Abstract:
We present Cosmological models with modified Chaplygin gas (MCG) in the framework of Horava-Lifshitz (HL) theory of gravity both with and without detailed balance. The equation of state (EOS) for a MCG contains three unknown parameters namely, $A$, $\alpha$, $B$. The allowed values of some of these parameters of the EOS are determined using the recent astrophysical and cosmological observational data. Using observational data from $H(z)-z$, BAO peak parameter, CMB shift parameter we study cosmologies in detailed-balance and beyond detailed-balance scenario. In this paper we take up the beyond detailed-balance scenario in totality and contribution of dark radiation in the case of detailed-balance scenario on the parameters of the EOS. We explore the effect of dark radiation on the whole range the of effective neutrino parameter to constrain matter contributing parameter $B$ in both the detailed-balance and the beyond-detailed balance scenario. It has been observed that greater the dark radiation less the matter contribution in the MCG in both the scenario considered here. In order to check the validity of beyond detailed balance scenario we plot supernovae magnitudes ($\mu$) with redshift of Union2 data and then the variation of state parameter with redshift is studied. It has been observed that beyond detailed balance scenario is equally suitable in HL gravity with MCG.

Abstract:
We investigate the linear growth function for the large scale structures of the universe considering modified Chaplygin gas as dark energy. Taking into account observational growth data for a given range of redshift from the Wiggle-Z measurements and rms mass fluctuations from Ly-$\alpha$ measurements we numerically analyze cosmological models to constrain the parameters of the MCG. The observational data of Hubble parameter with redshift ($Z$) is also considered. The Wang-Steinhardt ansatz for growth index $\gamma$ and growth function $f$ (defined as $f=\Omega_{m}^{\gamma} (a)$) are considered for the numerical analysis. The best-fit values of the equation of state parameters obtained here is employed to study the growth function $(f)$, growth index ($\gamma$) and state parameter ($\omega$) with redshift $z$. We note that MCG satisfactorily accommodates an accelerating phase followed by a matter dominated universe.

Abstract:
We investigate emergent universe model using recent observational data for the background tests as well as for the growth tests. The background test data comprises of Hubble data, Baryon Acoustic Oscillation (BAO) data, cosmic microwave background (CMB) shift data, Union compilation data. The observational growth data are obtained from Wiggle-Z measurements and rms mass fluctuations data from Lyman-$\alpha$ measurements at different red shifts. The flat emergent universe model obtained by Mukherjee {\it et. al.} is permitted with a non-linear equation of state (in short, EoS) ($p=A\rho-B\rho^{\frac{1}{2}}$), where $A$ and $B$ are constants. The observed cosmological data are used here to estimate the range of allowed values of EoS parameters numerically. The best-fit values of the EoS and growth parameters are determined making use of chi-square minimization technique. The analysis is carried out here considering the Wang-Steinhardt ansatz for growth index ($\gamma$) and growth function ($f$ defined as $f=\Omega_{m}^{\gamma} (a)$). Subsequently, the best-fit values of the EoS parameters are used to study the evolution of the growth function $f$, growth index $\gamma$, state parameter $\omega$ with red shift parameter $z$. The present value of the parameters, namely, $f$, $\gamma$, $\omega$, $\Omega_{m}$ are also estimated. The late accelerating phase of the universe in the model is accommodated satisfactorily.

