If "The singularity was not known to be infinite density," does that mean that all those references listed below are wrong? And as you imply knowledge, can you please guide me to a site where I too can learn?
The key question that I have is still "If density is near-infinite, can there really be any room for near-infinite thermal activities (molecular/atomic wiggling around), yielding near-infinite temperature?"
http://en.wikipedia.org/wiki/Gravitational_singularity: According to general relativity, the initial state of the universe, at the beginning of the Big Bang, was a singularity.
http://assa.saao.ac.za/features/cosmology-articles/Stephen-Hawking-Turns-70.pdf: Together with Roger Penrose he [Stephen Hawking] used Einstein’s equations to prove that the universe could have originated from a singularity, a point of infinite density, gravity and temperature. Initially Hawking described the singularity as a point of infinite density, temperature and gravity. He changed this from “infinite” to “incredible,” because he realized that the universe could not have evolved from a point of infinite gravity.
http://abyss.uoregon.edu/~js/ast123/lectures/lec17.html: Extrapolation from the present to the moment of Creation implies an origin of infinite density and infinite temperature (all the Universe’s mass and energy pushed to a point of zero volume). Such a point is called the cosmic singularity.
http://www.journaloftheoretics.com/articles/6-3/SM.pdf: Mathematical infinity is applied also in calculations about pressure, temperature, and density in singularity of big bang and black holes, where all of them have infinite values.
http://debunkingwlc.wordpress.com/2010/07/09/standard-big-bang-model: the universe began as a state of infinite density, infinite temperature, and zero size which is often referred to as a singularity
http://www.infidels.org/library/modern/quentin_smith/uncaused.html: As d2a/dt2 increases and a decreases, the density of matter p increases, until at t0 the value of p is infinite. At this time the entire universe is squeezed into at least one point of infinite density, infinite temperature, and infinite curvature. We have reached a space-time singularity.
http://www.stephenjaygould.org/ctrl/archive/hawking_universe.html: general relativity shows that under certain reasonable assumptions, an expanding universe like ours must have begun as a singularity.
http://www.astro.umd.edu/~miller/teaching/astr422/lecture27.pdf: in general relativity, if we project backwards in time we get to a point of actually infinite density and temperature.
http://12tuesday.com/william-lane-craig-vs-stephen-hawking: general relativity predicts there to be a point in time at which the temperature, density, and curvature of the universe are all infinite, a situation mathematicians call a singularity.