A general framework for an emergent universe scenario has been given which makes use of an equation of state. The general features of the model have also been studied and possible primordial composition of the universe have been suggested.

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In a spherically symmetric spacetime we find the general solution for a relativistic star in hydrostatic equilibrium having the spheroidal geometry for the 3-space embedded in 4-Euclidean space. The parameter is the measure of spheroidal character and determines the physical properties of the star. It has a lower bound ; stars with smaller mass to radius ratio can occur for all allowed while ultracompact stars, having ratios between 1/3 and 1/2, will have . It turns out that a wide range of values of can represent objects with the fluid density of a neutron star. The model is shown to possess all the desirable physical features.

The LOFT mission concept is one of four candidates selected by ESA for the M3 launch opportunity as Medium Size missions of the Cosmic Vision programme. The launch window is currently planned for between 2022 and 2024. LOFT is designed to exploit the diagnostics of rapid X-ray flux and spectral variability that directly probe the motion of matter down to distances very close to black holes and neutron stars, as well as the physical state of ultradense matter. These primary science goals will be addressed by a payload composed of a Large Area Detector (LAD) and a Wide Field Monitor (WFM). The LAD is a collimated (<1 degree field of view) experiment operating in the energy range 2-50 keV, with a 10 m2 peak effective area and an energy resolution of 260 eV at 6 keV. The WFM will operate in the same energy range as the LAD, enabling simultaneous monitoring of a few-steradian wide field of view, with an angular resolution of <5 arcmin. The LAD and WFM experiments will allow us to investigate variability from submillisecond QPO's to yearlong transient outbursts. In this paper we report the current status of the project

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 involves three parameters: B, A and α. The permitted values of these parameters are determined with the help of a dimensionless age parameter (H0t0) and H(z) −z data. Specifically, we study the allowed ranges of values of the B parameter in terms of α and As (As is defined in terms of the parameters in the theory). We explore the constraints of the parameters in the cold dark matter and unified dark matter energy models, respectively.

We obtain cosmological solutions which admit emergent universe (EU) scenario in the framework of Einstein Gauss-Bonnet gravity coupled with a dilaton field in four dimensions. The coupling parameter of the Gauss-Bonnet terms and the dilaton in the theory are determined for obtaining an EU scenario. The corresponding dilaton potential which admits such scenario is determined. It is found that the GaussBonnet (GB) terms coupled with a dilaton field plays an important role in describing the dynamics of the evolution of the early as well as the late universe. We note an interesting case where the GB term dominates initially in the asymptotic past regime, subsequently it decreases and thereafter its contribution in determining the dynamics of the evolution dominates once again. We note that the Einsteins static universe solution permitted here is unstable which the asymptotic EU might follow. We also compare our EU model with supernova data. * bcpaul@iucaa.ernet.in †

We present a class of new relativistic solutions with anisotropic fluid for compact stars in hydrostatic equilibrium. The interior space-time geometry considered here for compact objects are described by parameters namely, λ, k, A, R and n. The values of the geometrical parameters are determined here for obtaining a class of physically viable stellar models. The energy-density, radial pressure and tangential pressure are finite and positive inside the anisotropic stars. Considering some stars of known mass we present stellar models which describe compact astrophysical objects with nuclear density.

A specific class of flat Emergent Universe (EU) is considered and its viability is tested in view of the recent observations. Model parameters are constrained from Stern data for Hubble parameter and redshift [H(z) versus z] and from a model-independent measurement of BAO peak parameter. It is noted that a composition of exotic matter, dust and dark energy, capable of producing an EU, cannot be ruled out with present data. Evolution of other relevant cosmological parameters, viz. density parameter ( ) and effective equation of state (EOS) parameter (ω eff ), are also shown.