Abstract:
Synovial tissue may be obtained either at surgery, by blind needle biopsy, or at arthroscopy. It is likely that tissue obtained at joint replacement differs from that obtained by blind-needle biopsy or arthroscopy because of clear differences in patient selection. Obviously, surgery is inappropriate for studies on early rheumatoid arthritis (RA) or for serial investigations. The blind-needle biopsy technique is safe, well tolerated and is technically easy to perform. A limitation of this method is that its use in clinical practice is often restricted to the suprapatellar pouch of the knee joint. In addition, it is more difficult to obtain sufficient tissue from clinically uninvolved joints, for example after successful treatment. Arthroscopic sampling of synovial tissue under direct vision is a similarly safe and well tolerated procedure, but is more complicated and expensive [3,6,7]. Most measures of inflammation in needle biopsies are similar to those selected at arthroscopy [4]. An advantage of arthroscopy is that it is always possible to obtain tissue in adequate amounts, even in clinically quiescent joints. Moreover, arthroscopy allows access to most joints and to most regions within the joint, including the pannus-cartilage junction.There is large variability of synovial inflammation between individuals, different joints, and even within joints [2]. The degree of morphologic heterogeneity in synovial tissue samples obtained from a single joint could suggest that evaluation of synovial tissue is unreliable because of unavoidable sampling error. Several studies [8,9,10], however, have shown that, despite the degree of histologic variation, representative measures of several parameters of synovial inflammation may be obtained by examining a limited number of samples. For example, quantification of T-cell infiltration and activation in sections derived from at least six different biopsy specimens results in variance of less than 10% [10]. It is generally not neces

Abstract:
We study Modified Chaplygin Gas (MCG) as a candidate for dark energy and predict the values of parameters of the gas for a physically viable cosmological model. The equation of state of MCG ($p=B \rho - \frac {A}{\rho^\alpha} $) involves three parameters: $B$, $A$ and $\alpha$. The permitted values of these parameters are determined with the help of dimensionless age parameter ($H_{o}t_{o}$) and $H(z)-z$ Data. Specifically we study the allowed ranges of values of B parameter in terms of $\alpha$ and $A_{s}$ ($A_{s}$ is defined in terms of the constants in the theory). We explore the constraints of the parameters in Cold Dark Matter(CDM) model and UDME(Unified Dark Matter Energy) model respectively.

Abstract:
We study a composition of normal and exotic matter which is required for a flat Emergent Universe scenario permitted by the equation of state (EOS)($p=A\rho-B\rho^{1/2}$) and predict the range of the permissible values for the parameters $A$ and $B$ to explore a physically viable cosmological model. The permitted values of the parameters are determined taking into account the $H(z)-z$ data obtained from observations, a model independent BAO peak parameter and CMB shift parameter (WMAP7 data). It is found that although $A$ can be very close to zero, most of the observations favours a small and negative $A$. As a consequence, the effective Equation of State parameter for this class of Emergent Universe solutions remains negative always. We also compared the magnitude ($\mu (z)$) vs. redshift($z$) curve obtained in the model with that obtained from the union compilation data. According to our analysis the class of Emergent Universe solutions considered here is not ruled out by the observations.

Abstract:
We present a holographic dark energy model of the universe considering modified generalized Chaplygin gas (GCG). The modified GCG behaves as an ordinary barotropic fluid in the early epoch when the universe was tiny but behaves subsequently as a $\Lambda$CDM model at late epoch. An equivalent model with scalar field is obtained here by constructing the corresponding potential. The holographic dark energy is identified with the modified GCG and we determine the corresponding holographic dark energy field and its potential. The stability of the holographic dark energy in this case is also discussed.

Abstract:
We consider the evolution of a flat Friedmann-Roberstson-Walker Universe in a higher derivative theories, including $\alpha R^{2}$ terms to the Einstein-Hilbert action in the presence of a variable gravitational and cosmological constants. We study here the evolution of the gravitational and cosmological constants in the presence of radiation and matter domination era of the universe. We present here new cosmological solutions which are physically interesting for model building.

Abstract:
A class of Emergent Universe (EU) model is studied in the light of recent observational data. Significant constraints on model parameters are obtained from the observational data. Density parameter for a class of model is evaluated. Some of the models are in favour of the recent observations. Some models have been found which are not interesting yielding unrealistic present day value of the density parameter.

Abstract:
We study evolution of a flat Friedmann-Robertson Walker universe filled with a bulk viscous cosmological fluid in a higher derivative theory of gravity in the presence of time varying gravitational and cosmological constant. Cosmological models admitting both power-law and exponential expansions are explored here in the presence of imperfect fluid described by full Israel and Stewart theory. We note some new and interesting cosmological solutions relevant for model building including present accelerating phase. In the case of power law, it is found that gravitational constant increases as the time evolves for a positive cosmological constant whereas it decreases for a negative cosmological constant. The evolution of temperature of a viscous universe is also determined.