Discovering the Shape of Spacetime from the Big Bang: A Scientific Exploration

[AlbertE]

Howde all.

With reference to matter originating from the big bang. Nothing else. No multiverse, no pbranes - nothing. Just the Big Bang.

Ok - given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies.

Lets say now that you can hold this "shape" in your hand. What does it look like?

a) A donut?
b) A soccer ball?
c) A rugby ball/american football?
d) Saturn?
e) A spiral galaxy?
f) Science does not know?

Cheers all.

 

[ibysaiyan]

I think the general consensus is that it's shape is similar to a black hole , hyperbolic. Geometry is dependent on which model universe we are speaking of.. there are open/close systems...

P.S: Open system ( hyperbolic) has the following condition : k<1 , on the other hand a closed system (k>1) would collapse back to a singularity over the passage of time (cyclic universe model).

 

[AlbertE]

Ok - but which of my options would it most look like at this point in time - today - if I were able to hold all the matter in my hand in the shape it had come to form.

 

[Whovian]

First of all, this isn't the shape of matter in the universe. This is something topologically equivalent to the shape of space we're talking about. Also, these are just two-dimensional analogies for the shape of three-dimensional space.

Ok - given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies.

No.

But, again, let's assume you're wondering what the Universe is topologically equivalent to.

Science does not know?

That's pretty much it, though we have a good amount of evidence that the observable universe is flat.

A donut?

Assuming you're talking about a 3-Torus.

A soccer ball?

A rugby ball/american football?

The previous two are topologically equivalent.

Saturn?

Well, this would be two Universes, one topologically equivalent to a 3-sphere, one topologically equivalent to a ... something.

A spiral galaxy?

Too confused by what exactly you mean. There are a bunch of interpretations of what you said.

 

[AlbertE]

Hi Whovian.

Ok - today - right now - out there - there are galaxies.

If I wrapped the whole lot of them in a big cloth, that cloth would have a shape. Period.

Where am I going wrong :)

 

[Whovian]

The only thing you're getting wrong is assuming you could wrap all of them in a cloth (of course, assuming you could produce a large enough cloth, it would stand up to the enormous amount of energy being blasted into bits of it by GRBs and so on, and you would have an achievable way to wrap up the galaxies, all without disrupting them, but this is a though experiment.) While there is a limit to the size of the Observable Universe (I can't remember it, it was something like 40-something billion Ly,) we have no idea if the Universe itself is infinite. If it is, there's obviously no way to wrap the infinite galaxies up in a cloth.

 

[phinds]

Ok - given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies.

That is an unsupportable assumption. It MAY be true but most likely is not. The universe is almost certainly either infinite or finite but unbounded and in either case there is no "shape" such as you are looking for.

 

[AlbertE]

I disagree.

Yup - its a thought experiment - so I have strong and large bits of cloth :)

Ok - thinking along here...

We know the big bang occurred around 13.7? billion years ago.

If this is true - and I believe it to be the case, then unless it expanded at an infinite speed, it must be finite in size - this is not debateable and is absolutely set in stone.

As the above is not debateable, and we are happy with the timescales give or take - then there is no possibility of the matter being unable to form an outer shape.

Therefore there IS an outer shape which is formed by the fastest moving objects (as they are the outer objects).

LOL - still - where is this theory going wrong? I fear my convictions in simplicity are hindering my search!

 

[George Jones]

We know the big bang occurred around 13.7? billion years ago.

If this is true - and I believe it to be the case, then unless it expanded at an infinite speed, it must be finite in size - this is not debateable and is absolutely set in stone.

No, this is wrong. There are many situations to which everyday physical intuition does not apply. The Big Bang was not a place in space from which all matter emerged.

 

[phinds]

unless it expanded at an infinite speed, it must be finite in size - this is not debateable and is absolutely set in stone.

No, as George said, this is totally wrong. It happened everywhere at once, not a some point. You should check out the FAQ sticky in the cosmology section, or try this:

www.phinds.com/balloonanalogy

 

[AlbertE]

Sorry - "what" happened everywhere at once? There was at the beginning of time, no everywhere!

