AG, if you’re postulating a closed universe, that’s entirely different from claiming an infinite universe contradicts high temperature at the Big Bang. It just means you're favoring a specific topology.
The problem is that your argument keeps shifting. Initially, you argued that an infinite universe contradicts high temperature at the Big Bang to saying a finite, positively curved universe is a possible model—which is trivially true but irrelevant to your claim. If your point is just "a finite universe is possible," sure, but if you're still trying to argue that an infinite universe is incompatible with high density at early times, you haven't demonstrated that at all. Quentin Le mer. 12 févr. 2025, 21:03, Alan Grayson <[email protected]> a écrit : > > > On Wednesday, February 12, 2025 at 12:49:19 PM UTC-7 Quentin Anciaux wrote: > > AG, you're shifting from claiming a contradiction to merely suggesting a > possibility, which is a step forward, but your reasoning is still flawed. > > The Cosmological Principle states that the universe is homogeneous and > isotropic on large scales, but that does not mean "if the observable > universe is finite, then the entire universe is finite." That’s a > categorical error. The observable universe is just the portion of the > universe we can see due to the finite speed of light. Its size has no > bearing on whether the universe as a whole is finite or infinite. > > Your assumption that high temperature implies a very small global volume > is only valid if the universe was already finite. If the universe is > infinite now, it was infinite at the Big Bang, just in a state of uniform > extreme density. An infinite universe can still be compressed arbitrarily > while remaining infinite—density increases, but spatial extent doesn’t > shrink to a finite size. > > You say I "rely on one metric," but the FLRW metric isn't just a > convenient choice—it’s what general relativity and observational data > support. If you want to claim the universe was finite, you need a model > that explains why it would have a global boundary while still obeying > large-scale homogeneity. > > > I postulated a slightly positively curved spherically shaped univere with > no boundary, AG > > > So far, all you’ve done is assert that finiteness is "possible" without > providing a physical reason why it would be preferred. > > Quentin > > Le mer. 12 févr. 2025, 20:30, Alan Grayson <[email protected]> a écrit : > > > > On Wednesday, February 12, 2025 at 12:08:13 PM UTC-7 Quentin Anciaux wrote: > > AG, you're backpedaling again. You originally claimed that an infinite > universe contradicts high temperature at the Big Bang, now you're just > saying it's "possible" the universe was finite. Fine, but that’s not what’s > debated—the issue is whether an infinite universe must be contradictory to > high density, and it isn’t. > > > Please cease with accusations. I just see that stating a contradiction is > too strong, and I believe it is possible that the high temperature implies > very small volume. You're relying on a metric which allows your pov, but > that's just one metric. It doesn't prove that I am mistaken, or some > experts who claim the size of the universe decreases as we go backward in > time.. AG > > > The Cosmological Principle states that the universe is homogeneous and > isotropic on large scales. > > > And that it's the same everywhere. AG > > > This applies whether the universe is finite or infinite. Nothing about it > requires the universe to be finite. > > > It does, if the universe's observable region is finite, then the entire > universe is finite. AG > > > If the universe was spatially infinite at the Big Bang, it was just an > infinite, uniformly dense, hot state. The fact that the observable universe > shrinks as we go back in time doesn’t mean the entire universe had to be > finite. > > > I am just claiming it could be finite, and that would explain its high > temperature at or near the BB. The alternative is difficult to give > credence to --- that it's infinite *and expanding*, and remains infinite > as we go backward in time. AG > > > If you’re now saying finiteness is just "possible" rather than required, > then you’re conceding that your original contradiction doesn’t hold. So > what’s left of your argument? > > > What's left is that you can't categorically rely on one metric to assert > with finality what the physical reality might be. Apriori, hugely high > early temperature is consistent with very small volume. AG > > > Quentin > > Le mer. 12 févr. 2025, 20:04, Alan Grayson <[email protected]> a écrit : > > > > On Wednesday, February 12, 2025 at 11:49:23 AM UTC-7 Quentin Anciaux wrote: > > 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. > > > But this contradicts the Cosmological Principle (which might be wrong). AG > > > 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. > > > Although I posed it as impossible, but that's probably going too far. I > think It's possible that the entire universe is getting smaller as we go > back in time, and this accounts for its super high temperature at or near > the BB. AG > > > Quentin > > Le mer. 12 févr. 2025, 19:41, Alan Grayson <[email protected]> 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 <[email protected]> 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 <[email protected]> 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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