28,369 research outputs found

    Determining the Equation of State of the Expanding Universe Using a New Independent Variable

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    To determine the equation of state of the universe, we propose to use a new independent variable R≑(H0/c)(dL(z)/(1+z))R\equiv (H_0/c)(d_L(z)/(1+z)), where H0H_0 and dL(z)d_L(z) are the present Hubble parameter and the luminosity distance, respectively. For the flat universe suggested from the observation of the anisotropy of cosmic microwave background, the density and the pressure are expressed as ρ/ρ0=4(df/dR)2/f6\rho/\rho_0=4(df/dR)^2/f^6 and p/ρ0=βˆ’4/3(d2f/dR2)/f5p/\rho_0=-4/3(d^2f/dR^2)/f^5 where ρ0\rho_0 is the present density and f(R)=1/1+z(R)f(R)=1/\sqrt{1+z(R)}. In (R,f)(R, f) plane the sign as well as the strength of the pressure is in proportion to the curvature of the curve f(R)f(R). We propose to adopt a Pade-like expression of f(R)=1/uf(R)=1/\sqrt{u} with u≑1+βˆ‘n=1NunRnu\equiv 1+\sum\limits_{n=1}^{N}u_nR^n. For flat Ξ›\Lambda model the expansion up to N=7 has at most an error <0.2< 0.2% for z<1.7z < 1.7 and any value of Ξ›\Lambda. We also propose a general method to determine the equation of state of the universe which has Nβˆ’1N-1 free parameters. If the number of parameters are smaller than Nβˆ’1N-1, there is a consistency check of the equation of state so that we may confirm or refute each model.Comment: 12 pages, to be published in the Astrophysical Journa

    Determining the Equation of State of the Expanding Universe: Inverse Problem in Cosmology

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    Even if the luminosity distance as a function of redshift is obtained accurately using, for example, Type Ia supernovae, the equation of state of the Universe cannot be determined uniquely but depends on one free parameter Ξ©k0=k/(a02H02)\Omega_{k0} ={k}/(a_0^2H_0^2), where a0a_0 and H0H_0 are the present scale factor and the Hubble parameter, respectively. This degeneracy might be resolved if, for example, the time variations of the redshift of quasars are measured as proposed recently by Loeb. Therefore the equation of state of the Universe (or the metric of the universe) might be determined without any theoretical assumption on the matter content of the Universe in future.Comment: 5 pages, accepted for publication in MNRA
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