His Phase Space chart is just a visualization of the 2nd law of thermodynamics. Its just showing that the universe goes from low entropy to high entropy and eventually end in thermal equilibrium.
His theory does not really center around the phase space chart . The diagram makes no new claims...
Interview with Sir Roger Penrose
Attached is a .ram file that streams the interview with Roger Penrose where he talks about his theory amongst other topics. Very interesting and complements his lecture.
Roger Penrose's New Theory: What happened before the BIG BANG
This is a lecture by Sir Roger Penrose that I was lucky enough to attend. Here is the flash presentation of it:
http://www.Newton.cam.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/
From what I can understand his theory...