Relativity and Cosmology

   

Global and Local Cosmological Metrics

Authors: C. A. Laforet

In this paper, it is proposed that to fully describe the Cosmology of the Universe, we need to consider two metrics together: the FRW metric and the internal Schwarzschild metric. In static spacetime, if you zoom into a local region of the spacetime, you get the Minkowski metric locally. In this case, where the spacetime is dynamic, if we zoom in to a specific time slice of the internal Schwarzschild metric, we get the Minkowski-equivalent FRW metric for flat space with a spatial scale factor that depends on the specific time slice at which we are looking. By solving for the unknowns in the internal Schwarzschild metric using cosmological data, we obtain values for the scale factor at different times which can then be used in the FRW metric to obtain energy densities of the Universe at various times. No cosmological constant is required because the internal Schwarzschild metric provides a scale factor that generates a slowing expansion for some time after the Big Bang followed by an accelerated expansion that ultimately ends in a Big Rip. The entire Schwarzschild metric in Kruskal-Sezekeres coordinates is examined and we see that it describes two CPT symmetric Universes moving in opposite directions in the time dimension. One Universe contains matter while the other contains antimatter. When these Universes meet at the singularity, they annihilate each other resulting in a single, massless, pure radiation Universe. This state regenerates the Big Bang conditions where the radiation decays into matter and antimatter pairs, resulting in a new cycle where the two Universes again fall in time.

Comments: 16 Pages.

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Submission history

[v1] 2021-11-19 10:41:29

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