Aspects of cosmological relativity

In this paper we review cosmological relativity, a new special theory of relativity that was recently developed for cosmology, and discuss in detail some of its aspects. We recall that in this theory it is assumed that gravitation is negligible. Under this assumption, the receding velocities of galaxies and the distances between them in the Hubble expansion are united into a four-dimensional pseudo-Euclidean manifold, similarly to space and time in ordinary special relativity. The Hubble law is assumed and is written in an invariant way that enables one to derive a four-dimensional transformation which is similar to the Lorentz transformation. The parameter in the new transformation is the ratio between the cosmic time to the Hubble time (in which the cosmic time is measured backward with respect to the present time). Accordingly, the new transformation relates physical quantities at different cosmic times in the limit of weak or negligible gravitation. The transformation is then applied to the problem of the expansion of the universe at the very early stage when gravity was negligible and thus the transformation is applicable. We calculate the ratio of the volumes of the universe at two different times T₁ and T₂ after the big bang. Under the assumptions that T₂ - T₁ ≈ 10^-32 sec and T₂ ≪ 1 sec, we find that V₂/V₁ = 10^-16/√T₁. For T₁ ≈ 10^-132 sec we obtain V₂/V₁ ≈ 10⁵⁰. This result conforms with the standard inflationary universe theory, but now it is obtained without assuming that the universe is propelled by antigravity. New applications of the theory are presented. This includes a new law for the decay of radioactive materials that was recently developed by Carmeli and Malin. The new law is a modification of the standard exponential formula when cosmic times are considered instead of the ordinary local times. We also show that there is no need to assume the existence of galaxy dark matter; the Tully-Fisher law is derived from our theory. A significant extension of the theory to cosmology that was recently made by Krori, Pathak, Das, and Purkayastha is given. In this way cosmological relativity becomes a general theory of relativity in seven dimensions of curved space-time-velocity. The solutions of the field equations in seven dimensions obtained by Krori et al. are given and compared to those of the standard Friedmann-Robertson-Walker result. A completely new picture of the expanding universe is thus obtained and compared to the FRW one.