Ashtekar "Mathematical Structure of Loop Quantum Cosmology" http://www.arxiv.org/gr-qc/0304074 [Broken] It's with co-authors Martin Bojowald and Jerzy Lewandowski and the date is June 9, 2003 and its 29 pages with references Ashtekar and company have an ongoing program to quantize the geometry of spacetime, that is to quantize the equations of general relativity and around ten papers have been published or submitted so far about the fact that the singularity goes away when you quantize GR. General Relativity has this famous glitch at time zero where some parameters "blow up" i.e. go to infinity so that you cant calculate with the model back to zero-----and certainly cant calculate back before. this is considered to be a failure of the equations. "Big Bang" is a euphemism or a hand-waving gesture which by giving a name to it conceals the breakdown of the mathematics. They could as well call it General Relativity's "great glitch". In 2001 one of Ashtekar's postdocs discovered that when you quantize the model-----to get a kind of quantized Friedmann equations (assuming isotropy or homogeneity and including matter if desired)----then the glitch went away. So he found himself staring at a pre-zero universe collapsing and then evolving right thru where the old glitch had been and then beginning to expand and become our universe. So there has been a lot of activity, a lot of research action around this, since 2001. Now Ashtekar has weighed in and had his say about it in this paper I gave the link to and although a lot of the paper is rather technical (making use of "almost periodic functions" and the "Bohm compactification of the real line" and making references to Russians like Gel'fand) it also has some nice philosophical overview parts for non-technical enjoyment. So I am posting a thread on this paper for that reason and also because removing the glitch at time zero seems to reduce the need for "Inflation Scenarios". The flatness would have been there because in either a matter-dominated or radiation-dominated universe flatness is PRODUCED by collapse. There is a nice formula about this which I will copy from Lineweaver in a followup post. The equilibrium of temperature between one part of space and the other would have had time to emerge already before time zero---so inflation is not needed as a rather extreme kludge to fix up that either. No disrespect to the Brilliant Minds like Guth and Linde who thought up inflation but removing the glitch seems to change the intellectual landscape so that having inflation in the first picosecond after time zero is no longer such an urgent requirement----and it is still just a scenario, nobody having come up with a magic "inflaton" to make it happen or a proof that it ever actually did happen. So it may have happened or it may not have, but now that does not seem to be such a burning issue.