What Would an Infinite Universe Look Like at the Time of the Big Bang?

[Backwoods]

Several books have indicated that the Universe was infinite at the time of the BB. This was in "Gravitation" by Misner, et al., as an excercise. This would only be true, according to Misner, with the flat and hyperbolic solutions to GR, not with the spherical solutions.

What would the Universe look like at the time of the BB if it is inifinite? If it is finite, a point or little tiny ball would seem a likely shape to imagine, but an infinite BB gives me some trouble. Would it be an infinite sheet, two dimensions, no thickness? Could such a sheet be folded? Would it have to have a thickness?

Or am I missing something?

 

[Chronos]

It is unknown how large the universe was when the BB occured. It may have been infinitely large, and this is impossible to rule out. The laboratory available to us is the observable universe. That part appears to be finite.

 

[Backwoods]

Thank you Chronos for the prompt reply.

I was actually hoping for a different answer, as yours makes it a little more difficult for me to understand the current cosmological paradigm.

Talking about the Universe being infinite seems popular right now, with Max Tegmark talking about it with an infinite number of duplicate Earth's, and with NASA having a web page talking about it as well. There seem to a number of scientists who talk as if the Universe being infinite is a good assumption. Anyway, the following is a list of some of the points that I think reflect the current scientific consensus, although I cannot find any knowledgeable scientist discussing them.

I would look forward to any corrections or comments.

o The FRW metric allows for three solutions to the GR equations. Only one, the spherical solution, result in a Universe that is of finite volume. The other two, the flat and hyperbolic, are both infinite in size.

o Inflation results in a Universe that is still of finite volume, but is large enough to appear flat locally.

o The infinite solutions, the actual flat Universe and the hyperbolic Universe, are infinite in size at the time of the BB. This is quite surprising to me, as I have never heard of discussion of this point, and only came across it in an exercise in a textbook. I do not recall seeing it here in PF, for example, but you probably do.

o My "visualization aid" of thinking of the infinite BB as an unbounded two dimensional sheet, very hot and dense, is a legitimate description of the event.

o The current state of knowledge in Astronomy is that the Universe is close to flat, yet it is still impossible to tell which, if any, of the above three solutions to GR apply. That is we still do not know if the the Universe is flat and infinite, or near-flat and not.

Most of my life I have heard of the BB described as either a point, or Planck length, which is dense but finite, and then which expands. This is substantially different then a sheet with an infinite mass and dimensions, which then expands. It would also seem to result in a different set of theories about the origin of the BB. So, the following question seem relevant.

o The current discussion of the Hartle-Hawking theory of the origin of the BB talks of uncertainty and quantum fluctuations. Do the Uncertainty Equations allow for a quantum fluctuation that is infinite in both size and energy?

o If not, does that inability to use the Uncertainty Principle in Cosmology negate all such theories in the case that the Universe is either flat or hyperbolic?

There would seem to be quite a few questions about a BB with infinite size and mass, however I am just trying to find out if I am on a Snipe Hunt here.

Allow me to thank you for your many informative postings over the years, it has been an fascinating education.

 

[DevilsAvocado]

There would seem to be quite a few questions about a BB with infinite size and mass, however I am just trying to find out if I am on a Snipe Hunt here.

[Disclaimer: I’m only a layman]

Hi Backwoods,

This question is on my mind as well. I had a long and https://www.physicsforums.com/showthread.php?t=170056&page=8" with Dmitry67 & Gan_HOPE326, and I'm afraid it all boils down to mathematics in the end. (Dmitry67 if you read this, I will get back to you when I get the time to solve the equations.)

I think we have to sort out some 'facts', before continuing:

Local geometry
Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is used as a model for the local geometry, i.e. the observable universe, with a diameter of about 93 billion light-years (and remember; observable universe = calculated visible universe).

A light ray (red line) can travel an effective distance of 28 billion light years (orange line) in just 13 billion years


Global geometry
Global geometry covers the geometry of the whole universe - both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities.


Omega (Ω)
In FLRW the density parameter Omega (Ω) is related to the curvature of space (all forms of dark energy are ignored).

Ω > 1 positive curvature, spherical universe
Ω < 1 negative curvature, hyperbolic universe
Ω = 1 zero curvature, flat universe


Special relativity
FLRW is an exact solution of Einstein's field equations of general relativity. On the other hand, from the point of view of special relativity, speaking of "the shape of the universe" (at a point in time) is difficult due to the relativity of simultaneity. Thus you cannot speak of "the shape of the universe at some point in time", however with a chosen set of comoving coordinates this is possible, and is widely accepted in present-day cosmology.

Views of spacetime along the world line of a rapidly accelerating observer, moving in a one-dimensional "universe"

Even if Chronos points out that "the laboratory available to us is the observable universe", it seems to be an 'open question' whether the global geometry may or may not be within our ability to measure.


Using Occam's razor
(I must stress that this is my most personal view of the problem!)
We have already in the observable universe a problem with the 'propagation' of CMB (and the physical laws) to parts that never have been connected (due to speed of light). A solution to this problem is cosmic inflation, during early stages of BB.

