• B C Paul

      Articles written in Pramana – Journal of Physics

    • Relativistic star solutions in higher-dimensional pseudospheroidal space-time

      P K Chattopadhyay B C Paul

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      We obtain relativistic solutions of a class of compact stars in hydrostatic equilibrium in higher dimensions by assuming a pseudospheroidal geometry for the space-time. The space-time geometry is assumed to be ($D - 1$) pseudospheroid immersed in a 𝐷-dimensional Euclidean space. The spheroidicity parameter (𝜆) plays an important role in determining the equation of state of the matter content and the maximum radius of such stars. It is found that the core density of compact objects is approximately proportional to the square of the space-time dimensions (𝐷), i.e., core of the star is denser in higher dimensions than that in conventional four dimensions. The central density of a compact star is also found to depend on the parameter 𝜆. One obtains a physically interesting solution satisfying the acoustic condition when 𝜆 lies in the range $\lambda$ > $(D + 1)/(D − 3)$ for the space-time dimensions ranging from $D = 4$ to 8 and $(D + 1)/(D − 3)$ < $\lambda$ < ($D^{2} - 4D + 3$)/($D^{2} - 8D - 1$) for space-time dimensions $\geq 9$. The non-negativity of the energy density (𝜌) constrains the parameter with a lower limit (> 1). We note that in the case of a superdense compact object the number of space-time dimensions cannot be taken infinitely large, which is a different result from the braneworld model.

    • Observational constraints on modified Chaplygin gas in Horava–Lifshitz gravity with dark radiation

      B C Paul P Thakur M M Verma

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      Cosmological models with modified Chaplygin gas (MCG) in the framework of Horava–Lifshitz (HL) theory of gravity, both with and without detailed balance, are obtained. 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 $H(z)-z$, baryon acoustic oscillation (BAO) peak parameter and cosmic microwave background (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 detailedbalance scenario on the parameters of the EOS. We explore the effect of dark radiation on the whole range of the effective neutrino parameter ($\Delta N_{\nu}$) to constrain matter contributing parameter $B$ in both the detailed-balance and the beyond detailed-balance scenarios. 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 red-shift of Union2 data and then the variation of state parameter with redshift is studied. It is noted that beyond detailed-balance scenario is suitable for cosmological model in HL gravity with MCG.

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