masses as well as needs to have a sufficient number of high mass halos to model the large-scale clustering properly. For this, one typically needs a simulation of very large box size ( ∼ 1 Gpc) with huge number of particles ( ∼ 30 billion) resulting in a huge computational budget. The situation becomes worse as one needs several realizations of those simulations to reduce the error in the estimation of the correlation function of the dark matter halos. To overcome this difficulty, Niladri Paul , Isha Pahwa , and Aseem Paranjape came up with a novel approach of combining simulations of three different box sizes. They used simulations per- formed by Paranjape and Pahwa with a single realization of 150 Mpc box, 10 realizations of 300 Mpc boxes and 3 realizations of 600 Mpc boxes each with 1 billion particles. In this way, effectively they could resolve halos of small masses and also get a substantial number of high mass halos. They mea- sured the halo mass function, halo density profile and two-point correlation function of halos directly from all the simulation boxes as a function of halo mass. They combined these measurements weighted by the available number of dark matter particles in each of the measurements in each halo mass bin. Error from the simulation measurements was ∼ 3%, much less compared to that from the error in the observations. They introduced a global constraint of the HOD parameters combining all the available luminosity bins to account for the possible correla- tion between the HOD parameters across different luminosity thresholds, and also imposed the infor- mation of colour-dependent clustering in the anal- ysis, which improved the constraints on the HOD parameters. While doing this, they also modelled the red fraction of satellite galaxies as a function of luminosity, and the calibration of this quantity is free from the assumptions of galaxy group cat- alogues. Their calibrations were accurate enough to describe the correlation and abundance data to- gether within a good precision level. They could provide robust fitting formulae for the HOD param- eters as a function of magnitude thresholds, and ( 57 )