Is the Cosmological Principle Limited to Space Only?

[Calimero]

AWA, universe evolves through time. It means that it is not same today as it was earlier, and that it will be in the future. Universe with scale factor, say, 0.5 is not homogeneous (same in composition) with universe with scale factor 1. Now, I know that you get this, but still you are talking about false paradox. I fail to see what that paradox is.

 

[AWA]

We see a universe that changes in time, but is consistent with a particular set of equal-time slices being approximately homogeneous on large scales. We see a thin cone through this universe stretching backwards in time and outwards in space. All of our observations are consistent with the nearby universe stemming from a different realization of the same underlying statistical distribution of homogeneities as the far away universe.

This is all correct here, my point was only to remark that when we look around with our telescopes we see not only space but due to the finite value of c, we see spacetime, and in as much as what we observe is homogenous it would seem that spacetime is homogenous in the past direction. It is as simple a remark as this. If this has nothing to do with the perfect cosmological principle or with cosmology, or it's irrelevant, fine. But so far no one has questioned this simple observation.

 

[Chalnoth]

This is all correct here, my point was only to remark that when we look around with our telescopes we see not only space but due to the finite value of c, we see spacetime, and in as much as what we observe is homogenous it would seem that spacetime is homogenous in the past direction.

Except this just isn't true. The universe changes quite dramatically as we move to higher and higher redshift.

I mean, sure, if you stay at very low redshifts, it all looks fairly homogeneous in both time and space. But once you head to higher redshifts (say, greater than 1)., really dramatic changes start to become apparent. The further out you go, the more dramatic the changes become.

 

[AWA]

Except this just isn't true. The universe changes quite dramatically as we move to higher and higher redshift.

I mean, sure, if you stay at very low redshifts, it all looks fairly homogeneous in both time and space. But once you head to higher redshifts (say, greater than 1)., really dramatic changes start to become apparent. The further out you go, the more dramatic the changes become.

If you are saying that the universe is not homogenous past redshift z=1, I think that is not only wrong but clearly ATM.

 

[Chalnoth]

If you are saying that the universe is not homogenous past redshift z=1, I think that is not only wrong but clearly ATM.

What I'm saying is that the universe at low redshifts (say, z=0.01, for instance) looks very different from the universe at z=1 when you look at the details, such as the separation between galaxies and the sorts of galaxies you see. The differences increase as you go further back.

 

[AWA]

What I'm saying is that the universe at low redshifts (say, z=0.01, for instance) looks very different from the universe at z=1 when you look at the details, such as the separation between galaxies and the sorts of galaxies you see. The differences increase as you go further back.

If you want to talk about the detalis , that's OK but it's got nothing to do with the paradox I was referring to, the details are totally inhomogenous of course, it only takes a look at my garage to confirm that.
We are concerned here with large scale only, not with the evolution of a star, a galaxy or fish out of the fridge.

 

[Chalnoth]

If you want to talk about the detalis , that's OK but it's got nothing to do with the paradox I was referring to, the details are totally inhomogenous of course, it only takes a look at my garage to confirm that.
We are concerned here with large scale only, not with the evolution of a star, a galaxy or fish out of the fridge.

What I mean is that the z=0.01 universe is statistically distinguishable from the z=1 universe. That is, many of the average properties of the universe at z=0.01 are very different from the universe at z=1. So yes, at large scales, low redshifts are very different from high redshifts.

 

[AWA]

What I mean is that the z=0.01 universe is statistically distinguishable from the z=1 universe. That is, many of the average properties of the universe at z=0.01 are very different from the universe at z=1. So yes, at large scales, low redshifts are very different from high redshifts.

Ahaaa, but that is because we are not talking about homogenous scales yet, I can assure you the z=0.000001 universe is very diferent from the z=1 universe. That is trivial and solves nothing.

 

[George Jones]

Let's suppose we had super-advance telescopes (let's forget technical and time limitations for the sake of the argumen) with ultra high deep field that allows us to make a map similar to the SDSS map but up to a redshift z from a little after decoupling, according to standard cosmology, at this scale the map surely would show homogeneity (if we don't find it at this scale I wonder at what scale we might expect to).
But this map is also a look-back time map of the time dimension of the last 13 bly, so it would also be showing us homogeneity in the time dimension.

