Astronomy and Astrophysics – Astrophysics
Scientific paper
1998-02-15
Astronomy and Astrophysics
Astrophysics
39 pages including 8 figures and captions. To appear in ApJ 507 (Nov. 1998)
Scientific paper
10.1086/306355
Analytic expressions for distance-redshift relations which have been corrected for the effects of inhomogeneities in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) mass density are given in terms of Heun functions and are used to illustrate the significance of inhomogeneities on a determination of the mass parameter $\Omega_m$ and the cosmological constant $\Lambda$. The values of these parameters inferred from a given set of observations depend on the fractional amount of matter in inhomogeneities and can significantly differ from those obtained by using the standard magnitude-redshift ($m$-$z$) result for pure dust FLRW models. As an example a determination of $\Omega_m$ made by applying the homogeneous distance-redshift relation to SN 1997ap at $z=0.83$ could be as much as 50% lower than its true value.
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