Astronomers and physicists have been searching for such differences for as long as those fields of study have existed, and found no evidence for those differences. Here is a short list of what those differences might look like.
The inner workings of stars and how those workings evolve over the lifetime of any given star are determined by a short list of fundamental laws and can be studied from afar by collecting the light given off by a star using a telescope, and then breaking down that light into its fundamental spectrum using a spectrograph connected to the telescope. If a distant star was operating according to a different set of physical laws, then the difference would probably show up in its spectrum. No such differences have shown up which cannot be satisfactorily accounted for on the basis of the size, age, and time of birth of the particular star under study.
In those cases where the stars are too far away to study individually, the same sort of trick can be exploited to study entire galaxies. In this case, the results are the same: the galaxy spectra do not suggest that the laws of physics are any different in any corner of the universe we care to look, no matter how far away.
Supernova events, as detected and recorded by a variety of different instruments here on earth and in orbit, furnish the opportunity to look for differences in other physical laws and fundamental constants of nature. Excellent data on this was collected from Supernova 1987A, which happened close enough to us to enable detailed analysis, and no evidence was found of any differences between the known values of those constants as measured here and those which were back-calculated from those observations.
The overall conclusion remains: the laws of physics and constants of nature seem to be the same as they are on earth, everywhere we can see out into the very distant parts of the universe. If they were different, it would be the stuff from which Nobel prizes would be earned.