Is the univers flat or curved?

[TalonD]

Any results from the Planck probe? Has it narrowed down the possibilities ?

 

[Matterwave]

I don't know the results from the Planck probe, but last I heard (maybe a year ago...), the Universe was found to be approximately flat. If there is a curvature, the radius of curvature must be on the order of hundreds of billions to trillions of light years IIRC (several universes in size).

 

[marcus]

Thanks for reminding us of that question!

Back in 2008 there was the report based on the 5-year WMAP data (plus SN and galaxy counts) and I recall that a 95% confidence LOWER BOUND was given for the radius of curvature, which was right around 100 billion lightyears. As a lower bound, that would be a 600 billion lightyear circumference. If you could freeze expansion it would take 600 billion years to circumnavigate at the speed of light.

So it might be infinite, or it might be finite with positive curvature, but in a kind of vague subjective sense NEARLY flat. We don't know which. both are possible.


With the same standard model, and same distance concept, the radius of the observable portion is about 45 billion lightyears. The currently visible portion, that we are getting light from, is roughly same order of magnitude size as the radius of curvature lower bound.

Now we have the 7-year WMAP data. The picture hasn't changed qualitatively very much. Estimated lower bound on radius of curvature still about the same. The RoC could be infinite :-D like space is flat infinite. Or it could be nearly flat, but finite. And there are various other logical possibilities. But AFAICS we just don't know.

And as far as I know we don't have estimates of the cosmo parameters from PLANCK yet.

But it is good to keep asking! Maybe someone will see your question and give us some fresh news on this!

 

[nicksauce]

I am fairly confident that if Planck had released any data I would have heard about it.

According to Wikipedia: "Some preliminary results are scheduled for release in December 2010, and the final results (with all processed data) are expected to be delivered to the worldwide community towards the end of 2012."

 

[Chalnoth]

Any results from the Planck probe? Has it narrowed down the possibilities ?

The first public release of Planck data will be the early-release compact source catalog, which should be available around the end of the year.

The first CMB science release will be two years following the end of the second full scan of the sky (which occurs one year after the start of the survey, which was last August).

So, we still have a little over two years to go before the CMB science from Planck is released.

 

[TalonD]

Thanks everyone. I'm no expert but I knew Planck was out there and would have greater resolution than wmap so figured I would ask. So we still have to wait awhile. :)

 

[AWA]

I know is highly improbable but if hypothetically the Plank probe found that after all ,in large scales, the universe is not flat and has a negative curvature, giving a hyperbolic geometry, would this change in any way our interpretation of the redshift of far galaxies? I mean, are photons supposed to behave the same way in this type of space with respect to an observer placed at huge distances from the source of light? Even if it's most unlikely this turns out to be the real scenario, I'm still curious, any thoughts?

 

[Chalnoth]

I know is highly improbable but if hypothetically the Plank probe found that after all ,in large scales, the universe is not flat and has a negative curvature, giving a hyperbolic geometry, would this change in any way our interpretation of the redshift of far galaxies? I mean, are photons supposed to behave the same way in this type of space with respect to an observer placed at huge distances from the source of light? Even if it's most unlikely this turns out to be the real scenario, I'm still curious, any thoughts?

Given that our current estimates of spatial flatness are that it is flat to within less than about a percent, there is no conceivable way that Planck's results will differ so dramatically from existing experimental results for there to be any sort of qualitatively new picture here.

To answer your question, though, no, photons don't behave in any sort of dramatically-different ways in negatively-curved space.

 

[AWA]

Given that our current estimates of spatial flatness are that it is flat to within less than about a percent, there is no conceivable way that Planck's results will differ so dramatically from existing experimental results for there to be any sort of qualitatively new picture here.

Gee, what a waste of money and time then. Who wants to make experiments for something that's already settled?

To answer your question, though, no, photons don't behave in any sort of dramatically-different ways in negatively-curved space.

Please could someone elaborate on that? Such categorical answers are kind of useless

 

[nicksauce]

Gee, what a waste of money and time then. Who wants to make experiments for something that's already settled?

It does other things, you know.

 

[Chalnoth]

Gee, what a waste of money and time then. Who wants to make experiments for something that's already settled?

As nicksauce mentioned, there are other reasons for Planck than just re-confirming the spatial flatness of our universe. It measures the sky at a much broader range of frequencies, which will help in understanding the foregrounds (such as our galaxy), and therefore in removing them. It is a much more sensitive instrument than WMAP, which allows for better estimation of polarization of the CMB (there is some hope, for instance, that it can measure the gravitational wave signal in the CMB from inflation, but this is not by any means yet clear). It measures the CMB at much higher angular resolution, which allows for better estimation of a number of the properties of inflation.