As a matter of fact we don't need that supertelescope, we are watching an isotropic and homogenous to more than a part in 10^5 map from further time back already, the CMB, so we seem to have homogeneity in time at least up to 13.64 bly which for a universe 13.7 bly old is a good proportion of the total.

But this is just observation of spatial homogeneity at different epochs. I think the problem is that your definition of time homogeneity is different than everyone else's definition of time homogeneity.

Well for me this seems to conflict with this statement from wikipedia:"The Perfect Cosmological Principle is an extension of the Cosmological Principle, which accepts that the universe changes its gross feature with time, but not in space." I mean if it doesn't change in space, it shouldn't change in time to keep congruence with the lookback time we see when we look at the space surrounding us at great distances.

The only solution I find is that our universe follows the "perfect cosmological principle" except at the initial singularity, which could mean that ultimately it doesn't.

 

[Chalnoth]

Ahaaa, but that is because we are not talking about homogenous scales yet, I can assure you the z=0.000001 universe is very diferent from the z=1 universe. That is trivial and solves nothing.

Huh? These scales are most certainly homogeneous scales. The z=0.01 universe represents a spherical shell approximately 22,000Mpc^2 in surface area, while the z=1 universe represents a spherical shell approximately 138Gpc^2 in surface area. If we set the length scale of homogeneity to be ~80Mpc or so, then the area scale would be ~6,400Mpc^2 or so. In either case, both of these spherical shells are far beyond that, and thus we'd only need to observe a decent but not too huge fraction of the sky at z=0.01 to get homogeneity, and only a tiny fraction of the sky at z=1.

 

[AWA]

Huh? These scales are most certainly homogeneous scales. The z=0.01 universe represents a spherical shell approximately 22,000Mpc^2 in surface area, while the z=1 universe represents a spherical shell approximately 138Gpc^2 in surface area. If we set the length scale of homogeneity to be ~80Mpc or so, then the area scale would be ~6,400Mpc^2 or so. In either case, both of these spherical shells are far beyond that, and thus we'd only need to observe a decent but not too huge fraction of the sky at z=0.01 to get homogeneity, and only a tiny fraction of the sky at z=1.

Let's set this straight for accuracy sake. Maybe my source is misleading or I am misinterpreting it.

From the image in this page: http://www.sdss.org/includes/sideimages/sdss_pie2.html
I interpret that the SDSS galaxy map has data up to about a z=0.14, much higher than the z=0.01 that you mention. But most likely the data is scarce at the outer zone of the map.

Authors have differing opinions about whether we can already say we are observing homogeneity at this distances, depending on the statistical analysis they perform on the data, but for many we haven't reach yet what we can call properly statiscal homogeneity.

I would suspect that at redshift z=1 there is certainly homogeneity as you say. And obviously a sphere at z=2 also, and at 3,4...20,200, etc. And logically the spatial spherical surfaces between z=1 and 2: 1.0000...1 up to 1.999...9. All this arbitrarily(well, not arbitrary, it's given by the resolution of our instruments but in the OP I ignored technical difficulties) large number of homogenous spherical spatial surfaces represent arbitrarily small time interval snapshots towards the past. And yet you claim they don't tell us anything about the homogenity of the time dimension. But this set of snapshots give you a timeline, and every point on this timeline with an arbitrarily small separation of the points is homogenous. My impression is that this makes the timeline homogenous at least from z=1 onwards. Otherwise I'd like to have someone explain me why not.
Source: http://cas.sdss.org/public/en/sdss/default.asp#time

 

[Chalnoth]

I would suspect that at redshift z=1 there is certainly homogeneity as you say. And obviously a sphere at z=2 also, and at 3,4...20,200, etc. And logically the spatial spherical surfaces between z=1 and 2: 1.0000...1 up to 1.999...9. All this arbitrarily(well, not arbitrary, it's given by the resolution of our instruments but in the OP I ignored technical difficulties) large number of homogenous spherical spatial surfaces represent arbitrarily small time interval snapshots towards the past. And yet you claim they don't tell us anything about the homogenity of the time dimension.

I do claim they tell us something about the homogeneity of the time dimension. I claim that they tell us that there isn't homogeneity in the time dimension, that we see a variety of trends in the statistical behavior of the universe across redshift.

 

[AWA]

I do claim they tell us something about the homogeneity of the time dimension. I claim that they tell us that there isn't homogeneity in the time dimension, that we see a variety of trends in the statistical behavior of the universe across redshift.

