Abstract
We design a cosmological model that expands at a speed less than that of free fall and which allows accelerations of the recession velocity. In addition, the underlying geometry of the model can be adjusted in such a way that attractive forces arise in the cosmos, forces whose sources are not matter. This could explain dark matter as a property of space and one could also address the question of why galactic systems are not subject to expansion.
Highlights
Careful measurements have proven that there must be attractive forces in the galaxies that cannot be explained by the action of mass of the stellar objects
As a first step towards a generalized model which admits attractive forces, we examine a static cosmological model by introducing the projector technology borrowed from the interior Schwarzschild solution
A strict geometric treatment of cosmology allows for the ability to modify the underlying geometry to reveal certain physical properties of the cosmos
Summary
Careful measurements have proven that there must be attractive forces in the galaxies that cannot be explained by the action of mass of the stellar objects. We can imagine that the forces do not come from localizable objects, but stem from the geometric structure of space. This concept is in perfect harmony with the principles of general relativity. This metric is a metric on a pseudo-hyper sphere, in the second case it is a metric on a cap of a hypersphere From both metrics repulsive forces are derivable, which can be interpreted in the dS case as the cause of an expansion.
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