Saturday, 17 September 2016
Thursday, 8 September 2016
Using Newtonian Approximation of Einstein’s Field Equation to Determine the Cosmological Constant
Introduction
Newton’s law of gravity was
replaced by General Relativity for both theoretical and observational reasons
and in spite of being essentially different from General Relativity, Newton’s
law of gravity can be recovered from the field equation of General Relativity
as an approximation in special cases, this fact played an important role during
the construction of the field equation. What I am going to put in front of the reader
is another major role for this fact.
Analysis
According to the standard
modern cosmology, there are three possibilities of the shape or the large-scale
geometry of our universe but whatever is the real shape of the universe, the
field equation of General Relativity should be applicable and correct in all
these possibility.
Let us fist pay our attention to
the fact that every case in Newton’s Gravity can be proved with General
Relativity.
Now when we consider the
possibly of spherical shape of the universe in which the matter is uniformly
and homogenously distributed throughout the space as appears in the large scale
(our argument will not be affected even if this is not a precise description of
our universe because General Relativity and Newtonian Approximation is
applicable and correct also in the ideal case)
we will find according to Newton’s law of gravity that the value of the
gravitational field in any region of such a space must be zero because of the total
symmetry and similarity of all directions ( there is no preferable direction
for a gravitational force that could act on an object) so we arrive at the
important fact that in this case the gravitational field is zero regardless of
the value of the density of matter in the universe . But can this be explained
by General Relativity? In General Relativity, as we are always told, the
existence of matter must be associated with the geometrical deformation of
space that causes gravitational effects? Is it a contradiction?
This conflict between general
theory of relativity and its Newtonian
Approximation cannot be resolved except if we abandon the unnecessary and
unjustified assumption that the large scale geometry of the universe should
depend on the average density simply by assuming that this average density of
the universe is a part of the cosmological constant and therefore the
large-scale geometry of the universe well not be affected by this density while
the local application of the field equation ,in which deviations from
uniformity come to light, remains with its well-known successful results .
More arguments to support this
inevitable idea and more details and results including the resolution of the Cosmological
Constant Problem is found in other
papers by the author such as:
- The
Independence of the Global Geometry of the Universe from Its Average Density
- The
Detestability of the Zero-Point Energy in General Relativity and Quantum
Mechanics
- A logical Analysis of
the Cosmological Constant Problem and Its Solution
- Another Cosmological
Constant to Solve Major Problems of Cosmology
- The Resolution of the
Flatness Problem without Inflation
- A Comparison between the
Standard Cosmological Model and a Proposed Model with Radial Time and Spherical
Space
- Adaptable Cosmological
Constant to Solve Major Problems of Modern Cosmology
Tuesday, 6 September 2016
A Logical Analysis of the Cosmological Constant Problem and Its Solution
What I am about to put before the reader is an exploration of the logical relations between the propositions which constitute the structure of modern cosmology within which the Cosmological Constant Problem is created in order to avoid the risks inherent in unjustified confidence in absolute validity of some of these relations in hope that the problem will be solved within our well-defined existing concepts by refutation of such false relations instead of invoking metaphysical notions such as dark energy, multi-verse … etc.
The Analysis
Let us first make a list of the basic propositions and statements of modern cosmology associated with the cosmological constant problem:
⦁ Einstein’s Field Equation is correct.
⦁ Zero-Point Energy exists and is very large.
⦁ The global curvature of space is very small.
⦁ The observational data about cosmological red-shifts are correct.
⦁ The accelerating expansion of the universe is true.
⦁ The global geometry of the universe depends on its average density.
Then we turn to the claimed logical relations between these statements:
⦁ The 1st statement implies the 6th statement.
⦁ The 4th statement implies the 5th statement.
⦁ The 6th statement implies that the 2nd statement contradicts the 3rd.
Now let us examine the validity of these relations carefully:
Starting from the first relation the author argues that it is incorrect, a fact which has often been overlooked, because the dependence of the global geometry of the universe in the average density which is thought to be a necessary result of the field equation can be taken away by assuming that the cosmological constant (or part of it) is the average density of the universe.
In this case any homogeneous distribution of matter and energy throughout the universe cannot affect the geometry of the universe because the contribution of this distribution on the stress-energy tensor in one side of the equation is canceled out by its contribution on the cosmological constant in the other side of the equation and thus the field equation is not affected by such a distribution regardless of its density.
Beside its simplicity and ability to cut the cosmological constant problem at its roots there is nothing to be lost by adopting this assumption because the successful local applications of the field equation will not be affected.
Now let us turn to the second relation , perhaps another advantage is gained if we managed to get rid of more restrictions caused by this relation if proved to be false. The important question to be answered is whether or not the accelerating expanding of the universe is the unique explanation of the observational data of the cosmological red-shifts. The accelerating expanding is a very undesirable idea because it is responsible for the excluding of the best of all cosmological models in terms of physical simplicity and mathematical beauty which is the cosmological model of spherical 3-space and radial time.
Fortunately and interestingly the second relation is false and the cosmological red-shift observational data attributed to acceleration of the expansion can be explained easily as a result of geodesic path of light associated with the shape of space-time in the cosmological model with radial time and spherical space.
(More arguments which support this resolution and more details are found in other papers by the author.)
The Analysis
Let us first make a list of the basic propositions and statements of modern cosmology associated with the cosmological constant problem:
⦁ Einstein’s Field Equation is correct.
⦁ Zero-Point Energy exists and is very large.
⦁ The global curvature of space is very small.
⦁ The observational data about cosmological red-shifts are correct.
⦁ The accelerating expansion of the universe is true.
⦁ The global geometry of the universe depends on its average density.
Then we turn to the claimed logical relations between these statements:
⦁ The 1st statement implies the 6th statement.
⦁ The 4th statement implies the 5th statement.
⦁ The 6th statement implies that the 2nd statement contradicts the 3rd.
Now let us examine the validity of these relations carefully:
Starting from the first relation the author argues that it is incorrect, a fact which has often been overlooked, because the dependence of the global geometry of the universe in the average density which is thought to be a necessary result of the field equation can be taken away by assuming that the cosmological constant (or part of it) is the average density of the universe.
In this case any homogeneous distribution of matter and energy throughout the universe cannot affect the geometry of the universe because the contribution of this distribution on the stress-energy tensor in one side of the equation is canceled out by its contribution on the cosmological constant in the other side of the equation and thus the field equation is not affected by such a distribution regardless of its density.
Beside its simplicity and ability to cut the cosmological constant problem at its roots there is nothing to be lost by adopting this assumption because the successful local applications of the field equation will not be affected.
Now let us turn to the second relation , perhaps another advantage is gained if we managed to get rid of more restrictions caused by this relation if proved to be false. The important question to be answered is whether or not the accelerating expanding of the universe is the unique explanation of the observational data of the cosmological red-shifts. The accelerating expanding is a very undesirable idea because it is responsible for the excluding of the best of all cosmological models in terms of physical simplicity and mathematical beauty which is the cosmological model of spherical 3-space and radial time.
Fortunately and interestingly the second relation is false and the cosmological red-shift observational data attributed to acceleration of the expansion can be explained easily as a result of geodesic path of light associated with the shape of space-time in the cosmological model with radial time and spherical space.
(More arguments which support this resolution and more details are found in other papers by the author.)
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