Sean Carroll has some comments about the anti-big bang petition. He also points to Ned Wright’s explanation of what is wrong with various proposed alternatives to the big bang scenario. In particular this explains in detail what the problems with Irving Segal’s “Chronometric Cosmology” are, something I’d always wondered about.
Segal was a very good mathematician, who did serious work on quantum field theory in the 50s and 60s. He’s the “Segal” in what is sometimes called the “Segal-Shale-Weil” representation. Segal is a counter-example to Carroll’s observation that, for the most part, opponents of the big bang are not very smart. Unfortunately, it seems that quite smart and otherwise reasonable people can have unshakable faith in ideas that don’t work. Segal’s student John Baez wrote up some of his memories of his advisor and his cosmological research.