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I would just like to put it out there that I do believe that the Big Bang was a cosmic occurance. However, I have been asked to argue the fact that there was a point in the past when the density of the universe was infinite.

I know that the best way to argue this point is by using the formula relating expansion rate (H) and energy density (ρ). This formula is: H^2 = (8πG)ρ/3.

In my opinion, I could go about this in two ways:

  1. The energy density is energy/volume, and so the way for density to = infinity is that energy is infinity. So there must have been a poing in time where the energy was infinitely large enough to create this expansion.
  2. Expansion rate = (8πG)ρ/3 where (8πG)/3 are all constants, and so if the expansion rate was to increase by an infinate amount, the energy density must be the only aspect of the formula that increases by that amount as well, thus implying that energy density was at one point infinate.
ScienceGirl1234
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  • Your #1 seems wrong: $\rho=\dfrac{E}{V}=\infty,\rightarrow,V=0; E\ne\infty$. – safesphere Oct 28 '17 at 22:28
  • Even without quantum gravity, I'd say density never "was" infinite, but only asymptotically infinite at zero time. The concept of existence implies "existence in time". The present moment has a certain duration, however small, between the past and the future. Things "exist" in this brief duration. Therefore, nothing can "exist" at time=0 without the past. And then, at any point of time >0, however small, density already is not zero. Nothing infinite can exist in reality, as it becomes very clear after carefully reviewing the concepts of "infinite", "existence", and "reality". – safesphere Oct 28 '17 at 22:39
  • @safesphere. Your argument could be carried over to say volume was also never 0. But in GR indeed volume was zero at t = 0, and $rho$ was indeed infinite. That's why it's called a singularity, and it's reality or not will be determined, if ever, by some solution of the mystery of quantum gravity and how the universe started. – Bob Bee Oct 29 '17 at 05:47
  • And yes, @safesphere's first answer is right, it's volume that goes to zero. You'll have to argue how that can be so. The answer is that it does not start at a point, but at a region of infinite extent, everywhere in the then universe, which then has zero radius, and zero volume. From the RW metric, R is zero but all values of r and the angular coordinates exist cover the spacetime – Bob Bee Oct 29 '17 at 05:53
  • Btw, see a more complete answer at https://physics.stackexchange.com/questions/136860/did-the-big-bang-happen-at-a-point?noredirect=1&lq=1 – Bob Bee Oct 29 '17 at 06:04
  • @BobBee On your first comment above. To clarify, my argument is quantum, as you can see in my description of the "present moment" having a finite duration. For example if time went as 1 Plank time, 2 Plank times, etc., then there was never t=0, because the present is not a point, but a duration and 1 Plank time is not zero. Also, the argument that nothing purely "infinite" or "infinitesimal" can exit in reality is more fundamental than any particular theory, so one doesn't need quantum gravity to rule out "real" singularities. – safesphere Oct 29 '17 at 06:18
  • Let us continue this discussion in chat. – safesphere Oct 29 '17 at 06:19
  • @BobBee Please ignore the chat thing - a touch screen gone bad :) – safesphere Oct 29 '17 at 06:21
  • @BobBee On your second comment above. I am not claiming V=0, but merely pointing out the OP's error that the infinite density does not translate to the infinite energy for a point-type Big Bang. I am familiar with the "Infinite Big Bang" model, but do not endorse it, because it is singular for mass/energy (among other things) and thus non-physical. If the flat space condition makes FLRW singular, then FLRW is not an applicable model. The Milne model has been ruled out for being singular and so should the "Infinite Big Bang" FLRW. – safesphere Oct 29 '17 at 06:38
  • @safesphere. I was not talking about an infinite Big Bang, also called the Big Bounce (which infinitely repeats). i am simply pointing out that if you exclude quantum gravity (or whatever you call the physics at Planckian scales, which is required to explain anything further back that about $10^{-32}$ sec after the Big Bang) cosmology is the FLRW model with some known and very small non-isotropic and non-homogeneous, and FLRW, with $\Lambda CDM is the standard model of cosmology. For that the fact is that Volume approaches to zero at t=0, density to infinity, and a singularity.No need for chat – Bob Bee Oct 29 '17 at 20:05
  • Oh, and spacetime extends infinitely over all values of the coordinates, and is infinite, meaning no edges, no end. I'm not claiming anything new or interpretative, just what the model says. Most physicists (probably) think that there is new physics we don't know as we approach that time, and what the truth is nobody knows. – Bob Bee Oct 29 '17 at 20:10
  • @BobBee Understood. However, the link you've sent claims the infinite initial volume of matter with an infinite density and infinite total mass. This is not a physical solution. If it is the current consensus, then the consensus has lost its way and Earth is flat again ;) Also, I don't feel I'm getting my point across that time was never zero. Continuous manifolds are a nice math abstraction, but they are not physical. Nature is quantum. If you count time in Plank's quantums, the first one is t=1, not zero. So nothing is infinitely large or infinitely small. Only "very", but not "infinitely". – safesphere Oct 29 '17 at 21:19
  • I'll check the link. Anyways on 0 time, you have to think like a physicist. We don't know t =0, but t approaching zero is pretty clear. So is or approaches in some cases be taken as approximately the same in physics. In that sense density is infinite, volume 0, but mass is very little different than a little after, and not infinite. Books on GR, in the FLRW analysis show it. – Bob Bee Oct 30 '17 at 05:27

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