Please could someone elaborate on that? Such categorical answers are kind of useless

If you send out parallel light beams in negatively-curved space, they tend to get further apart with time.

 

[bapowell]

Gee, what a waste of money and time then. Who wants to make experiments for something that's already settled?

Yes, Planck will do much more. In particular, it will give an accurate constraint on the statistics of the temperature fluctuations in the CMB -- these are expected to be highly Gaussian if the simplest models of inflation are correct. However, other more exotic models of inflation predict that these fluctuations should deviate from Gaussian, and Planck might be able to shed some light on this important question.

Planck might also detect primordial gravity waves, another crucial prediction of inflation.

 

[AWA]

A flat universe is in contradiction with General Relativity. Are you guys seriously questioning this theory??

 

[nicksauce]

A flat universe is in contradiction with General Relativity. Are you guys seriously questioning this theory??

Errr what makes you think that?

 

[Chalnoth]

A flat universe is in contradiction with General Relativity. Are you guys seriously questioning this theory??

When people say flat, they mean only spatially-flat, and only on average on large scales (an expanding universe has a space-time which is curved, but the spatial components can easily be flat). This is not in contradiction to GR.

 

[AWA]

Chalnoth, how do you separate the components of a four-dimensional "space"(in the mathematical sense) into a time component and a spatial component having the latter flat. are we to suposse that time accounts for the total curvature? how is time curved? Doesn't make much sense to me.
Einstein's view based on his general postulate of relativity was that a Euclidean universe was untenable. Space-time had to be non-Euclidean, or quasi-Euclidean to use Einstein's term. Either way flatness does not fit in the GR.

 

[element4]

(...) Either way flatness does not fit in the GR.

As a simple model of the universe on may postulate that the universe is simply connected, homogeneous and isotropic (at scales much larger than clusters of galaxies), then there exist the famous http://en.wikipedia.org/wiki/Friedm...tric#Reduced-circumference_polar_coordinates" solution to the Einstein field equations. As you can see, $$k=0$$ (flat universe) fits well in GR.

Warning, I'm no expert on GR. So I might have misunderstood something.

 

[bapowell]

how is time curved? Doesn't make much sense to me.
Einstein's view based on his general postulate of relativity was that a Euclidean universe was untenable. Space-time had to be non-Euclidean, or quasi-Euclidean to use Einstein's term. Either way flatness does not fit in the GR.

So...why can't time, just an ordinary dimension of some 4D non-Euclidean manifold, not be curved? Seems like you are contradicting yourself. There's nothing wrong with 'curved time'. Look at the Schwarzschild or Friedmann solutions in GR. These are spatially flat but give motion to test bodies on account of a 'curved time'.

 

[AWA]

bapowell, I didn't express myself correctly, time as a component of a 4D-manifold can be curved, I just couldn't see how flatness can be divided up among dimensions but that's probably my own inability.

element4, I think the confusion arises from the fact that we are talking abot different scales.Of course every evidence includin CMB points to a LOCALLY flat universe, but I was referring to the global scale.

Anyway since I've seen my question anwered in other threads and mine wasn't even the OP issue, I'll leave it here
Thanks

 

[Chalnoth]

Chalnoth, how do you separate the components of a four-dimensional "space"(in the mathematical sense) into a time component and a spatial component having the latter flat. are we to suposse that time accounts for the total curvature? how is time curved? Doesn't make much sense to me.

The Ricci curvature tensor is a rank-2 tensor (meaning it has two indices, and can be thought of as a matrix). In flat space, the space-space components of this tensor are all zero, while the time-time and space-time components are non-zero.

Einstein's view based on his general postulate of relativity was that a Euclidean universe was untenable. Space-time had to be non-Euclidean, or quasi-Euclidean to use Einstein's term. Either way flatness does not fit in the GR.

Well, it isn't Euclidean, due to the non-zero time-time and space-time components of the Ricci curvature tensor.

 

[DevilsAvocado]

A flat universe is in contradiction with General Relativity. Are you guys seriously questioning this theory??

Please correct a layman if I’m wrong, but the WMAP CMB-measurements on 'flatness' deals with the Density parameter (Ω), resulting in a Closed, Open or Flat (local) universe, right?

Consequently, if the (local) universe turns out to be perfectly flat (in terms of Ω), it could still be spatially curved, in the shape of a torus, right...?

Or, did I miss something crucial... :uhh:

 

[bapowell]

Right.

 

[DevilsAvocado]

Thanks everyone. I'm no expert but I knew Planck was out there and would have greater resolution than wmap so figured I would ask. So we still have to wait awhile. :)

Good things come to those who wait...

http://www.sciops.esa.int/index.php?project=PLANCK

 

[DevilsAvocado]

Right.