 

[Whovian]

Sorry - "what" happened everywhere at once? There was at the beginning of time, no everywhere!

The Big Bang happened everywhere at once. It did not start at a point and the Universe came into existence as the spherical explosion propagated outward. The Big Bang occurred at every point in space simultaneously.

 

[George Jones]

This may not be completely accurate, but it might be better to think along the lines of

Very good stuff guys.
But it started from a singularity.Which is a single point .Hence a center.

No, a singularity is not necessarily a single point. A singularity is usually more like an edge. In the case of standard cosmological models, this "edge" is located in all directions.

Of course the singularity is nothing but the most Super Massive Black Hole there ever was.

No, the cosmological singularity is not a supermassive black hole.

 

[AlbertE]

"The Big Bang occurred at every point in space simultaneously."

How big was space when the big bang occurred?

 

[George Jones]

"The Big Bang occurred at every point in space simultaneously."

How big was space when the big bang occurred?

Observationally, we can't pin it down, but but it is theoretically possible that space has always been infinite, and current observations are consistent with both finite and infinite space.

 

[AlbertE]

This would contradict the following statement - with which I was "brought up" as it were.

"Galaxies are flying apart, this means that at one time in the past, they were all together in one place".

Is the above statement no longer true?

 

[ibysaiyan]

This would contradict the following statement - with which I was "brought up" as it were.

"Galaxies are flying apart, this means that at one time in the past, they were all together in one place".

Is the above statement no longer true?

Check this out...
http://www.astro.ucla.edu/~wright/BBhistory.html

 

[marcus]

... given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies.

Albert if you want to gradually get to understand standard expansion cosmology I susect you first need to get rid of the highlighted idea. I don't want to say it's WRONG (today's models are not final and can always be revised, they are just the most reliable accurate picture we've been able to construct so far) but it is a misconception from the standpoint of modern cosmology. It has nothing to do with the way working cosmologists think.

Current models they use to fit observational data to are not that of an explosion outward from some point in empty space.

... which of my options would it most look like at this point in time - today - if I were able to hold all the matter in my hand in the shape it had come to form.

Since matter is not supposed to be traveling outwards into empty space, away from some central point, there would not be any "overall edge shape" that it had "come to form".

So you are asking about something that is simply not part of our conception of the universe.
The question is based on a false premise and does not make sense.
====================

There are ANALOGIES that people use to illustrate expansion with one-dimensional or two-dimensional toy models. They can be very helpful but analogies tend to be imperfect and require care.

One analogy is a CIRCULAR RING with no surrounding space. All existence concentrated in this infinitely thin ring. Galaxies and stars are one-dimensional, little dots and dashes specklend along this ring.

As the ring expands it describes a flaring cone-shape, or a bell shape. The ring represents SPACE and the bell which it describes as it expands is SPACETIME, in this toy analog picture.

that particular analogy doesn't appeal to me personally, but you see picturesque versions of it around and about. Some NASA outreach documents use it as a kind of impressionistic illustration.

Another analogy is where today's space and the galaxies in it are infinitely thin two-dimensional, like all existence (all space all matter) concentrated in the surface of a spherical balloon.

In cosmology we do not assume there is any "space around space" or any "boundary" or border to space, or any "central point" from which things spread out. Therefore to get the good from this analogy we must imagine no inside or outside of the balloon. There is no surrounding 3D space, and therefore of course no center. Only the pure infinitely thin surface of the balloon exists. The mental concentration involved in thinking the balloon analogy can take some time to get used to.
=============

Those are just lower dimensional ("infinitely thin") analogies, that may or may not help you.
The goal is to be able to think of edgeless boundaryless THREE-dimensional space, with no "space outside of space"---i.e. all existence concentrated in this full-bodied 3D space that we experience.

