%0 Journal Article %T Cosmic Time Transformations in Cosmological Relativity %A Firmin J. Oliveira %J Journal of High Energy Physics, Gravitation and Cosmology %P 253-279 %@ 2380-4335 %D 2016 %I Scientific Research Publishing %R 10.4236/jhepgc.2016.22022 %X The relativity of cosmic time is developed within the framework of Cosmological Relativity in five dimensions of space, time and velocity. A general linearized metric element is defined to have the form $\"\"$ , where the coordinates are time $\"\"$ , radial distance $\"\"$ for spatials x, y and z, and velocity v, with c the speed of light in vacuum and t the Hubble-Carmeli time constant. The metric is accurate to first order in $\"\"$ and v/c . The fields $\"\"$ and $\"\"$ are general functions of the coordinates. By showing that $\"\"$ = $\"\"$ , a metric of the form $\"\"$ is obtained from the general metric, implying that the universe is flat. For cosmological redshift z, the luminosity distance relation $\"\"$ is used to fit combined distance moduli from Type 1a supernovae up to z<1.5 and Gamma-Ray Bursts up to z<7, from which a value of $\"\"$ is obtained for the matter density parameter at the present epoch. Assuming a baryon density of $\"\"$ , a rest mass energy of (9.79+ 0.47) GeV is predicted for the anti-baryonic $\"\"$ and $\"\"$ the particles which decay from a hypothetical