Distance‐Redshift Relations in Inhomogeneous Friedmann‐Lemaitre‐Robertson‐Walker Cosmology

We give distance-redshift relations in terms of elliptic integrals for three different mass distributions of the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology. These models are dynamically pressure-free FLRW cosmology on large scales but, due to mass inhomogeneities, differ in their optical properties. They are the filled-beam model (standard FLRW), the empty-beam model (no mass density exists in the observing beams), and the 2/3 filled-beam model. For special Ω m -Ω Λ values, the elliptic integrals reduce to more familiar functions. These new expressions for distance-redshift significantly reduce computer evaluation times.