AG, your reasoning is flawed because it assumes a contradiction where none exists. An infinite universe doesn’t have to "become" infinite—it can be infinite at all times, just evolving in density and scale factor. High temperature and density at the Big Bang don’t require finiteness; they describe local conditions, not global topology.
Cosmological diagrams showing a "point" origin are simplifications based on the observable universe, not statements about the entire cosmos. The observable universe was smaller, but an infinite universe was never "shrinking" in the way you imply—just getting denser everywhere. You ask why it’s not even a possibility that finiteness is required for high density. The answer is that GR and the FLRW metric allow for infinite spatial extent at all times, even under extreme density conditions. There’s no physical principle preventing this, so the burden is on you to show why infinity at high density would be impossible. Quentin Le mer. 12 févr. 2025, 19:41, Alan Grayson <agrayson2...@gmail.com> a écrit : > > > On Wednesday, February 12, 2025 at 10:10:40 AM UTC-7 Quentin Anciaux wrote: > > > > Le mer. 12 févr. 2025, 17:55, Alan Grayson <agrays...@gmail.com> a écrit : > > > > On Wednesday, February 12, 2025 at 2:09:58 AM UTC-7 Quentin Anciaux wrote: > > > > Le mer. 12 févr. 2025, 09:55, Alan Grayson <agrays...@gmail.com> a écrit : > > If the age of the universe is finite, which is generally believed, then no > matter how fast it expands, it can never become spatially infinite, So,* > IF* it is spatially infinite, this must have been its initial condition > at or around he time of the Big Bang (BB). But this contradicts the > assumption that it was at a super high temperature at or around the time of > the BB. > > > AG, your assumption that a finite-age universe must be spatially finite is > flawed. If the universe is infinite now, it was infinite at the Big Bang, > > > That's what I wrote. AG > > just in a much hotter and denser state everywhere. The Big Bang wasn’t an > explosion from a point > > > I didn't assume that. What it actually is, or was, we don't know. But at > that time it was hugely denser and hotter than at present. AG > > > No, you initially framed it as a contradiction—"If it’s infinite now, it > must have been infinite at the Big Bang, but that contradicts the high > temperature assumption." That’s what was wrong. There’s no contradiction > between an infinite universe and high density. If you now accept that, > great, but don’t pretend that was your original point. > > > I assumed that if the universe were infinite, it couldn't have become so > in finite time, so IF infinite that must have been its initial condition. I > later added, in summary, or that's what I meant to do, that this is > contradictory to a super high temperature at the time of the BB. You claim > this is inconsistent with GR. Can you prove that? AG > > > Yet, your reasoning implicitly relies on treating the universe as if it > "shrinks" to a single location when run backward. A spatially infinite > universe was never "smaller" in an absolute sense—just denser everywhere. > > > Well, that's what all the diagrams of the evolution of the universe show, > that it becomes smaller as we go back in time, begins as a point, and what > I've heard or read what some cosmologists claim. AG > > > > but a transition from an extremely dense, uniform state, which applies > whether the universe is finite or infinite. > > Eternal inflation suggests the universe was already infinite before the > Hot Big Bang phase. > > > Sure, provided eternal inflation is occurring, but it's speculative, as is > my conclusion. Most cosmologists believe it was smaller in the past than at > present, as implied by present day expanson run in reverse. AG > > > No, they believe the observable universe was smaller. > > > Why just the observable region? AG > > > That doesn’t mean the entire universe was ever finite. > > > > The observable universe was once small and dense, but the entire universe > could have been infinite at all times. > > > Yes, COULD HAVE BEEN. I assumed, for the sake of argument, that it COULD > NOT HAVE *BECOME* INFINITE IN FINITE TIME, and THEN inferred what that > implied; namely, that it became infinite at the time of the BB. Also, if > you believe in the Cosmological Principle, if the observable universe was > finite, then so was the entire universe.AG > > Spatial flatness doesn’t imply finiteness > > > I didn't assume it does. In fact, I assumed the reverse, as do > cosmologists. I don't object to your criticisms, but you seem to be reading > me with a jaundiced eye. AG > > > > —flat, infinite universes expanding from a dense state are fully > consistent with general relativity. > > Does my conjecture conflict with GR, or is it also consistent? AG > > > Yes, if you’re implying an infinite universe can’t be dense at early times > or that it had to "become" infinite > > > I am assuming it couldn't become infinite in finite time, so, IF it is > infinite now, it had to BE infinite at the time of the BB. AG > > > > There’s no contradiction between a spatially infinite universe and high > density at early times. The problem isn’t with cosmology—it’s with your > mistaken assumption that high density requires finiteness. > > > My assumption isn't necessarily mistaken. Rather, it's another > possibility. AG > > > No, it’s mistaken. Assuming high density requires finiteness is a > misunderstanding of both GR and cosmology. > > > You claim it's not even a possibility. Why not? AG > > > Quentin > > > Quentin > > IOW, if we run the clock backward, the universe seems to get incredibly > small, and for *this reason* incredibly hot, roughly analogous to a > highly compressed gas. Therefore, it cannot have a flat global geometry, > since such a geometry is infinite in spatial extent. QED. 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