Some solutions of the Einstein field equations for a dust source are given in explicit form. They are spatially homogeneous, irrotational, and anisotropic. They can be characterized as those spatially homogeneous expanding models that do not permit a simply transitive three-parameter group of motions. The models are compared in detail with observations and with the Friedmann models. In a few instances slightly longer time scales are obtained with the present models than from the corresponding Friedmann models.
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 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.Subject headings: cosmology: theory -large-scale structure of universe
Analytic expressions for distance-redshift relations which have been corrected for the effects of some inhomogeneities in the Friedmann-Robertson-Walker (FRW) mass density are used to illustrate the significance of inhomogeneities on a determination of q 0 made by using Type Ia supernovae. The value of q 0 inferred from a given set of observations depends on the fractional amount of matter in inhomogeneities and is up to 50 percent larger than that obtained by using the standard Mattig m-z result for pure dust FRW models.Subject headings: cosmology: theory -large-scale structure of universe
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.