Takashi Nakamura and Takeshi Chiba 2001 ApJ 550 1 doi:10.1086/319739
Determining the Equation of State of the Expanding Universe Using a New Independent Variable
FREETakashi Nakamura1 and Takeshi Chiba2
Show affiliationsTo determine the equation of state of the universe, we propose to use a new independent variable R ≡ (H0/c) 
, where H0 and dL(z) are the present Hubble parameter and the luminosity distance, respectively. For the flat universe suggested by the observation of the anisotropy of cosmic microwave backgrounds, the density and the pressure are expressed as ρ/ρ0 = 4(df/dR)2/f6 and p/ρ0 = -4/3(d2f/dR2)/f5, where ρ0 is the present density and f(R) = 1/ 
1/2. In the (R, f) plane the sign as well as the strength of the pressure is in proportion to the curvature of the curve f(R). We propose to adopt a Pade-like expression of f(R) = 1/u1/2 with u ≡ 1 + 
unRn. For the flat Λ models, the expansion up to N = 7 has at most an error less than 0.2% for z < 1.7 and any value of Λ. We also propose a general method to determine the equation of state of the universe that has N - 1 free parameters. If the number of parameters are smaller than N - 1, there is a consistency check of the equation of state so that we may confirm or refute each model.
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- Dates
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Issue 1 (2001 March 20)
Received 2000 October 1, accepted for publication 2000 November 9
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Determining the Equation of State of the Expanding Universe Using a New Independent Variable
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