The cmb dipole and existence of a center for expansion of the universe

Yukio Tomozawa

Michigan Center for Theoretical Physics

Randall Laboratory of Physics, University of Michigan and

Ann Arbor, MI. 48109-1040, USA

(Dated: February 2, 2008)

In the Friedman universe, one possible interpretation of the coordinates is that the whole

space is on the surface of an expanding balloon and has no center. (A center exists outside

the universe in a way.) This accommodates the Hubble law naturally. There are no velocities

associated with points of the universe, but the relative distance and relative velocity of any

two points increase with the expansion of the balloon. I will show that in such a universe,

there is no cosmic microwave backgroud (cmb) dipole even in the presence of a peculiar

velocity. In other words, the observation of a cmb dipole excludes such an interpretation of

the coordinates for the Friedman universe…

…All three proofs give the same result. Another way to look at this theorem is that the

equivalent speed of a cmb emitter is close to that of light and speed of light is identical

for moving frames. We have reached the important conclusion that in a cosmology without

center there is no cmb dipole. As a corollary, we state a theorem.

Theorem 2 The observation of the cmb dipole excludes the possibility of a cosmology without

center. Thus, there has to be a center for the expansion of the universe, since a cmb

dipole has been observed for the solar system[1].