And no center from which it is expanding. And since there is no "outside" it can have no shape as seen from the outside. No person looking from the outside, or "holding it in my hand" as you said.

We experience the expansion and the curvature of this 3D space INTERNALLY, by witnessing large triangles that do not add up to 180 degrees (as they would in a zero curvature space).
We do not stand outside to view the curvature, it is something experienced by creatures within the space. Likewise expansion. We witness it in several ways, not only in the enlargement of wavelengths of light and the cooling of background temperature but also in the curious fact that beyond a certain distance objects actually look LARGER (take up wider angle in the sky) the farther away.

this strange beautiful optical effect of expansion is something to understand. It is as if the ancient sky was smaller and so objects of a given size (e.g. compression waves in a cloud of gas) took up a wider sector of the sky. and so they look bigger than more recent objects the same size would look.

I'm telling you to think of "shape" that is geometry as something experienced from the inside, from within the space that realizes that geometry, that curvature, that expansion.
Geometry and the change it undergoes are not something to visualize from the outside, because there is no outside.

(according to the normal cosmic model that folks use, and fit their observational data to.)

(of course as I think you know there are those more speculative models in which there is a higher-dimensional outside surrounding our space but they aren't needed to fit data to and aren't used in normal everyday cosmology.)

 

[marcus]

This would contradict the following statement - with which I was "brought up" as it were.

"Galaxies are flying apart, this means that at one time in the past, they were all together in one place".

Is the above statement no longer true?

That never was the idea. "flying apart" is a kind of poetical half-truth.
"one place" is a highly misleading expression since it suggests a point sitting in empty space.
That was certainly never the idea even if you go back to the beginnings of expansion cosmology in the 1920s.

Those words are more appropriate to irresponsible JOURNALISM than to an honest description of the usual expansion model cosmos.

 

[AlbertE]

"The goal is to be able to think of edgeless boundaryless THREE-dimensional space, with no "space outside of space"---i.e. all existence concentrated in this full-bodied 3D space that we experience."

I need pictures. :(

 

[AlbertE]

I need pictures - DEFINATELY :)

 

[ibysaiyan]

I need pictures - DEFINATELY :)

Not to sound rude but why are you so keen into visualizing things , I agree Einstein's mind worked that way however , he did extensive study . Marcus has given you an excellent detail even beyond what your typical first year UG books cover.

 

[marcus]

...Marcus has given you an excellent detail even beyond what your typical first year UG books cover.

Thanks for the positive evaluation, Ibysaiyan! A good comment like that now and then makes the effort to write about cosmology worthwhile.

 

[Naty1]

Lets suppose for a moment the big bang DID begin at some point in space...like from a stick of dynamite...a discussion by Alan Guth [originator of Inflation Theory, this from THE INFLATIONARY UNIVERSE], 1997]:

..light is emitted and matter strewn outward. After a short time light would have moved beyond the matter we ride on...the light [radiation] would disappear, so why can we see it [all around us]??

He is referring here to that fact the cosmic micowave background radiation [CMBR]is all around us and very uniform in all directions.

he goes on to explain: ..The Friedman Robertson walker [FRW] cosmological model [which closely matches our astronomical observations] was constructed to be homogeneous and isotropic.

...This means matter is assumed to have uniformly filled all of space at all times, right back to the instant of the big bang. There is no edge and no center to the distribution of matter. Since matter fills all of space, it is impossible for the radiation to leave the matter filled region as it would for a stick of dynamite.

Why believe this model?

...because a localized explosion cannot explain the observed uniformity in the CMBR. Either we would have to be at the exact spot the explosion happened or else we would observe a local hotspot

from the heavens around us. And the extreme uniformity of the CMBR, about 1 part in 1000,000 variation, means the background was extremely uniform as modeled, and is a virtually perfect black body emitter as expected. Things must have been very uncomplicated, very uniform, when this ancient radiation was emitted...

 

[marcus]

"The goal is to be able to think of edgeless boundaryless THREE-dimensional space, with no "space outside of space"---i.e. all existence concentrated in this full-bodied 3D space that we experience."

