TITLE:
Single Parameter Model for Cosmic Scale Photon Redshift in a Closed Universe
AUTHORS:
Andre P. Steynberg
KEYWORDS:
Photon Redshift, Cold Dark Matter Model, Single Parameter Model, Cosmic Background Radiation
JOURNAL NAME:
Open Journal of Modelling and Simulation,
Vol.9 No.4,
October
21,
2021
ABSTRACT: A successful single parameter model has been formulated to match the observations of photons
from type 1a supernovae which were previously used to corroborate the standard ?? cold dark matter model. The new single parameter
model extrapolates all the way back to the cosmic background radiation (CMB)
without requiring a separate model to describe inflation of the space
dimensions after the Big Bang. This single parameter model assumes that
spacetime forms a finite symmetrical manifold with positive curvature. For the
spacetime manifold to be finite, the time dimension must also have positive
curvature. This model was formulated to consider whether the curvature of the
time dimension may be related to the curvature of the space dimensions. This
possibility is not considered in the more complex models previously used to fit
the available redshift data. The geometry for the finite spacetime manifold was
selected to be compatible with the Friedmann equation with positive curvature.
The manifold shape was motivated by an assumption that there exists a matter
hemisphere (when considering time together with a single space dimension) and
an antimatter hemisphere to give a symmetrical and spherical overall spacetime
manifold. Hence, the space dimension expands from a pole to the equator, at a
maximum value for the time dimension. This is analogous to the expansion of a
circle of latitude on a globe from a pole to the equator. The three space
dimensions are identical so that any arbitrary single space direction may be
selected. The initial intention was to modify the assumed geometry for the
spacetime manifold to account for the presence of matter. It was surprisingly
found that, within the error of the reported measurements, no further
modification was necessary to fit the data. The Friedmann equation reduces to
the Schwarzschild equation at the equator so this can be used to predict the
total amount of mass in the Universe. The resulting prediction is of the order
of 1051 kg. The corresponding density of matter at the current time
is approximately 1.6 × 10-28 kg·m-3.