Does the term center of mass of universe mean anything? Why why not?
No, for something to have a center of mass, it has to have a center and the universe does not.
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What do you mean by centre? does every body has a geometrical centre what does geometrical centre even mean?
Not in standard cosmology. The standard cosmology assumes that the universe is spatially homogenous and isotropic. The homogeneity precludes having a center.
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