Qualitative picture for a Lemaître's Cold Big Bang theory Warning: please, consider this question to be motivated by  historical curiosity or as an exercise in model-building. I believe this cannot be considered non-mainstream physics as it was very much mainstream in the past.
Historical overviews of the Hot Big Bang theory usually concentrate on its steady state rival — the Fred Hoyle's theory where the Universe was expanding but essentially stayed the same due to creation of energy in space that locally balanced out the expansion.
But I often think about another and naively more plausible idea of Lemaître: the "primeval egg" or the Cold Big Bang theory. I've read that it was disproven my WMAP's discovery of BAO (baryon-acoustic oscillations), but this strikes me as strange because my understanding of this idea is that it would be undistinguishable from the modern Standard Cosmology.
My sketch of the Cold Big Bang
As we know, the Universe is expanding, so it was smaller in the past. But instead of being hotter, it might have been a very cold and dense neutron star-like state which later expanded and heated up by nuclear decay of neutrons. In the end, the Universe will reach equilibrium state as we know it and will seamlessly merge with the history of Standard Cosmology, leaving small amounts of baryons comparing to light electrons, neutrinos and massless photons.
I see the following attracting features of this idea:

*

*We really have no proof that the temperature of the Universe ever was above $\sim 10 MeV$ (number comes from primordial nucleosynthesis as we know no other way to produce elements from protons and neutrons)


*This picture has a natural matter-antimatter asymmetry: neutrons are everywhere and there are no anti-neutrons.


*Binding energy of the neutron is small, so decays will slowly build up the temperature while non-relativistic nature of the system will control the expansion speed as $\frac{\ddot{a}}{a} < 0$
Questions

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*What is the original description of this theory by Lemaître and contemporaries?


*Will this cold neutron state be stable against collapse? How dense it should be?


*Is it possible to reach $~MeV$ temperatures and equilibrium?


*What would be the observable differences of this picture — i.e., why it was disproven?
 A: I've answered the questions I can below.


*

*@John Rennie already gave a link to Lemaitre's paper. Here's a summary from John Gribbin's The Scientists, on page 596-597:



...the Belgian astronomer Georges Lemaitre (1894-1966), who was also an ordained priest, independently published similar solutions [to those of Aleksandr Friedmann's] to Einstein's equations in 1927...this [and the discovery of redshift] implies a beginning to the universe - a concept...Lemaitre embraced whole-heartedly. Lemaitre developed the idea of what he called the Primeval Atom (or sometimes, the Cosmic Egg), in which all of the matter of the universe was originally in one lump, like a superatomic nucleus, which then exploded and fragmented, like a colossal fission bomb.



*According to the Challenges section of Wikipedia's article () 



Extensive searches for dark matter particles have so far shown no well-agreed detection; the dark energy may be almost impossible to detect in a laboratory, and its value is unnaturally small compared to naive theoretical predictions.
Comparison of the model with observations is very successful on large
  scales (larger than galaxies, up to the observable horizon), but may
  have some problems on sub-galaxy scales, possibly predicting too many
  dwarf galaxies and too much dark matter in the innermost regions of
  galaxies. These small scales are harder to resolve in computer
  simulations, so it is not yet clear whether the problem is the
  simulations, non-standard properties of dark matter, or a more radical
  error in the model.

A: Lemaitre was both a priest and a scientist, and his "primeval atom" or "cosmic egg", from which an "emergent universe" would have emerged, coincidentally accomodated the Aristotelian idea that time itself had no beginning (which had been adopted by Roman Catholicism about 1215 A.D.) within that dynamic view of the universe which currently prevails.
A religious origin for that cosmological model can be traced back, in Hindu philosophy, at least as far as 1200 B.C., so that Einstein's oft-cited 1927 remark to Lemaitre (that his math was great but his physical insights were "abominable") may have been a little harsh.
Nevertheless, Alexander Vilenkin and Audrey Mithani were able, in 2012, to produce a paper, visible at https://arxiv.org/abs/1204.4658, which showed that, although a "primeval atom" (or Big Bang potential) traceable back through all of past eternity would have remained stable under classical perturbations, it would have been subject to quantum perturbations, and, consequently, would "probably" not have made it to the present.  As neutrons are quanta, I believe this answers the OP's sub-question #2, although Vilenkin's answer is explicitly probabilistic and not categorical, and the sources he cites directly (which are not currently accessible to me) do not include Lemaitre.  He also specifies that he's using the "geodesic" equations of General Relativity (which differ from the "autoparallel" equations of the Einstein-Cartan Theory, developed soon after the discovery of particulate spin).
Neither of the two publications in the Wikipedia item "Cold big bang", to which the OP refers, cited Lemaitre at all. Gribbin's reference to a large nuclear explosion (cited in Heather's answer) reflected a change in Lemaitre's cosmological views which occurred late in 1931, which the commentator Luminet describes as the priest's "miracle year".  As remarked by John Rennie, the Big Bang did not happen at a point:  What most resembles an explosion is, in what's perhaps the most standard cosmology at the moment (field-based cosmic inflation), only the temperature of the Bang.  (That temperature is, in the version of inflation that's based on a hypothesized scalar field, the result of the hypothetical "inflaton" partices becoming photons as the rate of expansion drops below levels that had been increasing almost exponentially.)  So, in spite of their sharing of a common quality (heat), Lemaitre's imagined "cosmic egg" is not the same as the post-"Bang" inflationary fireball; also, if it does somehow exist, Luminet considers that it would be "several astronomical units" in size, which is vastly larger than that "false vacuum bubble" which is usually depicted as initiating field-based inflation.
I've read Lemaitre's November 1931 paper "L'expansion de l'espace" (available thru NASA, but only in French) putting forward the idea of the primeval atom, and he makes no reference to any specific temperature at all, so, at least in relation to the questions' title, the OP's sub-question #3 (about whether it's possible to reach "10 MEV temperatures and equilibrium") remains unanswerable.  (The paper did include a purely verbal description of nebulae passing out of equilibrium "in time", while specifying that such a passage would not necessarily occur "in space".)  A ping requesting clarification, sent about a week ago, has received no response, so I've deleted it from my public comments.
