I have been trying to work out the solutions to a homogenous line universe using special relativity, and have found that, as per special relativity, one of the solutions is $$v = tanh(d)$$, where $v$ is the velocity and $d$ is the distance of recession of galaxies in this one dimensional case. Now, by homogenous, i mean that between any two points in my line universe, the velocity of recession of the two points can be given by $$v = g|d|$$ where $g$ is some function to be found [irrespective of the location of points]. One can then observe that due to velocity addition, considering three points on the stretching line: $$\frac{g|b-a| + g|c-b|}{1+g|b-a|g|c-b| = g|c - a|.$$ [The fact that this right hand side is $$g|c-a|$$ is due to the assumption of homogeneity]. Now, when i try to extend this to two dimensions or higher. i encounter difficulties and impossibilities, and this is hinting that homogeneous space, as i have defined it at least, is not possible. Does anyone know of any solution to this problem?(adsbygoogle = window.adsbygoogle || []).push({});

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# Homogeneous line universe

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