The Effects of Inhomogeneities on Evaluating the Mass Parameter Ωmand the Cosmological Constant Λ

Analytic expressions for distance-redshift relations that 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 Ω m and the cosmological constant Λ. 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 Ω 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.