## An approximate solution for luminosity distance in zero-pressure relativistic model universes that have the U-property |

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absolute magnitude acceleration parameter analysis of observational apparent magnitude Approximate expressions approximate solution CD is given CD that depends closed-form expressions cosh count-magnitude relation curvature constant curve for a0 density parameter difference distance is obtained equa Equation 12 equation 7a evolutionary correction exact and approximate exact solution finite-density model finite-density zero-pressure model form of equation function of CD galaxies brighter given by equation higher values Hubble parameter km/sec/Mpc Langley Research Center Langley Station log1Q luminosity distance magnitude and redshift Mattig metric subspace model universe ref nonzero cosmical constant number of galaxies number of square observational data Observed Universe obtained by substituting parameter from apparent parsecs radial metric variable redshift data redshift-magnitude relation RELATIVISTIC MODEL UNIVERSES Robertson-Walker metric S(cd scale factor Sherman Langley Research simple closed-form solutions sinh sis of observational speed of light tion U-PROPERTY By Windsor universe that possess zero cosmical constant zero-density models zero-pressure model universes