Where do you see those trends across redshift? If you claim to observe inhomogeneity at large scale across redshift, your claiming spatial inhomogeneity, 'cause radial distances from here are defined by redshift.

 

[Calimero]

No, distances are not defined by redshift.

 

[Chalnoth]

Where do you see those trends across redshift? If you claim to observe inhomogeneity at large scale across redshift, your claiming spatial inhomogeneity, 'cause radial distances from here are defined by redshift.

Not at all, because the spatial homogeneity is only claimed for equal-time slices, and the radial direction is looking across a succession of equal-time slices. So we expect statistical isotropy as a consequence of homogeneity, but we do not expect the radial direction to appear homogeneous. And it doesn't.

As for the particular trends, well, you've got structure formation, you've got evolution of galaxy populations, you've got density evolution. Going deep into the past you've got reionization, the "dark ages", and, of course, the phase transition that emitted the CMB.

 

[Chalnoth]

No, distances are not defined by redshift.

Sort of. Redshift is typically used as a proxy for distance in galaxy surveys. And it's a reasonable enough proxy once you're out high enough in redshift that the local motion is small compared to the cosmological redshift (which isn't actually that far...typical peculiar redshifts max out at around \Delta z = 0.003, with most being much much smaller).

 

[AWA]

Not at all, because the spatial homogeneity is only claimed for equal-time slices, and the radial direction is looking across a succession of equal-time slices. So we expect statistical isotropy as a consequence of homogeneity, but we do not expect the radial direction to appear homogeneous. And it doesn't.

We don't expect it. But it shows up, a succesion of homogenous equal-time slices is what I call the time dimension.

As for the particular trends, well, you've got structure formation, you've got evolution of galaxy populations, you've got density evolution. Going deep into the past you've got reionization, the "dark ages", and, of course, the phase transition that emitted the CMB.

Formation and evolution of galaxies are rather local events compared to the scales we are dealing with;the others are my solution to paradox.

 

[Calimero]

Sort of. Redshift is typically used as a proxy for distance in galaxy surveys. And it's a reasonable enough proxy once you're out high enough in redshift that the local motion is small compared to the cosmological redshift (which isn't actually that far...typical peculiar redshifts max out at around \Delta z = 0.003, with most being much much smaller).

Yes, but what I mean is that object at z=4 is not twice as far as object at z=2.

 

[AWA]

Yes, but what I mean is that object at z=4 is not twice as far as object at z=2.

Sure, the distance-redshift relation is not linear, so?Borrowing a little from cosmology textbook stuff, this is from Hobson's General Relativity:

"In general relativity the concept of a ‘moment of time’ is ambiguous and is replaced by the notion of a three-dimensional spacelike hypersurface. To define a ‘time’ parameter that is valid globally, we ‘slice up’ spacetime by introducing a series of non-intersecting spacelike hypersurfaces that are labelled by some parameter t. This parameter then defines a universal time in that ‘a particular time’ means a given spacelike hypersurface. We may construct the hypersurfaces t = constant in any number of ways. In a general spacetime there is no preferred ‘slicing’ and hence no preferred ‘time’coordinate t.
According to Weyl’s postulate, there is a unique worldline passing through each (non-singular) spacetime point. The set of worldlines is sometimes described as providing threading for the spacetime."

In our case one of the three spatial dimensions of the spacelike hypersurfaces represents visually (thanks to light's nature) the timelike worldline passing thru each spacetime point defined by a specific redshift.

 

[Chalnoth]

Yes, but what I mean is that object at z=4 is not twice as far as object at z=2.

Yes, that is very true.

 

[Chalnoth]

Formation and evolution of galaxies are rather local events compared to the scales we are dealing with;the others are my solution to paradox.

As I keep saying, the population of galaxies at z=1 is, for instance, very different from the population of galaxies at z=0.01. The reason for this is that there are more older galaxies in the nearby universe, and more younger galaxies in the early universe. Clusters are more numerous and larger in the nearby universe. Active galactic nuclei are more common a bit further away (that is, AGN's are typically characteristic of younger galaxies).

