I think this is an interesting question; but I also think one should define what exactly is meant by 'the centre of the universe', 'circumference of the universe', 'nowhere', 'entire universe' before we can really assign a meaning to it in a way that permits a rationalist answer!

@zzen

Good question

Some cosmologists believe that our observable Universe and its cosmological horizon (or three times that for the particle horizon)  is all there is .

Far from it, the observable universe is only a small part of the whole and therefore our observable Universe appears relatively homogenous and of course "flat".

However, there can be a center where the actual Big Bang occurred.

Equally the Circumferenace is vastly bigger than the observable universe and can be claculated at as having a radius some 600 times bigger than that of our observable Universe and undoubtedly not a  perfect shere (probably more like a crab nebula.

If you wish I can demonstarte where this figure derives from.

@Amrit

Well  once upon a time the Earth was Euclidean and "flat" as far as scientists were concerned.

NASA is just making the same mistake!

"Flat" in this context means that over large scales, space is close to Euclidean, not a 4-dimensional saddle or a glome.

@Dishman

We all know that,

But flat in this case is the same mistake we made with the Earth being flat- it may appear that our observable part of the Universe appears flat.

But then take into account our entire Universe

Andrew, you need to consider what other people will take from what you write. You said

• "Well  once upon a time the Earth was Euclidean and "flat" as far as scientists were concerned."

Well first, that is a myth anyway, see the first link.

In that sense, it means a two dimensional surface and there are seem to be many people on this site who know little of cosmology and might take that as meaning the universe was like the thin disc of our galaxy with the content in a narrow 'plane'.

AW: NASA is just making the same mistake!

The best current result is from the Planck Mission which was run by ESA, nothing to do with NASA. The 2015 results show curvature less than 0.005 (second link) with a mean of 0.0001 (Table 5, column 3) so that allows slight positive or negative curvature as well as perfectly flat. Using the assumption of flatness is a working hypothesis based on Ockham's Razor, no measurement can ever be without some uncertainty.

Of course you are right, that is only a sample from the observable universe, not the whole but that's all we can ever measure by definition, so using that as a working value is not going to give errors in any other observable.

If you want to ask questions like "is the universe finite or infinite" which depends on the sign of the curvature then the chances are we can never answer it.

https://en.wikipedia.org/wiki/Myth_of_the_flat_Earth

http://xxx.lanl.gov/abs/1502.01589

@Dishman

Thanks, curvature less than 0.005. All that means that our entire Universe is at leaast 200 times bigger than the obsevable universe.

@Zzen/Dishman

So you are quite right. But it is precisely the measure of flatness that wiil give is the size of the entire Universe

The trouble though Andrew is that if you think of the dimples of the skin of an orange, if you can only measure a small area, you might happen to be in the saddle between two dimples and measure negative curvature when overall it is positive, and vice versa, you could be measuring a local convex bump in an overall saddle shape so get a positive result when overall it is negative.

That's why I think we can only ever know what the local region is and never confirm the overall curvature by observation.

@Dishman

Dimples pimples, we might have to take the overall result as a best guess.

The point is,  we cannot say it is "flat" with certainty.

Otherwise we would be making the same mistake as they did in  the 15th century.

@Dishman

P.S.

Wiki dosn't mnetion this.  But there is still a flat Earth society going strong even today.

Yes the center ,is arbitrary anywhere and the distance to horizon is infinite

Article The Infinite Distance Horizon and the Hyperbolic Inflation i...

AW: The point is, we cannot say it is "flat" with certainty.

The point is, nobody in the scientific community has said that it is falt with certainty, that is a strawman argument. The Planck results are currently our best measurement and they have an uncertainty 2 orders of magnitude larger than the value. That means in any serious work we hav to allow for open, flat or closed and I suspect that will always be the case.

AW: Wiki dosn't mnetion this. But there is still a flat Earth society going strong even today.

I'm aware of that and it may have been a lay understanding for a long time, but that's very different from your previous claim:

AW: "Well once upon a time the Earth was Euclidean and "flat" as far as scientists were concerned."

@ Dishman.

All good points.

But, it is stil under-emphasised that just because it appears almost flat to us - does not make it at all flat, especially if the Universe were on a far larger scale than we humans can imagine.

I think if you read scientific papers, there is no assumption of flatness beyond Ockham's Razor but I do agree that the popular press, especially the click-bait web sites, can just ignore the science in favour of eye-catching headlines.

Cosmologists tend to adopt a pragmatic flat assumption, hence spatially infinite, since it can only introduce at most 0.5% error into equations that are seldom within an order of magnitude of that. I think QM people assume a closed but low curvature universe because that avoids the problem of including "boundary conditions" in an infinite universe, one that is finite but wraps round can be handled.

