Cosmic Time Transformations in Cosmological Relativity

Abstract

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 $d{s}^2=(1+\varphi )c^{2}d{t}^2-d{r}^2+(1+\psi ){\tau }^{2}d{v}^2$, where the coordinates are time $t$, radial distance $r=\sqrt{x^2+y^2+z^2}$ for spatials $x$, $y$ and $z$, and velocity $v$, with $c$ the speed of light in vacuum and $\tau$ the Hubble-Carmeli time constant. The metric is accurate to first order in $t/\tau$ and $v/c$. The fields $\varphi$ and $\psi$ are general functions of the coordinates. By showing that $\varphi =\psi$, a metric of the form $d{s}^2=c^{2}d{t}^2-d{r}^2+{\tau }^{2}d{v}^2$ is obtained from the general metric, implying that the universe is flat. For cosmological redshift $z$, the luminosity distance relation $D_L(z,t)=r(1+z)/\sqrt{1-t^2/{\tau }^2}$ is used to fit combined distance moduli from Type Ia Supernovae up to $z<1.5$ and Gamma-Ray Bursts up to $z<7$, from which a value of ${\Omega }_M=0.800\pm 0.080$ is obtained for the matter density parameter at the present epoch. Assuming a baryon density of ${\Omega }_B=0.038\pm 0.004$, a rest mass energy of $(9.79\pm 0.47)\mathrm{GeV}$ is predicted for the anti-baryonic $\bar{Y}$ and the ${\Phi }^{\ast }$ particles which decay from a hypothetical ${\bar{X}}_1$ particle. The cosmic aging function $g_1(z,t)=(1+z)(1-t^2/{\tau }^2)$ makes good fits to light curve data from two reports of Type 1a supernovae and in fitting to simulated quasar like light curve power spectra separated by redshift $\Delta z\approx 1$. We determine the multipole of the first acoustic peak of the Cosmic Microwave Background radiation anisotropy to be $l\approx 224\pm 5$ and a sound horizon of ${\theta }_{sh0}\approx (0.805\pm 0.020){}^{\circ }$ on today's sky.

36 pages, 1 table, 13 figures

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Cited by in corpus (2)

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• Sparse formulae for the distance modulus in cosmology