 

[AWA]

As I keep saying, the population of galaxies at z=1 is, for instance, very different from the population of galaxies at z=0.01. The reason for this is that there are more older galaxies in the nearby universe, and more younger galaxies in the early universe. Clusters are more numerous and larger in the nearby universe. Active galactic nuclei are more common a bit further away (that is, AGN's are typically characteristic of younger galaxies).

I thought we agreed before that the universe at z=0.01 is not yet homogenous so it is obviously different than the universe at z=1.
Besides the examples you are giving about galactic age shouldn't affect the universe density at large scale. The clusters part I would have to check it. I'm not sure that has been statistically shown to happen.

 

[Chalnoth]

I thought we agreed before that the universe at z=0.01 is not yet homogenous so it is obviously different than the universe at z=1.

You said it. I didn't agree to it.

What you have to bear in mind is that there is a fundamental difference between the typical length scale of homogeneity and actually statistically demonstrating it (given an appropriate threshold). To statistically demonstrate it, you need a region much larger than the scale of homogeneity (because you have to show that all such regions of said size are statistically identical, to within some pre-defined threshold).

It's not such a surprise to me that there's argument about this, because it's mathematically a difficult thing to demonstrate, and the threshold of homogeneity is arbitrary anyway.

Besides the examples you are giving about galactic age shouldn't affect the universe density at large scale. The clusters part I would have to check it. I'm not sure that has been statistically shown to happen.

Well, density is one of the most significant things to evolve with redshift. The average density of the matter in our universe at z=1 is eight times the density today. Baryon Acoustic Oscillation observations, which measure the typical separation between galaxies at different redshifts, are a good measurement of how this density changes with redshift.

 

[Calimero]

Sure, the distance-redshift relation is not linear, so?.

So it depends on input parameters.

Borrowing a little from cosmology textbook stuff, this is from Hobson's General Relativity:

"In general relativity the concept of a ‘moment of time’ is ambiguous and is replaced by the notion of a three-dimensional spacelike hypersurface. To define a ‘time’ parameter that is valid globally, we ‘slice up’ spacetime by introducing a series of non-intersecting spacelike hypersurfaces that are labelled by some parameter t. This parameter then defines a universal time in that ‘a particular time’ means a given spacelike hypersurface. We may construct the hypersurfaces t = constant in any number of ways. In a general spacetime there is no preferred ‘slicing’ and hence no preferred ‘time’coordinate t.
According to Weyl’s postulate, there is a unique worldline passing through each (non-singular) spacetime point. The set of worldlines is sometimes described as providing threading for the spacetime."

In our case one of the three spatial dimensions of the spacelike hypersurfaces represents visually (thanks to light's nature) the timelike worldline passing thru each spacetime point defined by a specific redshift.

Thanks. Very nice quotation.

I thought we agreed before that the universe at z=0.01 is not yet homogenous so it is obviously different than the universe at z=1..

There is the source of your confusion. Please look http://www.math.lsa.umich.edu/mmss/coursesONLINE/Astro/Ex2.2/" . You are comparing homogeneity of two different time slices, which, obviously, when compared are not the same, and talking about 'not yet' homogeneous universe. Universe is just as much homogeneous now as it ever was, just on different scale.

 

[AWA]

There is the source of your confusion. Please look http://www.math.lsa.umich.edu/mmss/coursesONLINE/Astro/Ex2.2/" . You are comparing homogeneity of two different time slices, which, obviously, when compared are not the same, and talking about 'not yet' homogeneous universe. Universe is just as much homogeneous now as it ever was, just on different scale.

Thanks, cool site.
A couple of remarks: first, that is a simulation school exercise and they stress it that as a simulation it is not expected to match the real universe.
Second, according to GR (and as pointed out in the quote from my last post) you can slice up spacetime arbitrarily (general covariance, remember?) : "We may construct the hypersurfaces t = constant in any number of ways. In a general spacetime there is no preferred ‘slicing’ and hence no preferred ‘time’coordinate t."
Given a statistically significant number of slices you should find homogeneity across the sufficiently long time-like worldline formed by the statistically large stack of spacelike slices if each of the different time spacelike slices is itself homogenous. If you don't agree with this, I should remind you that GR is to this day the best theory to understand the universe that we have.

 

[AWA]

The average density of the matter in our universe at z=1 is eight times the density today.

Please, back up that figure with some reliable reference. Specifying how do you exactly measure the universe density time spacelike slice at precisely z=1.

