Was the universe is infinitely large at the big bang?

[Green dwarf]

My understanding is that the universe seems quite likely to be flat, and therefore infinite. Following an infinitely large object back in time to the big bang, it would never become finite. (However many times you divide infinity by 2, it is still infinity.)
We tend to picture the big bang as something starting smaller than an atom. But that would be just our observable universe. The whole universe, (the totality of matter, the omniverse?) would have to have been infinitely large always.
Am I misguided here?

 

[weirdoguy]

We tend to picture the big bang as something starting smaller than an atom.

No we don't. It's a common misconception. The answer to your question is yes, if Universe is spatially infinite now, then it was during the BB.

 

[Green dwarf]

Thanks weirdoguy. Could you enlarge on the 'No we don't', because that surprised me. Was our observable universe not at some time very small?

 

[DaveC426913]

We have tracked universe's evolution back to a very hot, very dense volume many, many orders of magnitude smaller than an atom. Our physics is consistent back to that point, yes.

 

[Bandersnatch]

My understanding is that the universe seems quite likely to be flat, and therefore infinite

This does not necessarily follow, in case the universe has some exotic topology. For example, a torus is intrinsically flat, but finite.
Other than that, you're not misguided - as weirdoguy said, if the entire universe is infinite now, then it must have been infinite always.

No we don't. It's a common misconception.

If you read the sentence that immediately follows, you'll see the OP was referring to the observable universe only. Which is correct.

 

[weirdoguy]

If you read the sentence that immediately follows, you'll see the OP was referring to the observable universe only. Which is correct.

Yes, of course. I misunderstood the OP

 

[pinball1970]

We have tracked universe's evolution back to a very hot, very dense volume many, many orders of magnitude smaller than an atom. Our physics is consistent back to that point, yes.

I cannot equate that with still being spatially infinite, am I missing something?

 

[PeroK]

I cannot equate that with still being spatially infinite, am I missing something?

It's just the difference between the observable universe (which can be given a size) and the spatially infinite universe, which can be given a density, but it's size is always infinite.

 

[pinball1970]

It's just the difference between the observable universe (which can be given a size) and the spatially infinite universe, which can be given a density, but it's size is always infinite.

Thanks Perok. Not the simplest concept in the world for me to try and visualise.

 

[PeroK]

Thanks Perok. Not the simplest concept in the world for me to try and visualise.

Mathematically it's quite straightforward. But, physically, it does seem paradoxical. Not just the expansion, but the concept that space, matter, galaxies go on for ever.

 

[pinball1970]

Mathematically it's quite straightforward. But, physically, it does seem paradoxical. Not just the expansion, but the concept that space, matter, galaxies go on for ever.

Mathematically straightforward to you fresh 42 Dale Phinds and others is a tad daunting to me. That's why I'm here though.

 

[PeroK]

Mathematically straightforward to you fresh 42 Dale Phinds and others is a tad daunting to me. That's why I'm here though.

$\mathbb{R}^3$ shouldn't be too difficult a concept, mathematically. After all, if the number line is not infinite, then there must be a largest number. But, how can some number $N$ be the largest? You can always add $1$, surely, to get $N+1$.

So, $\mathbb{N}, \mathbb{R}, \mathbb{R}^2, \mathbb{R}^3$ must all be infinite in size.

In that sense, an infinite flat universe shouldn't be a particularly difficult concept.

But, these infinite mathematical sets have certain properties that make them conceptually difficult as a model for the physical universe. You get ideas like the Bolzmann Brain, for example, which may be a paradox; or may be sheer nonsense! But, in an infinite universe, these paradoxical issues are difficult to ignore.