There is no center, the universe is as far as can be seen, the same all over. That is, no one place is any different than any other place, hence there is no center.
However, if you gave yourself a large velocity with respect to the local matter (in any direction) you would find as time goes by that your velocity with respect to the matter you are travelling by, becomes less and less-- never exactly zero, but it assymptotically approaches zero. This is the same effect as the red shift -- for example the Cosmic Microwave Background radiation emitted at the end of the Big Bang had a temperature then of about 10,000K, and now has a temperature when we see it of 3K. In this case of course the velocity has not decreased (light always goes at the velocity of light) but the energy has decreased.
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