I need pictures. :(

Yes you need pictures, we all use mental diagrams, sketches, which illustrate useful analogies. But you also need PATIENCE. Feed your brain honest concepts little by little and give yourself time for it to soak in.

The balloon model of expanding geometry is only a toy analog (in reduced dimensionality, no thickness) but it might be good for you to watch the actual movie.
Google "wright balloon model".
It is different each time so watch several times.
Notice that each galaxy stays in the same place on the balloon, while the photons of light move from place to place always traveling the same speed.

On my computer screen it looks as if the speed of light is constant at about one centimeter per second, or about 1/3 of an inch per second.

You will see distances between pairs of stationary galaxies increasing faster than that, if they are far enough apart (larger distances increase more rapidly).

I keep the link to "wright balloon model" in my signature at the end of the post, for easy access. It can help a lot, even though it is only a 2D infinitely thin analogy. Pictures help. Repeated exposure helps. Give yourself time for ideas to sink in.

 

[Ken G]

We experience the expansion and the curvature of this 3D space INTERNALLY, by witnessing large triangles that do not add up to 180 degrees (as they would in a zero curvature space).

Be careful, that is actually a misconception that the balloon analogy tends to confer (that expansion of space is somehow connected with curvature of the space), because a balloon has spatial curvature but the current Big Bang model does not. People used to wonder if the universe curved back on itself like a balloon, and if it did, then we'd have this nice 2D version of the 3D universe we can use in analogies. But when such curvature was looked for and not seen, and indeed we instead found good reason to expect the universe to be spatially flat (due to inflation, perhaps), somehow the balloon analogy did not get put in the dustbin where it belongs! The universe does not need to be spatially curved in order to be able to expand, so triangles can add up to 180 degrees and still have all the effects that you mention. Indeed, that is exactly the state of affairs in the current best models.

What's more, expansion of a balloon (and expansion during inflation) tends to reduce spatial curvature with time, but general relativity (with no cosmological constant term) causes spatial curvature to grow with time-- that's kind of hard to do with balloons because balloons don't use curved time! Note that Ned Wright acknowledges this weakness in the model you cite when he says "Since this analogy uses a spherical spatial section, it corresponds to a closed Universe which recollapses." That is not the current expectation in modern cosmology, as he well knows. But analogies are always a mixed bag.

Despite its flaws, I think a better analogy is the "raisin bread rising in the oven" analogy-- it is both spatially 3D, and has no spatial curvature, yet allows raisins (galaxy clusters) to get farther apart with time. Like you say, it is still just an analogy-- and unfortunately still has the problem of seeming to require a boundary and an "external space". But this is an infinitely large loaf of raisin bread, so it's better for understanding the effects of expansion than it is for understanding why we don't need any boundaries, or any "external space", in the model. The balloon analogy is better for seeing why there doesn't have to be any boundaries, but comes at the expense of being not at all the current way we visualize the expansion, so it may be too high a price to pay! Resolving one misconception at the price of a bunch of new ones, and so forth.

Although it is highly unorthodox, I prefer to just imagine (as a working picture, the observations do not adjudicate the point and nature is probably ambivalent) that matter and rulers are shrinking, and this resolves all the misconceptions, but comes at a price of requiring us to think very differently about what distance is!

 

[marcus]

Be careful, that is actually a misconception that the balloon analogy tends to confer (that expansion of space is somehow connected with curvature of the space), because a balloon has spatial curvature but the current Big Bang model does not. People used to wonder if the universe curved back on itself like a balloon, and if it did, then we'd have this nice 2D version of the 3D universe we can use in analogies. But when such curvature was looked for and not seen, and indeed we instead found good reason to expect the universe to be spatially flat (due to inflation, perhaps), somehow the balloon analogy did not get put in the dustbin where it belongs! The universe does not need to be spatially curved in order to be able to expand, so triangles can add up to 180 degrees and still have all the effects that you mention. Indeed, that is exactly the state of affairs in the current best models.
...

