The Effects of Inhomogeneities on Evaluating the mass parameter ${\Omega }_m$ and the cosmological constant $\Lambda$

Abstract

Analytic expressions for distance-redshift relations which have been corrected for the effects of inhomogeneities in the Friedmann-Lemaître-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.

39 pages including 8 figures and captions. To appear in ApJ 507 (Nov. 1998)

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