Cycles of time
The big bang was a time of low entropy, when things happened quickly and energy was highly concentrated. The heat death of the universe seems to be very different - high entropy, things happening very slowly, and energy becoming ever more dilute. However, the distribution of energy is very smooth for both, and Penrose points out that as the universe winds down there will be no rulers or clocks, or anyone to do the measuring. If we allow the universe to 'lose track of time' then the heat death of one universe can become the big bang of another. There's the problem of the entropy difference, but Penrose devotes a substantial part of the book discussing thermodynamics, and showing how his ideas on black holes and quantum state reduction can avoid the entropy discrepancy.
The book is aimed at a popular science readership, but I would say that it is too technical for beginners. If you've read a few books on similar subjects then you'll be better placed to appreciate the inriguing ideas presented in this book.