Does gravity's strength vary if its speed varies across the universe?

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lnsanity
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According to some physicist and cosmologist observation the speed of light is not a constant depending on region of the universe they observe and according to Einstein theory gravity move at the speed of light now my question is if gravity move at speed of light than gravity should move faster or slower in some region of the universe than would gravity be stronger or weaker if it travel faster or would it be the same ?
 
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It would be the same, although it should be noted work saying that universal constants like c vary throughout the universe are tenuous.
 


ok why it would be the same what is the mechanism of gravity that explain that it would remain the same ?
 


locally, the speed of light and gravity is constant...when viewed from a distance, measurement speeds can be different than c when gravity is present as spacetime curvature affects the observed measurements. Local measurements eliminates the observational affects of curvature.
 


Usually results that are reported about "the speed of light changing" are actually results about variations in the fine structure constant.

See for instance http://www.phys.unsw.edu.au/einsteinlight/jw/module6_constant.htm

This is reported in the popular press as "the speed of light changing over time", because news reporters seem to like that the lay audience will like that idea, and the editors think it makes a catchier title. The actual situation is rather less clear - physicists are more likely to interpret the resujlts in terms of atoms changing their properties than the speed of light varying.

Note that the two descriptions are experimentally indistinguishable, once the details of what you mean when you say "mesaure the speed of light" is worked out.

These effects are NOT predicted by relativity, and are not really confirmed either, so the best way to think about them (assuming they do actually exist) isn't especially clear.
 


I should have included: all massless particles are believed to travel at the fixed speed 'c'..of course that includes photons [light = electromagnetic radiation] and gravitons [gravity].