28,369 research outputs found

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

To determine the equation of state of the universe, we propose to use a new
independent variable $R\equiv (H_0/c)(d_L(z)/(1+z))$, where $H_0$ and $d_L(z)$
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
$\rho/\rho_0=4(df/dR)^2/f^6$ and $p/\rho_0=-4/3(d^2f/dR^2)/f^5$ where $\rho_0$
is the present density and $f(R)=1/\sqrt{1+z(R)}$. In $(R, f)$ 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
$f(R)=1/\sqrt{u}$ with $u\equiv 1+\sum\limits_{n=1}^{N}u_nR^n$. For flat
$\Lambda$ model the expansion up to N=7 has at most an error $< 0.2%$ for $z <
1.7$ and any value of $\Lambda$. We also propose a general method to determine
the equation of state of the universe which 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.Comment: 12 pages, to be published in the Astrophysical Journa

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

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
$\Omega_{k0} ={k}/(a_0^2H_0^2)$, where $a_0$ and $H_0$ 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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