A Way Out of The Cosmological Constant Problem

 

Other papers with more details of the proposal can be found in:

http://vixra.org/author/mueiz_gafer_kamaleldeen 

Or:

http://gsjournal.net/Science-Journals-Papers/Author/874/Mueiz,%20Gafer 

 

The Impracticability of Interior Solutionsof Einstein's Field Equation

Before discussing the question whether the assumption that the universe is isotropic and homogeneous in the large scale is a good approximation or not, we have to be aware of the important fact that the general (global) curvature which is related to the shape , evolution and fate of the universe is quite different concept from the average curvature which is associated with the average density of the universes implied by Einstein's Field Equation.

Let us consider the application of the field equation in the universe as a whole ( this is an example of the interior application of the equation)

The average density of the universe is :

 ∑  𝛒(𝔁) v(𝔁) / V

 Where 𝛒(𝔁) ≡ the density in the region 𝔁 , v(𝔁)≡ the volume of the region 𝔁 , V ≡ the total volume of the universe.

Similarly, the Average Curvature of the universe is:

∑  R(𝔁) v(𝔁) / V 

The General or Global Curvature of the universe is the curvature which associated with the outline of the shape of the universe or the general geometrical description in which we ignore the details when they occur in small parts of the universe .

Interestingly , while wrongly and unconsciously assumed to be similar , the average curvature and the global curvature describe very different properties of the universe as a whole.

Let us clarify that this two terms are not equivalent by the following example using two-dimensional space for simplicity and it is clear that the same analysis can be generalized to any number of dimensions:

The average curvature of a uniform closed surface with large number of polygons and rounded edges is very close to zero while the global curvature of this surface can be thought of as the curvature of a sphere with the same size . The general curvature  depends only on the size of this shape and has nothing to do with the average curvature . Another example is the simple fact that  the general curvature of the surface of the earth depends only on the radius of the earth and is not related to the average curvature which is affected by the topological details .

Physicists unconsciously mix up global curvature which determines the shape , evolution and fate of the universe  with the average curvature which is  related to the average density of the universe according to the field equation of the general theory of relativity. This confusion is the main source of the current problems of the Standard Cosmological Model (See other papers by the same author such as : A Comparison between the Standard Cosmological Model and A Proposed Model with Radial Time and Independent Geometry).

The right key to the door of new cosmology without problems and contrived quantities is using two well-defined cosmological constants

when taking the two proposals of the spherical space with radial time and subtraction of the average density of the universe together they give results that consistant with observations and resolves all the major problems

For Details see: viXra:1509.0041

Two Cosmological Constants Can Solve All Major Problems of Modern Cosmology without Dark Quantities or Inflation

Using two cosmolological constants : geometrical one and matterial one can solve the cosmological constant problem without changining anything in GR or QM
For Details see:  viXra:1509.0041

The Cosmological Model with Radial Time and Spherical Space

         The simplest and the most  attractive  cosmological model with radial time and spherical space (RTSS) is not far from the imagination of physicists , but it is wrongly excluded mainly for  two false reasons which are: 

1) That it contradicts ( what is thought to be ) the result of genereral relativity that the global geometry of the universe depends on  its average density and not simply on the age of the universe as implied by  RTSS model.

2)That it Contradicts the observational fact of the acceleration of the expansion of the universe which which can be proved by the study of the cosmological red shift..

         As for the first reason it could be shown that the dependence of the global geometry of the universe is not a neccessary result of general relativity because we can make this geometry depend only on the age of the universe if we define the cosmological constant as aquantity that composed of two parts : the first part is geometrical one which is the curvature of the spherical space which depends only on the age of the universe and the second part is the material part which represents the density of matter which appears to be distributed in the large space (compared to the region of the application of the field equation) around the region of the application of the field equation ,that is to say : the backgroud density . In the case of the global application of the equation this background density is the density of the universe . This definition of the cosmological constant will solve all the major problems of modern cosmology such as the cosmological constant problem without any change in General Relativity or Quantum Mechanics and also remove all contrived concepts such as dark matter , dark energy and inflation.

          The second reason is also a false one because the cosmological red shift which is thought to be the result of the acceleration can be explained simply as a result of the shape of the universe in our proposal of the radial time and spherical space as shown in detail in many of my papers .

         The details of this proposal can be found in :

http://vixra.org/abs/1510.0097
http://vixra.org/abs/1509.0041
http://vixra.org/abs/1510.0011
http://vixra.org/abs/1509.0175
http://vixra.org/abs/1411.0100