Abstract

Gravitation in flat space-time is described as field and studied in several articles. In addition to the flat space-time metric a quadratic form formally similar to that of general relativity defines the proper-time. The field equations for the gravitational field are non-linear differential equations of second order in divergence form and have as source the total energy-momentum tensor (inclusive that of gravitation). The total energy-momentum is conserved. It implies the equations of motion for matter in this field. The application of the theory gives for weak fields to measurable accuracy the same results as general relativity. The results of cosmological models are quite different from those of general relativity. The beginning of the universe starts from uniformly distributed gravitational energy without matter and radiation which is generated in the course of time. The solution is given in the pseudo-Euclidean metric, i.e. space is flat and non-expanding. There are non-singular solutions, i.e. no big bang. The redshift is a gravitational effect and not a Doppler effect. Gravitation is explained as field with attractive property and the condensed gravitational field converts to matter, radiation, etc. in the universe whereas the total energy is conserved. There is no contraction and no expansion of the universe.

Highlights

  • The most accepted theory of gravitation is general relativity (GR) of Einstein

  • GFST is a covariant theory of gravitation in flat space-time

  • It gives for weak gravitational fields to measurable accuracy the same results as GR

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Summary

Introduction

GR gives for homogeneous, isotropic, cosmological models a singularity of the solution in the beginning with infinite density of matter, the so-called big bang. The theory of gravitation in flat space-time (GFST) is applied to cosmological models. Let us study by the use of GFST homogeneous, isotropic, cosmological models in the pseudo-Euclidean metric, i.e. space is flat. GFST gives two field equations for a and h and the conservation of the total energy It follows by suitable combinations of these equations and integration by the use of the initial conditions (2.5) The field equations of gravitation give two differential equations of order two and one equation by the use of the conservation of the total energy Suitable combinations of these three differential equations imply by longer calculations (see article [2]) the differential equation ( ) ( ) = aa 2. The differential Equation (2.18) is rewritten by the introduction of the proper-time τ :

Ωm a
This gives for the energy of the photon
Conclusion

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