Why do some diagrams of the particle horizon, observable universe etc show the past light cone as hitting ~20glyr out from us at time zero? This question is mainly in reference to this question:
Is the observable universe equivalent to 'our' light cone?,
and the answer, which is great.
But what I can't wrap my head around is why the past light cone covers an area of around 20glyr comoving distance at time zero. Maybe it's just a misunderstanding of what comoving distance is. A related diagram, the first one, in the answer to this question: The future limit of the observable universe,
seems to make much more sense, where in that diagram the scale is proper distance rather than comoving distance. In that diagram the past light cone forms a sort of teardrop shape collapsing on the point at time zero and distance zero, which makes way more intuitive sense to me. I can't imagine that light occuring at time zero and at a distance of 20glyr "comoving" distance from the Earth would ever be able to reach the Earth, as I thought space was expanding too rapidly for that light to ever reach our event horizon.
 A: At https://arxiv.org/abs/astro-ph/0310808, you'll find three diagrams.  The top two diagrams have naturalistic cross-sections, and show the universe to have an area of zero at time zero.  The bottom diagram (the one Pela used in his good answer to the question in the 1st of the references you sighted) shows the universe diagrammatically and "conformally" (preserving angles but not lengths, and sometimes described as concerned with shapes but not with their sizes), and is compatible with the "Conformal cyclic cosmology" developed by Penrose in 2010, which starts from the assumption of a low-entropy beginning of the universe's current iteration (as, in his model, it has had an infinite number of iterations to the past, and will have an infinite number of iterations in the future).
A low-entropy beginning had, I believe, been more-or-less the standard assumption of cosmologists until the late 1980's, when Guth and others devised the inflationary model that has since become more-or-less standard (because of its resolution of such observational incongruities as "the horizon problem" and "the flatness problem", whose details I won't be discussing here).  The inflationary model relies on asymptotically exponential (i.e., nearly exponential) spatial expansion, and begins with extremely high entropy (extreme disorder, or the most disorder which can be wreaked by temperatures changing over an uncertain but phenomenally great length of time).
So, what you're basically asking is the purpose of the conformal diagram, but, first, let me lift a quote from Wikipedia to make sure we're on board about the other two diagrams, as the extremely important information provided by Lineweaver  and Davis (the physicists who designed these very widely-used diagrams) is, truly, one intimidating "wall of type":  I'll never know why they didn't throw in a couple of blanks or indentations.
Here's that quote:
"Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe. Comoving distance factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space (though this may change due to other, local factors, such as the motion of a galaxy within a cluster)."
Now comes the fasten-your-seat-belt moment:  The speed of light is the fastest speed at which anything can travel within its inertial frame of reference, but it is (rather unamazingly) not the fastest rate at which anything can happen.  If you read the linked Lineweaver & Davis paper (which is really very light on the math), you'll see that they agree with me that the expansion of the universe is something that happens, not something that travels, as "the universe" is already everywhere.  The expansion's more accurately described as a change in the scaling rate per unit distance, and the rapidity with which it can spread is unlimited.
So, what conformal time allows for are periods or (since they're not necessarily regular) durations, during which all particles having rest mass may evaporate, a la Hawking radiation, into bosons representing their energy, which leaves those intervals of indeterminate duration, as per the Heisenberg Uncertainty Principle's prevention of simultaneous knowledge of energy and time.  As clocks lacking any rest mass cannot be formed by any known process (either natural or artificial), it consequently appears possible that the universe may divide itself into temporal iterations, and that possibility is utilized by Roger Penrose in a 2010 cosmological model which allows for a single and unique universe to be characterized by eternality both to the past and to the future, with the maximum disorder that results in thermal equilibrium becoming the "Big Bang" of another iteration, possibly on the larger scale that you've noticed, or possibly on a smaller one.
I can't speak for the possibility that Pela might subscribe to that model, but, aside from the 2020 Nobel Prize in Physics that was awarded to Penrose, his model does allow for a low-entropy beginning to the universe, which I believe had been the case for most cosmological models prior to Guths's field-based inflationary model of the late 1980's, which has the advantage of explaining the so-called "horizon" and "flatness" problems, but seems to imply an unexplained source of high entropy at the Big Bang.  The Nobel award was not based specifically on Penrose's "Conformal cyclic cosmology", but occurred only months after a revision of a paper written by him in collaboration with several other physicists, which described "anomalous spots of significantly raised temperature", definitely observed within the Cosmic Microwave Background,  as evidence for that conversion of the mass of black holes into radiation which he and Hawking had hypothesized decades earlier:  It was awarded more ambiguously, for Penrose's work on black holes, which are generally expected to be the last massive objects to survive whatever complete decoherence of particulate matter might occur, and would consequently leave the universe in an equilibrium that, in his view, might be of indefinite duration.
His model is, incidentally, not the only one providing for that eternality to the past which most versions of field-based inflation deny:  Others include Poplawski's "Cosmology with torsion", also formulated in 2010 and generally considered to be a form of inflation not reliant on "inflaton" particles (which remain undiscovered), and the "Steady-state eternal inflation" (essentially two field-based inflationary multiverses separated only by a Cauchy surface, with passage thru time in each of them occurring in the direction opposite passage thru time in the other) that was formulated by Aguirre & Gratton between 2001 and 2002, and vetted as compatible with inflationary theory by Borde, Guth, and Vilenkin, in the last footnote to the last--2003's--version of their BGV Theorem, which is often misconstrued as prohibiting past-eternality in cosmology).  References to all these works can be found by the names involved, on Cornell University's Arxiv site.
