Authors: C. A. Laforet
In the current paper, the internal Schwarzschild solution is examined in the context of a cosmological model. The expanding Universe is likened to a collapsing star in this context, where the future spacetime of the Universe is empty (justifying the vacuum solution) and the present is a 3-sphere boundary akin to the 2-sphere surface of a collapsing star. Because the present time of the Universe is the boundary, it sees the vacuum solution just as the surface of a collapsing star sees the vacuum solution. It is shown that the model predicts an accelerated expansion that agrees with 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. It is shown that the singularity at r=0 can be interpreted as a point in time where the geodesics reverse sharply, perhaps causing the expansion and collapse of the Universe to cycle. An examination of the Hubble parameter and redshift is made and it is shown that the model agrees with cosmological data in predicting the transition redshift when the expansion of the Universe changes from deceleration to acceleration. Distance modulus is plotted against redshift and compared to cosmological data. The consequences for an observer in freefall in a local gravitational field are then examined in the context of this model.
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