The quilted multiverse
So, I have been reading Brian Greene's "The Hidden Reality" and in the second chapter he discusses the possibility of a quilted multiverse. The main point of the second chapter is that with a limited amount of particle arrangements and an infinite amount of space means you are going to have parallel worlds for each "comic horizon" (expanse of 41 billion light years). This part is obviously understandable, but he does not really go in depth about the amount of matter in the universe, except for a short paragraph near the end.
My question is; Is it thought that there is an infinite amount of matter in the universe? And most importantly, does an infinite universe imply infinite matter?
Thanks for reading.