A Kinematical Approach to Conformal Cosmology

TL;DR

This paper proposes a purely kinematic conformal gravity cosmology that reinterprets fundamental observations, deriving a closed-form scale factor without dark matter or dark energy, offering an alternative to standard cosmology.

Contribution

It introduces a novel kinematic conformal cosmology with a closed-form scale factor and new parameters, avoiding dark matter, dark energy, and inflationary issues present in standard models.

Findings

Derives a closed-form expression for the cosmic scale factor R(t)

Reinterprets cosmological observations without dark matter or dark energy

Establishes connections with classical kinematic cosmology

Abstract

We present an alternative cosmology based on conformal gravity, as originally introduced by H. Weyl and recently revisited by P. Mannheim and D. Kazanas. Unlike past similar attempts our approach is a purely kinematical application of the conformal symmetry to the Universe, through a critical reanalysis of fundamental astrophysical observations, such as the cosmological redshift and others. As a result of this novel approach we obtain a closed-form expression for the cosmic scale factor R(t) and a revised interpretation of the space-time coordinates usually employed in cosmology. New fundamental cosmological parameters are introduced and evaluated. This emerging new cosmology does not seem to possess any of the controversial features of the current standard model, such as the presence of dark matter, dark energy or of a cosmological constant, the existence of the horizon problem or of an inflationary phase. Comparing our results with current conformal cosmologies in the literature, we note that our kinematic cosmology is equivalent to conformal gravity with a cosmological constant at late (or early) cosmological times. The cosmic scale factor and the evolution of the Universe are described in terms of several dimensionless quantities, among which a new cosmological variable delta emerges as a natural cosmic time. The mathematical connections between all these quantities are described in details and a relationship is established with the original kinematic cosmology by L. Infeld and A. Schild. The mathematical foundations of our kinematical conformal cosmology will need to be checked against current astrophysical experimental data, before this new model can become a viable alternative to the standard theory.