Cosmic Time Transformations in Cosmological Relativity

TL;DR

This paper develops a five-dimensional cosmological relativity framework to analyze cosmic time, redshift, and universe flatness, fitting supernova and gamma-ray burst data, and predicting particle masses and CMB features.

Contribution

It introduces a new five-dimensional metric in cosmological relativity, deriving flat universe conditions and fitting observational data to determine cosmological parameters and particle mass predictions.

Findings

Universe is flat with $oxed{ ext{flat}}$ metric derived from the model.

Matter density parameter $oxed{oxed{0.8 ext{ with uncertainty}}}$ obtained from supernova and gamma-ray burst data.

Predicted rest mass energy of particles around 9.79 GeV, consistent with hypothetical particles.

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 $ds^2 = (1+\phi) c^2 dt^2 - dr^2 + (1+\psi) \tau^2 dv^2$, 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 $\phi$ and $\psi$ are general functions of the coordinates. By showing that $\phi = \psi$, a metric of the form $ds^2 = c^2 dt^2 - dr^2 + \tau^2 dv^2$ 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 $( 9.79 \pm 0.47 ) \, {\rm GeV}$ is predicted for the anti-baryonic $\bar{Y}$ and the $\Phi^{*}$ 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.