1. As a result of his work, everyone began thinking about the origins of the universe.
In 1927 Georges Henri Joseph Édouard Lemaître observed the expansion of the universe and wrote his landmark article about the origin of the universe, “Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques” or “A homogeneous universe of constant mass and increasing radius, accounting for the radial velocity of extragalactic nebulae.” Applying a simple logic, he assumed at one time the universe had a single originating point. At that time, when he first introduced his ideas, he thought the universe started cold. Also, for many of his early readers that concept of an initial singularity was as much an expression of his priesthood, Jesuit education, and the story of Genesis.

Lemaître attempted to understand the origin of atoms in nature by proposing that before the expansion of the universe started there existed a primeval atom consisting of all the matter in the universe crushed to nuclear densities. It formed a gigantic ball of nuclear liquid which existed in this state at very low temperature. The low temperatures were required to keep this cosmic atom from falling apart via thermal agitation. But this fluid broke-up anyway under mechanical instabilities, into a mist of microscopic particles. He estimated that only 260 binary divisions would be needed to convert the cosmic mass into atom-sized particles. This idea was pursued by Maria Meyer and Edwin Teller, but ultimately this idea couldn’t explain why the universe should expand, or where the light elements came from.

“…if matter existed as a single atomic nucleus, it makes no sense to speak of space and time in connection with this atom. Space and time are statistical notions that apply to an assembly of a great number of individual elements; they were meaningless notions, therefore, at the instant of first disintegration of the primeval atom…” — Georges Lemaître

A variant on Lemaître’s cosmology was proposed in 1966 by David Layzer, developed a short-lived alternate to Hot Big Bang cosmology by proposing that the initial state was near absolute zero. The motivation for proposing such an initial state, reminiscent of Lemaître’s initial state. Through thermodynamic arguments, Layzer proposed that rather than the universe starting in a high entropy state, it began in a very low entropy state near Absolute Zero. It was matter-dominated with little free radiation, and the conditions were favorable for the formation of galaxies via fragmentation. The famous Cosmic Microwave Background Radiation discovered by Arno Penzias and Robert Wilson in 1965 was produced much later when galaxies were forming in a dusty environment.

Odenwald, Sten, Ph.D. (Contributing Author); Bernard Haisch (Topic Editor). 2009. “Universe: Cold Big Bang.” In: Encyclopedia of the Cosmos. Eds. Bernard Haisch and Joakim F. Lindblom (Redwood City, CA: Digital Universe Foundation). [First published January 13, 2008].
http://www.cosmosportal.org/articles/view/138894/. (very slow to post)

2. The finite-infinite bridge is not to be ignored.
You will find within this website an appreciation for a wide latitude of singularities, however, it would seem that the concept and term do not apply to an “initial” singularity understood by many to the foundations of the hot big bang. Here the finite-infinite bridge is real and dimensionless constants are an inherent part of every transformation. Instead of singularities, a better conceptual term might be a nexus of transformation.

3. The expansion of the universe is a key clue.
Very few question that there is a well-ordered expansion underway. Most likely the concept of an expanding universe originated with Alexander Friedmann in 1922 in Russia. In the heinous aftermath of the 1917 revolution, it would be a difficult place to build on theory and logic alone; nevertheless, using Einstein’s formula, Friedmann proposed the idea that the universe is expanding. Between 2001 and 2010 the Wilkinson Microwave Anisotropy Probe (WMAP) precisely measured the expansion and definitively confirmed Friedmann and Lemaître’s intuitions and observations.

4. Homogeneous and isotropic are keys to understanding our universe.
Most often, people attribute the cosmic microwave background radiation (CMBR) to a massive explosion and not to a geometric and exponentially-expanding universe in a highly-ordered, progressively-organized state. Yet, our explosive people will readily tout the fact that our universe is homogeneous and isotropic. More… the cosmological principle

5. The circle, sphere, and the dynamics of spheres is not appreciated enough.
The 1948 Lemaître essay about quaternions and elliptical space does not engage the much earlier work of Fourier and his analysis of the sine-and-cosine functions within and around the sphere. That will be picked up here: https://81018.com/fourier/

Much more to come…