The
Proposed Model
Perhaps,
the simplest shape of space-time one can think of is the 4-ball in which the
radius represents the cosmological time and the hypersurface (3-sphere) represents our 3-space ( x, y, z )
This attractive shape is not far from the imagination of physicists
but it is excluded for two reasons:
1) It seems to
contradict the results of the global application of Einstein’s field
equation because according to this model the global geometry of the
universe depends only on the age of the universe and has nothing to do with the
average density of the universe as (supposed to be) implied by the field
equation.
2) It
contradicts the acceleration of the expansion of the universe which is (supposed
to be) supported by the observational data about red-shifts because a model of
a spherical space with radial time implies a steady expansion of the universe.
Instead of hurriedly excluding this shape of space-time our
proposed cosmological model tries to overcome these difficulties.
We can overcome the first difficulty easily by adopting a
good definition for the cosmological constant which eliminates the dependence
of the global geometry of the universe on its average density and relates it
directly to the age of the universe. The cosmological constant which satisfies
these requirements is the quantity that composed of two parts: the geometrical
part which is the curvature of the universe determined by the age of the
universe and the material part which is the average density of the universe
.This proposed definition of the cosmological constant will not only enable us
to use the simple model of radial time and spherical space but will also solve all
the problems of modern cosmology which are generated from the dependence of the
global geometry of the universe on its density like the Cosmological Constant
Problem without hypothetical concepts (dark energy, inflation, multi-verse,
extra dimensions … etc.).
This
will not affect the successful local application of the field equation because
of the small value of the average density compared to the density of the source
of the gravitation field (the zero-point vacuum energy density is canceled out
because it is a part of both the cosmological constant and the stress-energy
tensor)
Now,
let us turn to the second difficulty with our proposed model of the
accelerating expansion of the universe or more precisely the cosmological
red-shift which is assumed to be a result of the acceleration of the expansion.
Surprisingly, our simple spherical model which denies this acceleration offers
another interpretation of this cosmological red-shift. It can be proved
mathematically by analyzing the world-line of light as it travels through this
shape of space-time between the source and the observer that it is a
logarithmic spiral which leads to a red-shift given by:
Where
theta is the angle between the world-line of the
source and the observer. This agrees with the observational data and reproduces
Hobble’s Law in small values of theta .The spiral path of light resolves the Horizon
Problem (The problem with the standard cosmological model that different
regions of the universe have not contacted to each other but have the same physical properties)
because all the radiations emitted from a source will converge to reach again
the same source from all direction which may suggests that the radiations with
the same properties which we receive from different directions could be emitted
from our own galaxy and led by the spiral path to meet our world line again .
This may also offers an answer to the problematic phenomena which was
discovered recently that some features of the cosmic radiation is aligned
with the orientation of our solar system
which can be thought of as the part of radiation which is emitted from the sun
the converged to reach it again from all direction and thus appears as aligned
with the ecliptic plane for any observer near the sun.
There
is indeed so much in these topics which such an approach cannot but miss, but
the intention in this stage of our argument is mainly to show that it is a
mistake to suppose that the acceleration of the expansion is the only possible
explanation of the observed cosmological red-shift or even the best of all
possibilities.
The
Observational Test of the Proposed Model
The
plan of this test is to identify some of the relations between physical
properties obtained from this cosmological model which distinguish it from the Standard
Cosmological Model and other existing models and compare these relations
with the model-independent observational data.
One
of the best of these relations is the Redshift-Flux relation because both redshift
and flux are model-independent physical quantities and fortunately some natural
phenomena such as type la supernova provides us with the tools needed to
construct the relation between these two quantities in different cosmological
models because this type of supernova give a certain known amount of light and
thus represents a standard candle that can be used to calculate luminosity
distance which can be used to link the flux to the red-shift according to the adopted
cosmological model.
Now,
let us see the mathematical form of this relation in our proposed cosmological model.
