# 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.

• Seriously, downvoted? Why would someone downvote this Commented Oct 25, 2021 at 12:33
• Hi Jack, I'm having troubles understanding what 20 Glyr you're referring to. Our past light cone extends ~43 Glyr from us at time 0, not 20, no? Anyway, as Eduoard says those are comoving coordinates — to convert those to physical coordinates at time $t$, you must multiply by the scale factor $a(t)$ at that time $t$. The scale factor is a way to describe the expansion of the Universe, and is defined to be 1 today (implying that today, physical and comoving coordinates are the same, by construction), and 0 at time $t=0$. That's why in physical coordinates you get the teardrop shape.
– pela
Commented Nov 9, 2021 at 14:17
• Although I think my answer's valid, maybe I should've suggested an edit of the OP's question, rather than writing it: The vertical line designated as "20" glyr (20 billion light years), in Pela's answer to the previous question, is the nearest vertical line, in the diagram used in that answer, to the point in spacetime where the past & future light cones meet, which represents the present moment at our own location in space. What my answer's saying is that, if Penrose's model is as valid as the Nobel Committee seems to think it might be, we can't actually know "when" we are, in all of time. Commented Nov 11, 2021 at 20:04
• Not sure where to put my responses really, but: I must have had a Freudian slip of a separate question in my mind of that point nearest to 20glyr where the particle horizon and past light cone seem to intersect. I certainly have more questions about that but won't get into them now. I actually meant that spot at about 40glyr and 60glyr where the past light cone and event horizon meet time zero. I think it arose from a confusion I had about comoving distance, I was taking it to mean something that was literally 40 glyr at t=0 could reach us by now, which seemed like too much for light to travel Commented Nov 14, 2021 at 15:31
• In any case, I think I have it now, the comoving distance is not actually a real measure of distance, but instead with inflation factored in? I actually have another question, which is that in that diagram with the teardrop past light cone, is that essentially saying if you looked out with a telescope now to that distance, you would see what was there at the time corresponding to that point on the line. In other words, is everything we can currently see ONLY ON that teardrop line, or is it WITHIN it? Commented Nov 14, 2021 at 15:39

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.

• What all this boils down to, is that Davis & Lineweaver may have included a conformal diagram because the problems with the origin of most versions of inflation were known months before their 2003 paper. Commented Nov 9, 2021 at 2:47
• What the Borde-Guth-Vilenkin Theory does require, is that the worldline of a GR-based universe (either a local "Universe" within a multiverse, or a single universe possibly divided into temporal iterations) that is "on average expanding" must have a beginning: In the Aguirre & Gratton model, the expansion averages zero, and in Penrose's model, the duration of the temporal iterations may vary, with their average no more ascertainable than anything infinite. (Infinity is a concept or symbol, but not a number.) Poplawski's model, based on Einstein-Cartan Theory, differs from any GR model. Commented Nov 9, 2021 at 12:15