Some say we live in an infinite universe or an infinite chain of [infinite?] universes.
This seems fanciful, there seems to be to be no evidence for it except a Flat Space (compare with Flat Earth) theory that spacetime is flat, not curved, and therefore the universe has always been infinite, and if the Big Bang occured, it would have been merely an explosion in scale factor of a pre-existing infinity. This seems like handwaving, l mean, what exactly is being said by the Flat Space-ers?
The Flat Spacers say that spacetime shows a very very very minute gradient and thus is virtually flat. A lot like a big big picnic blanket. Yet the earth is still not flat is it, so why would they be so precociouis as to say spacetime is flat? Wait for a few centuries of corroborating data to arrive surely?
Were the universe infinite, then there would be white dwarves and hypothetical black dwarves everywhere as they are the end of average stellar evolution (the sun is a large-ish star, contrary to what people say, but it is still considered average - one measure is modal av. the other is mean av.). Also where does the energy for new stars come from, across the timescale of infinity, if black holes consume matter do they radiate it all as energy in bursts, or does some of that energy also disappear? If the latter, then across an infinite timescale, the infinite universe fails again and doesnāt match observation.