The laws of gravity seems to be the same everywhere in the Universe. There have been experiments using distant objects in the Universe to try and measure if it might be different far away (or back in time!), but no effect has been found to date.
In fact, the question seems to tie in with the question whether the laws of physics are the same everywhere in the Universe. This is because one can derive the equations of general relativity assuming the laws are the same everywhere for everyone. This is a bit technical, but basically if you want the laws of physics to be the same for everyone you MUST have gravity in the form Einstein proposed, there is no other way.
Of course other deviations from our laws of physics have been looked for, but again none have been found.
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