Big bang occuring everywhere vs everything "compressed"

Hi
I am trying to reconcile the concept of the Big Bang of occurring "everywhere" (an infinite Universe) - v - the concept of the origin of the Big Bang occurring in a particular compressed state and then expanding?
Thanks
Martyn Arthur

What needs reconciling? In an infinite universe the density is the same everywhere (ideally) and simply increases towards infinity as you run time backwards towards the initial singularity.

It depends on whether you embed the Universe in more dimensions. Consider a balloon being expanded. If only the rubber surface exists, there is no dimension that includes a "center". That is the image that a bug on the rubber surface would have. If you want to include another dimension, as we see it, there is a center point. But in the currently favored physics of the Universe, there is no justification for adding dimensions that would include a "center".

CORRECTION: The above is only valid for a finite, curved Universe. Current theory is that the Universe is infinite and flat. (thanks, @PeterDonis )

Moderator's note: Thread moved to Cosmology forum.

Martyn Arthur said:

TL;DR Summary: I am trying to reconcile the concept of the Big Bang of occurring "everywhere" (an infinite Universe) - v - the concept of the origin of the Big Bang occurring in a particular compressed state and then expanding?

... the Big Bang of occurring "everywhere" (an infinite Universe) ...

Just to clarify that the Big Bang occurred everywhere regardless of the universe being infinite or not.

FactChecker said:

Consider a balloon being expanded.

This analogy only works for a universe that is spatially finite. Our best current model of our universe says it is spatially infinite and spatially flat. For such a universe there is no way of embedding it in a higher dimensional space such that there is a "center" in that higher dimensional space (and physically, we have no evidence of any such embedding anyway).

Thank you; I think that there is not a subject that I can deal with at my current level of "understanding" lack of "physics" understanding.
This requires me to progress to my next leveL of my degree and look at stuff from that context.
As such my question is fully satisfied!
Thanks to all as always!
Martyn Arthur

Assume the Universe is infinite and isotropic (the same density everywhere). Then it has an infinite amount of mass. The density is then an infinite amount of mass divided by an infinite amount of space. No number can be calculated in this way. However we can measure the density directly. If the density decreases then we say the Universe is expanding.

The only way a finite universe can become infinite is to expand at an infinitely fast rate. This seems nonphysical. So if the Universe is infinite now then it was always so. No matter how dense the Universe may have been it was still infinite in extent.

Hornbein said:

The only way a finite universe can become infinite is to expand at an infinitely fast rate. This seems nonphysical.

I believe the same thing, however, I seem to understand that, in the link below, Alan Guth says that it is possible that the universe started out finite and became infinite. Isn't that what he says?

Jaime Rudas said:

I believe the same thing, however, I seem to understand that, in the link below, Alan Guth says that it is possible that the universe started out finite and became infinite. Isn't that what he says?

He's saying that from the "outside" it's finite in space but on the inside appears to be infinite in space.

Such things are beyond my pay grade. But I would guess that on the inside -- where I suppose we are -- it always appears infinite.

I believe the model Guth is describing in the video is the basic eternal inflation model that he also describes in Section 2.1 of this paper:

https://arxiv.org/abs/hep-th/0702178

The paper appears to show the individual "pocket universes" as spatially finite, but I'm not sure that's actually required by the model. I think we have had other PF threads on this general topic.

It is worth noting, also, that our current evidence does not rule out the possibility that our universe is spatially finite, just much larger than our observable universe. I believe some inflation proponents, at least, view inflation as predicting that we will eventually find that our universe is spatially finite.

PeterDonis said:

I believe some inflation proponents, at least, view inflation as predicting that we will eventually find that our universe is spatially finite.

Finite and closed, like textbook FLRW? Or finite with a boundary?

Ibix said:

Finite and closed, like textbook FLRW? Or finite with a boundary?

It's hard to tell. Many discussions of inflation involve bubble nucleation, where a bubble of post-inflation spacetime forms and expands, which, at least to me, implies an expanding boundary between the bubble and the inflating region. However, I've also seen discussions that appear to be saying that an individual bubble is spatially closed, with 3-sphere topology and no boundary. I have not found a definitive description of a model that resolves this, but there is a lot of literature in this field that I have not read.

Thanks for continuing the dialogue; I hope my maths etc level gets to what you guys know. Cliff Richards is 82 and going strong, at my age 72 I so hope to get to your levels by 82.
thanks
martyn

PeterDonis said:

I believe some inflation proponents, at least, view inflation as predicting that we will eventually find that our universe is spatially finite.

I think the point here is that for the universe to be infinite requires spatial flatness before inflation. But that seems to be a matter of speculation, perhaps forever.

timmdeeg said:

I think the point here is that for the universe to be infinite requires spatial flatness before inflation. But that seems to be a matter of speculation, perhaps forever.

Why couldn't it be hyperbolic?

martinbn said:

Why couldn't it be hyperbolic?

As far as I understand it inflation flattens any curvature to a high extent.