Circles in the sky

I went to a lecture by Sir Roger Penrose, Emeritus Professor of Maths at Oxford, on the subject of the universe pre-Big Bang (ie over 14 thousand million years ago). He now believes that the universe is in a continuous cycle of beginning, expanding, contracting and beginning again with another Bang. He thinks black holes become relatively warm when the universe contracts and this causes them to shrivel up and that circles in the cosmic microwaves may be traces of black holes in the preceding universe. Will we all reappear in a future universe, thousands of millions of years from now? He didn't express a view about history repeating itself.