Now, this leads to severe difficulties in an infinite BB. As I discussed in https://www.physicsforums.com/showpost.php?p=2462473&postcount=113" that initial inflation may be a solution, but it must be described using the Quantum Gravity theory, which is not ready yet.


Layman’s conclusion
If and when the Quantum Gravity theory is completed, we will get a much better chance to find the right answer. Either quantum gravity inflation can handle 'infinite propagation' of the physical laws comfortably, or it cannot.

The final solution for this problem will be TOE. If there is no explanation of 'infinite propagation' of the physical laws in TOE - BB and the Universe must be finite! (I think )

 

[xantox]

Several books have indicated that the Universe was infinite at the time of the BB. This was in "Gravitation" by Misner, et al., as an excercise. This would only be true, according to Misner, with the flat and hyperbolic solutions to GR, not with the spherical solutions.

What would the Universe look like at the time of the BB if it is inifinite? If it is finite, a point or little tiny ball would seem a likely shape to imagine, but an infinite BB gives me some trouble. Would it be an infinite sheet, two dimensions, no thickness? Could such a sheet be folded? Would it have to have a thickness?

Or am I missing something?

It is not known if the universe is finite or infinite. Observations combined to current models allow both cases. If the universe is finite, then it started finite at the big-bang. If the universe is infinite, then it started infinite at the big-bang (meaning infinite 3-dimensional space).

 

[Backwoods]

Thank you Xantox and DA for your replies. DA thanks for your visuals, always a good way to teach.

It seems that the infinite universe at the BB is notoriously well-known to the Art.

DA, I went to your referenced previous postings and am working my way through them. The math is always the best part of these discussions, IMHO. Some thoughts generated by initial inspection of your discussions.

o I got to do better research. Rats.

o It seems that the idea of an infinite BB being a two dimensional hot sheet is wrong, we are talking of an infinite three dimensional space totally filled with energy denser then the average black hole. That is one VERY impressive phenomenon. And the relevant equations and observations remain consistent with this. I can see why everybody ignores two of the three solutions to the FLRW metric.

o The propagation of the CMB in an infinite universe bothers me somewhat less then it does you. The current crop of Monster Minds (Richard Feynman definition) talks of 11 dimensions in string and quantum theory. It would seem that with that many dimensions available to play around with, it should be possible to get a nice, homogeneous, infinite BB out of it somehow. As what everybody says seems right, we have to wait for Quantum Gravity.

o It is quite interesting that the PF Science Advisers seem to shun this subject, as they vary from brilliant to OMG! The reason for this avoidance could range from being tired of the subject, to somebody's theory being gored, to it adding another layer of difficulty to an explanation for the BB which is already over-the-top complex.

o I am going with the avoidance of this as an infinite big bang negates all concepts and discussions about the BB starting because of a "quantum fluctuation." A quantum fluctuation is better then Professor Guth's "free lunch," but it still does not seem all that rigorous.

My prior state seems to stand, so far, uncorrected. That is, it is impossible for a quantum fluctuation to create an infinite space with infinite energy. The equations of Uncertainty Principle disallow that. Thus, theories such as the Hartle-Hawking discussed in these Forums would not apply with a flat or hyperbolic Universe.

 

[DevilsAvocado]

Thank you Xantox and DA for your replies. DA thanks for your visuals, always a good way to teach.
...
I got to do better research. Rats.
...

Backwoods,
You're welcome.

For the research, here’s a little something to begin with:

http://en.wikipedia.org/wiki/Special_relativity
http://en.wikipedia.org/wiki/General_relativity
http://en.wikipedia.org/wiki/Universe
http://en.wikipedia.org/wiki/Expanding_universe
http://en.wikipedia.org/wiki/Big_Bang
http://en.wikipedia.org/wiki/Big_Bounce
http://en.wikipedia.org/wiki/Brane_cosmology
http://en.wikipedia.org/wiki/Causal_contact
http://en.wikipedia.org/wiki/Cosmological_Principle
http://en.wikipedia.org/wiki/Fine-tuned_universe
http://en.wikipedia.org/wiki/FRW
http://en.wikipedia.org/wiki/Galaxy_filament
http://en.wikipedia.org/wiki/Spacetime_singularity
http://en.wikipedia.org/wiki/Horizon_problem
http://en.wikipedia.org/wiki/Hubble_Ultra_Deep_Field
http://en.wikipedia.org/wiki/Infinity
http://en.wikipedia.org/wiki/Lambda-CDM_model
http://en.wikipedia.org/wiki/Large-scale_structure_of_the_cosmos
http://en.wikipedia.org/wiki/Loop_quantum_gravity
http://en.wikipedia.org/wiki/Lorentz_transformation
http://en.wikipedia.org/wiki/Schwarzschild_metric
http://en.wikipedia.org/wiki/Shape_of_the_Universe
http://en.wikipedia.org/wiki/Physical_cosmology
http://en.wikipedia.org/wiki/Quantum_field_theory
http://en.wikipedia.org/wiki/Quantum_electrodynamics
http://en.wikipedia.org/wiki/Quantum_gravity