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The generalized second law for the interacting generalized Chaplygin gas model

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 Added by Kayoomars Karami
 Publication date 2011
  fields Physics
and research's language is English




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We investigate the validity of the generalized second law (GSL) of gravitational thermodynamics in a non-flat FRW universe containing the interacting generalized Chaplygin gas with the baryonic matter. The dynamical apparent horizon is assumed to be the boundary of the universe. We show that for the interacting generalized Chaplygin gas as a unified candidate for dark matter (DM) and dark energy (DE), the equation of state parameter can cross the phantom divide. We also present that for the selected model under thermal equilibrium with the Hawking radiation, the GSL is always satisfied throughout the history of the universe for any spatial curvature, independently of the equation of state of the interacting generalized Chaplygin gas model.



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We compare the WMAP temperature power spectrum and SNIa data to models with a generalized Chaplygin gas as dark energy. The generalized Chaplygin gas is a component with an exotic equation of state, p_X=-A/rho^alpha_X (a polytropic gas with negative constant and exponent). Our main result is that, restricting to a flat universe and to adiabatic pressure perturbations for the generalized Chaplygin gas, the constraints at 95% CL to the present equation of state w_X = p_X / rho_X and to the parameter alpha are -1leq w_X < -0.8, 0 leq alpha <0.2, respectively. Moreover, we show that a Chaplygin gas (alpha =1) as a candidate for dark energy is ruled out by our analysis at more than the 99.99% CL. A generalized Chaplygin gas as a unified dark matter candidate (Omega_{CDM}=0) appears much less likely than as a dark energy model, although its chi^2 is only two sigma away from the expected value.
In this paper we consider a cosmological model whose main components are a scalar field and a generalized Chaplygin gas. We obtain an exact solution for a flat arbitrary potential. This solution have the right dust limit when the Chaplygin parameter $Arightarrow 0$. We use the dynamical systems approach in order to describe the cosmological evolution of the mixture for an exponential self-interacting scalar field potential. We study the scalar field with an arbitrary self-interacting potential using the Method of $f$-devisers. Our results are illustrated for the special case of a coshlike potential. We find that usual scalar-field-dominated and scaling solutions cannot be late-time attractors in the presence of the Chaplygin gas (with $alpha>0$). We recover the standard results at the dust limit ($Arightarrow 0$). In particular, for the exponential potential, the late-time attractor is a pure generalized Chaplygin solution mimicking an effective cosmological constant. In the case of arbitrary potentials, the late-time attractors are de Sitter solutions in the form of a cosmological constant, a pure generalized Chaplygin solution or a continuum of solutions, when the scalar field and the Chaplygin gas densities are of the same orders of magnitude. The different situations depend on the parameter choices.
Yes, but only for a parameter value that makes it almost coincide with the standard model. We reconsider the cosmological dynamics of a generalized Chaplygin gas (gCg) which is split into a cold dark matter (CDM) part and a dark energy (DE) component with constant equation of state. This model, which implies a specific interaction between CDM and DE, has a $Lambda$CDM limit and provides the basis for studying deviations from the latter. Including matter and radiation, we use the (modified) CLASS code cite{class} to construct the CMB and matter power spectra in order to search for a gCg-based concordance model that is in agreement with the SNIa data from the JLA sample and with recent Planck data. The results reveal that the gCg parameter $alpha$ is restricted to $|alpha|lesssim 0.05$, i.e., to values very close to the $Lambda$CDM limit $alpha =0$. This excludes, in particular, models in which DE decays linearly with the Hubble rate.
Unified generalized Chaplygin gas models assuming an interaction between dark energy and dark matter fluids have been previously proposed. Following these ideas, we consider a particular relation between dark densities, which allows the possibility of a time varying equation of state for dark energy that crosses the phantom divide at a recent epoch. Moreover, these densities decay during all the evolution of the Universe, avoiding a Big Rip. We find also a scaling solution, i.e. these densities are asymptotically proportional in the future, which contributes to the solution of the coincidence problem.
We investigate observational constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy from the latest observational data: the Union SNe Ia data, the observational Hubble data, the SDSS baryon acoustic peak and the five-year WMAP shift parameter. It is obtained that the best fit values of the GCG model parameters with their confidence level are $A_{s}=0.73^{+0.06}_{-0.06}$ ($1sigma$) $^{+0.09}_{-0.09}$ $(2sigma)$, $alpha=-0.09^{+0.15}_{-0.12}$ ($1sigma$) $^{+0.26}_{-0.19}$ $(2sigma)$. Furthermore in this model, we can see that the evolution of equation of state (EOS) for dark energy is similar to quiessence, and its current best-fit value is $w_{0de}=-0.96$ with the $1sigma$ confidence level $-0.91geq w_{0de}geq-1.00$.
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