No analogy is perfect. Raisinbread illustrates some things. Balloon illustrates some things (like some distances growing faster than the photons move, like galaxies staying at the same place on the balloon, analogous to being at rest relative to CMB).

In fact we do witness large triangles that do not add up to 180 degrees. Space is obviously not perfectly flat. Curvature was looked for and was seen in 1919 by Sir Arthur Eddington's group. And countless times since then by other observers.

I do not say anything about the OVERALL average curvature. Space could have overall zero curvature. We actually do not know. So I am an agnostic about that. You seem convinced with a high degree of certainty

BTW I did not say (as you seem to think I did) that space has to be curved in order to expand. The infinite raisin bread analogy, if you can picture raisin bread with no boundary, illustrates that uncurved expansion very well. I think you are over-interpreting the balloon analogy if you think it means curvature is required for expansion. It doesn't say that, nor did I. It can be useful to have several analog models. Raisin bread is good too

 

[Ken G]

In fact we do witness large triangles that do not add up to 180 degrees. Space is obviously not perfectly flat. Curvature was looked for and was seen in 1919 by Sir Arthur Eddington's group.

But not on cosmological scales. It is cosmological space that is what we say is expanding, and has never been observed to be anything but flat. So the current best Big Bang model involves a completely flat space on the scales of the cosmological principle. Hence, there is no need to connect expansion, which is something that happens at the largest scales, with triangles that add up to less than 180 degrees (as on balloons), which is not something that happens at the largest scales (so far as we know).

I do not say anything about the OVERALL average curvature. It could have overall zero curvature. We actually do not know. So I am an agnostic about that. You seem convinced with a high degree of certainty

Actually, I say nothing about what the universe is actually doing, we can only see so much of it anyway. I'm talking about what evidence we actually have to go on, and how we incorporate that evidence into our current best model-- which is flat, not like a balloon. Therefore, we don't want people to think that for space to expand and have no boundaries in our model, then our model must curve like a balloon-- what is really used is simply an infinite model, that is flat.

 

[Ken G]

This all might seem like a fairly moot issue, but in fact it has a lot to do with how we teach cosmology. The possibility of global curvature is almost always included as a central part of the cosmological possibilities, and then the balloon analogy is used with the case of a closed universe, as Ned Wright does. But over and over, the search for any spatial curvature has failed to find any (at cosmological scales), so I would argue that it is high time we simply start building in a spatially flat universe right into how we conceive and teach cosmology. So much wasted overhead goes into getting students to understand the possibility of spatial curvature, and then we just turn around and throw all that overhead away when we get to the actual observations and the current best models-- which are both flat! The flatness of space on cosmological scales is about as important of a cosmological principle as there is.

 

[marcus]

...
Although it is highly unorthodox, I prefer to just imagine (as a working picture, the observations do not adjudicate the point and nature is probably ambivalent) that matter and rulers are shrinking, and this resolves all the misconceptions, but comes at a price of requiring us to think very differently about what distance is!

... But over and over, the search for any spatial curvature has failed to find any (at cosmological scales), so I would argue that it is high time we simply start building in a spatially flat universe right into how we conceive and teach cosmology. So much wasted overhead goes into getting students to understand the possibility of spatial curvature, and then we just turn around and throw all that overhead away when we get to the actual observations and the current best models-- which are both flat! The flatness of space on cosmological scales is about as important of a cosmological principle as there is.

As I said, I'm an agnostic about the perfect spatial flatness issue. Perfect absolute spatial flatness (on cosmic scales) has not been ruled out, nor has it been proven. The latest NASA report I recall on that gave a 95% confidence interval that included zero and plenty of scope on both sides of zero: a possibility of either positive or negative overall curvature.

Not sure what you mean by "current best models" being flat. As I recall the WMAP 5 year report used several models, including one which was spatially closed (but destined to expand indefinitely rather than re-collapse.) They fit several models to the data.

