Expanding Universe and its manifestations beyond the General Relativity

TL;DR

This paper explores how the universe's expansion can be described using conformal geometry, revealing a local acceleration linked to the Hubble constant and providing new insights into cosmological observations like red-shift and the Pioneer anomaly.

Contribution

It introduces a conformal geometric framework for describing universe expansion, generalizes clock synchronization in special relativity, and derives explicit formulas for cosmological phenomena.

Findings

Universal local manifestation of expansion as background acceleration

Explicit red-shift dependence derived from conformal transformations

Quantitative explanation of Pioneer anomaly and accelerated expansion

Abstract

It has been demonstrated that a modern stage of the Universe expansion may be described in accordance with the observations within the scope of the space-time conformal geometry. The clock synchronization procedure in SR has been generalized to the case of the expanding space. It has been found that a universal local manifestation of the cosmological expansion is a background acceleration, the value of which is determined by Hubble constant. The formulae defining an explicit red-shift dependence of the cosmological distance and expressions for Hubble law have been obtained in a pure kinematic way from the conformal group transformation, providing a quantitative representation of the Pioneer anomaly and of the effect associated with the experimentally revealed Metagalaxy transition to its accelerated expansion