Indeed if inflation is right, your figure of "200 times" might be a few dozen orders of magnitude too small, and that would be very hard to distinguish from infinite ;-)

@dishman 

Indeed far too small,

Initial claculations show a Universe which has a volume of 300 million times our observable Universe, That is however only a radius which is 600 times larger than the 13.7 bn ly, which sounds more realstic.

I'm not sure where your volume comes from but bear in mind that the observable universe has a diameter of 93 billion light years (comoving distance, i.e. "now"). The figure if 13.8 billion years is the age, not a distance.

@ Yes I know

and the particle horizon is 41.1 bn ly

and a cosmological horizon of 13.7 bn ly, which is it s age

"13.7 bn years", not "13.7 bn light years"

Maybe it's just a typo.

And this is an important point 

The age is 13.7 bn years

The cosmological horizon is 13.7 bn ly

The mass is 10^53 Kg

The radius of the cosmological horizon is 2GM/c^2 = Rs

Is the Schwazschild radius. 

AW: The age is 13.7 bn years

Correct, or maybe closer to 13.8 billion.

AW (previously): and the particle horizon is 41.1 bn ly

AW: The cosmological horizon is 13.7 bn ly

No, that's the age. The particle horizon is around 47 billion light years (41.1 billion is in the same ball park) while the cosmological event horizon is less than 6 billion light years. There is no horizon at 13.7 billion light years.

AW: The mass is 10^53 Kg

That's the observable mass only of course.

AW: The radius of the cosmological horizon is 2GM/c^2 = Rs Is the Schwazschild radius. 

That would be the Schwazschild radius if the universe were described by the Schwazschild metric. It isn't.

@ Dishman

As regards your cosmological event horizon is concerned I think  you have got your pc and your ly  mixed .

As given by

The particle horizon differs from the cosmic event horizon, in that the particle horizon represents the largest comoving distancefrom which light could have reached the observer by a specific time, while the event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future.[3] The current distance to our cosmic event horizon is about 5 Gpc, well within our observable range given by the particle horizon.[4]

In general, the proper distance to the event horizon at time {\displaystyle t}is given by[5]

{\displaystyle d_{e}(t)=a(t)\int _{t}^{t_{max}}{\frac {cdt'}{a(t')}}}

where {\displaystyle t_{max}}is the time-coordinate of the end of the universe, which would be infinite in the case of a universe that expands forever.

For our case, assuming that dark energy is due to a cosmological constant, {\displaystyle d_{e}(t_{0})

Yes, you're right, I was rushing. 5Gpc is around 16G light years. The point remains though, the figure of 13.7 billion only applies to the age in years, it's not a significant number as a distance. I have the impression that the age is what you meant anyway or did you mean something else.

No 13.7 bn ly is effectively the schwarschild radius of the observable Universe for its given mass

Which has huge implications, which nobody seems to have understood.

It has no implications at all, the universe is not described by the Schwarzschild metric.

@ Dishman

I repeat.

The schwarschild radius is however the exact value for the cosmological event hrozon given the Universe's mass. And that has a good deal of significance.

An important fact overlooked by almost all.

Not really 'overlooked', I've seen many people asking about it, usually in the context of "is the universe a black hole". For that I suggest they read the old physics FAQ from Usenet, link attached.

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html

According to Kapila, the founder of Samkhya Philosophy, there are infinite number of Purusha (souls) with infinite number of circles running through the universe.

https://en.wikipedia.org/wiki/Samkhya#Philosophy

To understand this in the context of modern cosmology, you need to bring into discussion, the Observer of General Relativity. Each observer constitutes a center and since non of the observer has found a limit to how far he can see in the universe, we have to admit that the circumference of their universe is nowhere. Now the Samkhya philosophy admits multiple Purusha (Observers), but Vedanta philosophy proposes an unity underlying all observers, because infinity can only be one and not many.

Complete Works of Swami Vivekanada, vol.2, p.452--462.

https://www.google.co.in/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=swami%20vivekanand

a%20complete%20works

Following theory discusses the implications of the above arguments in the context of modern cosmology.

Article Unified field of consciousness

VZ: ... you need to bring into discussion, the Observer of General Relativity.

The observer in relativity is a grid of inanimate clocks and rulers that allow coordinates to be assigned to events. It's a shame that people who don't study science are led to imagine that the term "observers" has anything to do with "people", it causes a lot of confusion.

VZ: .. infinity can only be one and not many ..

Your philosopher needs to learn about Cantor's Theorem.

https://en.wikipedia.org/wiki/Cantor%27s_theorem