One can say that the data is consistent with overall spatial curvature being small. It could be zero, but we shouldn't pretend that we know that, when we actually do not.

 

[Ken G]

As I said, I'm an agnostic about the perfect spatial flatness issue. Perfect absolute spatial flatness (on cosmic scales) has not been ruled out, nor has it been proven.

I would go further-- I would say that "perfect flatness" is actually a meaningless scientific concept in the first place. We don't ascertain perfection in science, we simply make models. When we have some evidence that requires we put in spatial curvature, we will, but it is quite likely that we will never have any evidence to put that into our models-- so our models will probably always be flat. That will never tell us if the universe is actually perfectly flat, nor does science have any business even asking that question (because it cannot be parlayed into any testable hypothesis). All we can say is that expansion, and the cosmological principle, are issues that are completely independent of the issue of spatial curvature. That is why the balloon analogy is not really a description of the cosmological principle, it is merely one situation in which the cosmological principle could apply. One should not mistake that for a model of our universe-- there is no reason to model the universe as having any spatial curvature, and no consensus model does.

The latest NASA report I recall on that gave a 95% confidence interval that included zero and plenty of scope on both sides of zero: a possibility of either positive or negative overall curvature.

Exactly, so no model of the universe would involve spatial curvature, it's a simple matter of Occam's Razor. But even if we did someday have a finite curvature observation, it would not require what we extrapolate that measurement to beyond what we can see, any more than we would extrapolate the preponderance of matter over antimatter to realms that we cannot see. We simply have no idea if unobservable realms are mainly matter or antimatter, and can easily come up with arguments why we could expect antimatter to dominate elsewhere. There's just no point in extrapolating, that's what I'm saying-- the point of science is to use models to make testable hypotheses, not to ask unanswerable questions.

Not sure what you mean by "current best models" being flat. As I recall the WMAP 5 year report used several models, including one which was spatially closed (but destined to expand indefinitely rather than re-collapse.) They fit several models to the data.

There is clearly a "best model" that is currently used as the consensus model, and it is flat. There's just no reason to use any other model at present-- this is even called "precision cosmology" because the model is more accurate than most other classes of astronomical models that get used routinely (like treating stars as spheres and so on). It doesn't mean there's no room to include non-flatness, it means there's no reason to include non-flatness, and no testable hypothesis motivated by a non-flat model has ever been borne out yet.

One can say that the data is consistent with overall spatial curvature being small. It could be zero, but we shouldn't pretend that we know that, when we actually do not.

Note that I never said we know the curvature is zero-- I said that the best model does not need, nor does it include, any curvature, and if inflation is true, then it never will. Science doesn't tell us if the curvature is zero, it tells us if we need to include non-flatness in our model.

 

[AlbertE]

How can it be flat - when its clearly not flat? This is getting strange.

I sometimes wonder whether science has somehow lost the plot. Then again - maybe I lost the plot - then again - maybe I never had the plot in the first place.

I see what I see.

I see matter forming tiny structures called galaxies, billions of them, and they sit in space - which has no air so we call it a vacuum because we do have air down here and it puts pressure on us.

These tiny galaxies appear to be moving away from each other in 3D space, there is no flatness that I can see.

I thought science was all about (or at least partly about) proving by observation.

The universe is not flat - at all.

 

[twofish-quant]

This all might seem like a fairly moot issue, but in fact it has a lot to do with how we teach cosmology.

Agreed.

But over and over, the search for any spatial curvature has failed to find any (at cosmological scales), so I would argue that it is high time we simply start building in a spatially flat universe right into how we conceive and teach cosmology.

That's wrong.

1) You need to look at curvature to show that it doesn't exist.
2) The inflationary models of the universe predicts small but non-zero curvature.
3) It's a bad idea to remove essential physics for pedagological purposes.

All that overhead away when we get to the actual observations and the current best models-- which are both flat!

That's false, if the universe were perfectly flat, then we'd run into fine tuning problems with inflation.

