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Volume Expansion Rate and The Age of The Universe

Takashi Nakamura·Ken-ichi Nakao·Takeshi Chiba·Tetsuya Shiromizu
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Abstract

Under four assumptions such that 1) Einstein's theory of gravity is correct, 2) existence of foliation by geodesic slicing, 3) the trace of the extrinsic curvature, $K$, is negative at the present time in observed region, that is, the observed universe is now expanding, 4) the strong energy condition is satisfied, we show that $H_{v0} t_{0} \leq 1$, where $H_v \equiv - K/3$ agrees with the Hubble parameter in the case of a homogeneous and isotropic universe, and $t_0$ is the age of the Universe. If $H_{v0} t_0 > 1$ is confirmed observationally, at least one of the four assumptions is incorrect.

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Takashi Nakamura, Ken-ichi Nakao, Takeshi Chiba, Tetsuya Shiromizu. 1995-07-22. Volume Expansion Rate and The Age of The Universe. https://doi.org/10.1093/mnras%2F276.1.l41

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