The present work analyzes the various conditions in which there can be a bouncing universe solution in f (R) gravity. In the article an interesting method, to analyze the bouncing FRW solutions in a spatially flat universe using f (R) gravity models using an effective Einstein frame description of the process, is presented. The analysis shows that a cosmological bounce in the f (R) theory need not be described by an equivalent bounce in the Einstein frame description of the process where actually there may be no bounce at all. Nevertheless the Einstein frame description of the bouncing phenomena turns out to be immensely important as the dynamics of the bounce becomes amenable to logic based on general relativistic intuition. The theory of scalar cosmological perturbations in the bouncing universe models in f (R) theories has also been worked out in the Einstein frame.

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In the present work, we have adopted a kinematic approach for constraining the extended null diagnostic of concordance cosmology, known as the statefinder hierarchy. A Taylor series expansion of the Hubble parameter has been utilised for the reconstruction. The coefficients of the Taylor series expansion are related to the kinematical parameters like the deceleration parameter, cosmological jerk parameter etc. The present values of the kinematical parameters are constrained from the estimated values of those series coefficients. A Markov chain Monte Carlo analysis has been carried out using the observational measurements of Hubble parameter at different redshifts, the distance modulus data of type Ia supernovae and baryon acoustic oscillation data to estimate the coefficient of series expansion of the Hubble parameter. The parameters in the statefinder diagnostic are related to the kinematical parameters. The statefinder diagnostic can form sets of hierarchy according to the order of the kinematical parameters. The present values of statefinder parameters have been constrained. The first set in the statefinder hierarchy allows ΛCDM to be well within the 1-σ confidence region, whereas the second set is in disagreement with the corresponding ΛCDM values at more than 1-σ level. Another dark energy diagnostic, namely the Om-parameters, is found to be consistent with concordance cosmology. 1

We present a Halo Occupation Distribution (HOD) analysis of the luminosity-and colour-dependent galaxy clustering in the Sloan Digital Sky Survey. A novelty of our technique is that it uses a combination of clustering measurements in luminosity bins to perform a global likelihood analysis, simultaneously constraining the HOD parameters for a range of luminosity thresholds. We present simple, smooth fitting functions which accurately describe the resulting luminosity dependence of the best-fit HOD parameters. To minimise systematic halo modelling effects, we use theoretical halo 2-point correlation functions directly measured and tabulated from a suite of N -body simulations spanning a large enough dynamic range in halo mass and spatial separation. Thus, our modelling correctly accounts for non-linear and scale-dependent halo bias as well as any departure of halo profiles from universality, and we additionally account for halo exclusion using the hard sphere approximation. Using colour-dependent clustering information, we constrain the satellite galaxy red fraction in a model-independent manner which does not rely on any group-finding algorithm. We find that the resulting luminosity dependence of the satellite red fraction is significantly shallower than corresponding measurements from galaxy group catalogues, and we provide a simple fitting function to describe this dependence. Our fitting functions are readily usable in generating low-redshift mock galaxy catalogues, and we discuss some potentially interesting applications as well as possible extensions of our technique.

We use the Halo Model to explore the implications of assuming that galaxy luminosities in groups are randomly drawn from an underlying luminosity function. We show that even the simplest of such order statistics models -one in which this luminosity function p(L) is universal -naturally produces a number of features associated with previous analyses based on the 'central plus Poisson satellites' hypothesis. These include the monotonic relation of mean central luminosity with halo mass, the Lognormal distribution around this mean, and the tight relation between the central and satellite mass scales. In stark contrast to observations of galaxy clustering, however, this model predicts no luminosity dependence of large scale clustering. We then show that an extended version of this model, based on the order statistics of a halo mass dependent luminosity function p(L|m), is in much better agreement with the clustering data as well as satellite luminosities, but systematically under-predicts central luminosities. This brings into focus the idea that central galaxies constitute a distinct population that is affected by different physical processes than are the satellites. We model this physical difference as a statistical brightening of the central luminosities, over and above the order statistics prediction. The magnitude gap between the brightest and second brightest group galaxy is predicted as a by-product, and is also in good agreement with observations. We propose that this order statistics framework provides a useful language in which to compare the Halo Model for galaxies with more physically motivated galaxy formation models.