One issue is topology. You can make a sphere *look* flat by expanding it, but a big sphere is still topologically a sphere.

The flatness of space on cosmological scales is about as important of a cosmological principle as there is.

Strongly disagree.

 

[twofish-quant]

I would go further-- I would say that "perfect flatness" is actually a meaningless scientific concept in the first place.

Strongly. There is a term in the FLRW that jumps discontinuously between k=-1, k=0, and k=+1. Perfect flatness is k=0.

When we have some evidence that requires we put in spatial curvature, we will, but it is quite likely that we will never have any evidence to put that into our models-- so our models will probably always be flat.

This is false. If k=0, then certain numbers have to take exact values. If those values are even slightly off, then k=-1, or k=1.

One should not mistake that for a model of our universe-- there is no reason to model the universe as having any spatial curvature, and no consensus model does.

Again this is false. Lambda-CDM allows you to calculate the spatial curvature given input parameters. It so happens that the observations are consistent with k=0, but they are also consistent with small positive or negative curvature.

The model of gravity that we use *depends* on spatial curvature to exist. If you *impose* zero curvature, then you are using something other than GR to do your calculations. Inventing gravity models out of thin air, is not advisable.

The fact that the world looks flat if you look at distances of 500 feet, doesn't mean that it is, and you can take some precision measurements to show curvature.

We simply have no idea if unobservable realms are mainly matter or antimatter, and can easily come up with arguments why we could expect antimatter to dominate elsewhere.

It's testable. We can exclude anti-mater within a radius of "x light years" since that would change the CMB.

There's just no point in extrapolating, that's what I'm saying-- the point of science is to use models to make testable hypotheses, not to ask unanswerable questions.

You don't know that the questions are unanswerable unless you try to answer them.

There is clearly a "best model" that is currently used as the consensus model, and it is flat.

No it's not. It has curvature < N, where N is a number less than observation, but curvature < N is not the same as N=0.

Also, people are not inclined to argue that if curvature < N means N=0. People were making similar arguments in the 1970's and 1980's about the matter content of the universe. The observations as of 1985 were consistent with a flat universe that consistent only of dark matter. It turns out that model was wrong.

It doesn't mean there's no room to include non-flatness, it means there's no reason to include non-flatness, and no testable hypothesis motivated by a non-flat model has ever been borne out yet.

Non-flatness is not excluded by current observations.

Note that I never said we know the curvature is zero-- I said that the best model does not need, nor does it include, any curvature, and if inflation is true, then it never will.

That's false. If inflation is true than the amount of curvature is small but non-zero. The amount of non-zeroness can rule out different inflation models.

If the curvature is in fact *exactly* zero, that rules out inflationary explanations for flatness. If the curvature is *exactly* zero then it must have been that way before inflation which would tell us something really important about quantum gravity.

Science doesn't tell us if the curvature is zero, it tells us if we need to include non-flatness in our model.

Theory tells us that if curvature is zero, then we live in a very weird universe with a very weird coincidence. Now if the curvature is merely "small" then that coincidence disappears.

 

[twofish-quant]

As I said, I'm an agnostic about the perfect spatial flatness issue. Perfect absolute spatial flatness (on cosmic scales) has not been ruled out, nor has it been proven.

Same here. I'm very strongly opposed to removing flatness from cosmological models unless there is a strong theoretical or observations reason to do so, because having a cosmological model that is perfect flat introduces a lot of "fine tuning" problems.

One can say that the data is consistent with overall spatial curvature being small. It could be zero, but we shouldn't pretend that we know that, when we actually do not.

Especially when we've been burned before. The cosmological observations circa 1985 were consistent with zero dark energy and baryon/dark matter masses creating a flat universe.

Yup, and if we did have any reason to think that it is exactly zero, then it would create lots of theoretical issues. Simple inflation would no longer work as an solution to the flatness problem. There are forms of inflation that would work as solutions. Conversely if we beat down the error bars and find that the universe is almost flat, that kills several classes of models.