A Static Cosmological Model Based on the Group of Conservative Transformations

Abstract

The group of Conservative transformations is an enlargement of the group of diffeomorphisms which leads to a richer geometry than that of general relativity. The field variables of the theory are the usual orthonormal tetrads and also internal space tetrads. Using the fundamental geometric object which is the curvature vector, an appropriate Lagrangian has been defined for both free-field and fields with sources. Solutions to the corresponding field equations have been developed. In this paper we use the static spherically symmetric tetrad field with sources to model the universe. Our fundamental assumption is that the total density comprised of both ordinary and dark matter should be constant. The resulting model with one adjustable parameter predicts that ordinary matter is approximately 77\% of the total mass content, but this percentage is near 0\% for regions near the center of the universe. The space is approximately isotropic for $r$ near zero. The radial and tangential pressures are negative and unequal. The redshift is also modeled without the expanding universe and an explanation of the value of the cosmological constant is given. Equations governing particle motion are also derived which can produce a repulsive effect and produce even larger redshifts. Finally, the cosmic microwave background and its anisotropies are addressed and heuristic arguments are given that suggest that our theory is not inconsistent with these observations. These results add further confirmation that the theory developed by Pandres is the fundamental theory of physics.