Thanks bapowell, it feels 'reassuring'.

 

[AWA]

Well I have to come back to this thread because rereading it I find something confusing or incoherent in the answers.
If what DevilsAvocado says is right (as it seems in bapowell's opinion) then the the WMAP CMB-measurements on 'flatness' (and the Planck probe) cannot tell us anything about the Global space curvature, therefore when I asked whether a global hyperbolic space could be found with the Planck probe, the answer should have been that this experiment is only about Local geometry so it can't respond about Global geometry.
Instead of that what Chalnoth anwered made no distinction between local and global and said the hyperbolic geometry was discarded by the experiment without further clarifcation.
Can someone clear this up? Do I see it right this time?

 

[bapowell]

Well I have to come back to this thread because rereading it I find something confusing or incoherent in the answers.
If what DevilsAvocado says is right (as it seems in bapowell's opinion) then the the WMAP CMB-measurements on 'flatness' (and the Planck probe) cannot tell us anything about the Global space curvature, therefore when I asked whether a global hyperbolic space could be found with the Planck probe, the answer should have been that this experiment is only about Local geometry so it can't respond about Global geometry.
Instead of that what Chalnoth anwered made no distinction between local and global and said the hyperbolic geometry was discarded by the experiment without further clarifcation.
Can someone clear this up? Do I see it right this time?

Cosmological observations only constrain the local geometry of the universe, because we can only observe our local neighborhood. What Chalnoth was saying was that while Planck only measures the local geometry of the universe, it is already constrained to be pretty flat (to within 1% or so). Therefore, while the global geometry of the universe could well be hyperbolic, it can't be too hyperbolic. I think that's all he's saying. The fact of the matter is that no local cosmological observation can place bounds on the global geometry of the universe. It's perfectly consistent for the universe to actually be open or closed, but appear locally rather flat.

 

[AWA]

Thanks. I think I understant it better now.
The other source of confusion for me was that sometimes it is easy to get mixed-up with 3 dimensional space and 4-dimensional spacetime when it is not well emphasized.
For instance, when in GR we say that mass curves spacetime we refer to the 4-manifold,
It doesn't necesarily mean the 3 dim-space component curves too, but it might as well, right?

 

[bapowell]

It doesn't necesarily mean the 3 dim-space component curves too, but it might as well, right?

Right. The Schwarzschild solution is spatially flat, but has a 'curved' time dimension. So does the flat FRW solution relevant to cosmology. However, the closed FRW solution has curved space as well.

 

[skippy1729]

Flat (critical density = 1.00000000...... +/-0) and approximately flat (critical density = 1.00000000001 +/-0.000000000005 for example) are two entirely different animals; one is infinite and the other is really, really, really big). NO experiment can determine if the universe is EXACTLY flat. The only way to say that the universe could be said to be exactly flat would be to come up with a strong, compelling THEORETICAL reason why it is flat (and always has been flat).

Of course open=>infinite and flat=>infinite only apply for simply connected topology. The multiply connected Poincare Dodecahedron model still seems possible: arXiv:0801.0006v2 (also published in Astronomy & Astrophysics).

Skippy

 

[Chronos]

Planck is designed to probe the high energy [gamma] spectrum. It is well suited for exploring the very early universe where high energy events were common.

 

[Chalnoth]

Planck is designed to probe the high energy [gamma] spectrum. It is well suited for exploring the very early universe where high energy events were common.

I'm sorry, but I believe you're thinking of Fermi. Planck is primarily a CMB instrument, and probes radiation from 30GHz to 857GHz, which is in the millimeter wave range (wavelengths from 10mm to 0.35mm).

 

[Ich]

Cosmological observations only constrain the local geometry of the universe, because we can only observe our local neighborhood.

...with "local" meaning out to z=1089. Our observable universe is flat.
We can't know what's behind the observable universe. Further, topology is not really constrained by curvature, too.

The Schwarzschild solution is spatially flat

No, it's curved like http://en.wikipedia.org/wiki/Schwarzschild_metric#Flamm.27s_paraboloid".

 

[bapowell]

No, it's curved like http://en.wikipedia.org/wiki/Schwarzschild_metric#Flamm.27s_paraboloid".

By flat, I mean $$R = 0$$.

 

[Ich]

By flat, I mean R = 0 .

Yes. It isn't flat.

 

[caspiansea3]

I recently came across this paper:
How flat can you get? A model comparison perspective on the curvature of the Universe
http://arxiv.org/abs/0901.3354"

In it the authors say "We show that, given current data, the probability that the Universe is spatially infinite lies between 67% and 98%". By spatially infitite do they mean that the curvature is exactly zero (omega = 0)?