preprints.org > physical sciences > astronomy and astrophysics > doi: 10.20944/preprints202201.0301.v13

Preprint Article Version 13 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 18 January 2022 / Approved: 20 January 2022 / Online: 20 January 2022 (11:11:44 CET)
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This paper investigates a relativistic model of the Universe in which the geometry describes a 4D version of the 2-sheeted hyperboloid that is isotropic, homogeneous in space at a given time and inhomogeneous in time. The internal Schwarzschild metric is used for this model, which is justified by the fact that spherically-symmetric empty spaces in the Universe are effectively surrounded by a shell of infinite mass (the surrounding Universe and in particular, the infinitely dense mass at the Big Bang). Thus the metric for the empty spaces must be described by the Schwarzschild metric according to Birkhoff’s theorem. Since the shell’s mass is infinite, the external solution cannot describe this spacetime and therefore the internal Schwarzschild solution must be the correct metric for this spacetime. The important insight here is that the source of the metric is not at r = 0, but that the event horizon is the metric source in both cases, representing a location/time of infinite density. This is supported by looking at the internal geometry in Kruskal coordinates where the event horizon surrounds the vacuum at an infinite distance, meaning the Schwarzschild radius, and therefore mass, of the source shell is infinite. The full spatial homogeneity of the internal metric is also demonstrated by visualizing at the Schwarzschild geometry (with 2 spatial dimensions and the time dimension) in Kruskal coordinates. The model predicts both a Universe and Anti-Universe moving in opposite directions of time undergoing an expansion phase, followed by a collapsing phase. Using only the current coordinate age of the Universe and transition redshift, it predicts the accelerated expansion and it is shown that its Hubble diagram fits currently available supernova and quasar data as well as predicting a Hubble constant H₀ ≈ 71.6km/s/M pc. The angular term of the metric describes time dilation caused by the relativistic kinematic precession effect known as Thomas Precession which can be interpreted as spin about the time dimension. The model also makes two novel predictions: that the early Universe should have structures older than expected due to an increased amount of proper time relative to coordinate time in that era and that the background Universe should appear brighter than current models predict.

Cosmology; Black holes; Dark Energy; Schwarzschild metric

Physical Sciences, Astronomy and Astrophysics

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