I did not read that book, though I do know prevailing cosmological models say that the universe is expanding continually. If it keeps it up, eventually, no galaxy will be able to see any other galaxy, because the distances between them have increased so much. Later, galaxies all collapse into mega black holes. Still later, these mega black holes all evaporate over a very long epoch (10^60 years or something like that) via the process of Hawking Radiation. Once this happens, there is nothing left in the universe except radiation, and various short-lived "quantum vacuum" particles perhaps. Nothing but a homogeneous soup of particles that are not even atoms. Penrose has recently argued that this state could trigger another big bang, and start another "cycle" but I don't know that that view is very much accepted presently. The general thinking is that this final state of scattered radiation is all the fat lady sings.
