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A Kinematical Approach to Conformal Cosmology
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.Comment: Improved version, with minor changes. 58 pages, including 7 figures
and one table. Accepted for publication in General Relativity and Gravitation
(GERG