Authors: C. A. Laforet
In the current paper, the internal Schwarzschild solution is examined in the context of a cosmological model. The model gives a vacuum solution where the center of gravity is an infinitely dense point in time rather than space. The internal metric is dynamic and describes two phases. In the first phase, space starts off infinitely sparse and then collapses to infinite density in a finite proper time measured by an inertial observer. In the second phase, the space expands out from this infinitely dense state (the temporal center of gravity) back to the zero density state. The geodesics remain well defined when traversing this infinitely dense state. It is shown that the second phase corresponds to current observations of the expansion history of our Universe, namely that the initial expansion is infinitely fast, and then the expansion slows for some time followed by an accelerated expansion. With a simple coordinate change we get a metric resembling the FRW metric for flat space with a time dependent scale factor. It is shown that the singularity at r=0 can be interpreted as a point in time where the geodesics reverse sharply, causing the expansion and collapse of the Universe to cycle.
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