Roger Penrose is forwarding fred hoyles steady state universe that guth's inflationary big bang poo pooed many years ago. personaly i prefered freds and penroses theory. guths explains very well the after big bang inflation, not the conditions before.
einstien/desitter model is also classic model.
i) If there is enough matter in the expanding universe, the expansion will one day stop and the universe will contract again - positive space-time curvature.
ii) If there is too little mass in the universe, it will expand forever - negative space-time curvature.
iii) If the amount of matter is “just right”, the expansion rate will approach zero, but the universe will never contract - zero space-time curvature.
In 1932 Einstein and de Sitter together proposed that this “just right” cosmological model be accepted. The Einstein-de Sitter model assumes a homogeneous, isotropic universe, with zero curvature, zero cosmological constant and zero pressure.
The circular features indicate that the cosmos itself circles through epochs of endings and beginnings, Penrose and Gurzadyan assert. The researchers describe their controversial findings in an article posted at arXiv.org on November 17.