 

[Chalnoth]

Please, back up that figure with some reliable reference. Specifying how do you exactly measure the universe density time spacelike slice at precisely z=1.

Matter density scales as a^{-3}. But 1+z = 1/a, so matter density scales as (1+z)^3.

Basically, proposing that the matter density wasn't eight times its current value at z=1 requires proposing a universe that has radial-dependent density for an equal-time slicing. This is, in principle, a rather difficult thing to accurately determine, but suffice it to say our theories that use a homogeneous matter distribution work, while alternative theories proposed to explain certain unpleasant aspects of the homogeneous theories don't.

 

[AWA]

Matter density scales as a^{-3}. But 1+z = 1/a, so matter density scales as (1+z)^3.

Right, that is a model-dependent calculation, not an observation. That is what is apparently contradicted (and thus where I see the paradox) by the hypothetical future SDSS 3D galaxy map up to a high redshift, that we expect to be homogenous. But perhaps, I'm misunderstanding something and cosmologists don't expect to find that map statistically homogenous. If so, please explain.

Basically, proposing that the matter density wasn't eight times its current value at z=1 requires proposing a universe that has radial-dependent density for an equal-time slicing.

I see what you mean, yes, that seems to follow logically.
The universe is a strange place, and is full of apparent contradictions, wish we knew it better, but let's be humble (and honest), we are barely starting to grasp it.

This is, in principle, a rather difficult thing to accurately determine, but suffice it to say our theories that use a homogeneous matter distribution work, while alternative theories proposed to explain certain unpleasant aspects of the homogeneous theories don't.

Ultimately, it seems to come down to a practical matter.
BTW, I don't know what are those theories proposed to explain unpleasant aspects of homogenous theories, and what these unpleasnt aspects are. Would you elaborate a little on this?

 

[Chalnoth]

Right, that is a model-dependent calculation, not an observation. That is what is apparently contradicted (and thus where I see the paradox) by the hypothetical future SDSS 3D galaxy map up to a high redshift, that we expect to be homogenous. But perhaps, I'm misunderstanding something and cosmologists don't expect to find that map statistically homogenous. If so, please explain.

You have to look into it in a bit more detail. For example, if you combine nearby measurements of the Hubble constant and supernovae with WMAP data, you end up with a nearly-flat universe.

If you then proceed with the assumption of flatness and make use of BAO data, you get a connection between length scales at different redshifts. If this link between length scales at different redshifts doesn't line up, then that would be evidence that the assumption of homogeneity was wrong. Basically, this length scale being at the expected place with the assumption of flatness is a reasonably direct test of the relationship z+1 = 1/a.

There are all sorts of different ways you can do this sort of experiment, but the basic idea here is that if you make a series of assumptions, and multiple independent experiments measure the same set of parameters based upon those assumptions, you gain confidence that those assumptions are, in fact, true, at least in an approximate sense. One of those foundational assumptions is homogeneity.

Ultimately, it seems to come down to a practical matter,it seems.
BTW, I don't know what are those theories proposed to explain unpleasant aspects of homogenous theories, and what these unpleasnt aspects are. Would you elaborate a little on this?

In this case, some have attempted to explain away the accelerated expansion by proposing a universe that has radial-dependent density. It turns out that such proposals are ruled out by observation.

 

[AWA]

You have to look into it in a bit more detail. For example, if you combine nearby measurements of the Hubble constant and supernovae with WMAP data, you end up with a nearly-flat universe.

If you then proceed with the assumption of flatness and make use of BAO data, you get a connection between length scales at different redshifts. If this link between length scales at different redshifts doesn't line up, then that would be evidence that the assumption of homogeneity was wrong. Basically, this length scale being at the expected place with the assumption of flatness is a reasonably direct test of the relationship z+1 = 1/a.

There are all sorts of different ways you can do this sort of experiment, but the basic idea here is that if you make a series of assumptions, and multiple independent experiments measure the same set of parameters based upon those assumptions, you gain confidence that those assumptions are, in fact, true, at least in an approximate sense. One of those foundational assumptions is homogeneity.

This is all understood and fine, I'm just taking that assumption to its last logical consequences if we take relativity seriously, and if we agree that if you observe long distances spaces you are also observing the past, one cannot be homogenous if the other isn't too, and viceversa. As they say, you can't have one without the other.

This leads to some contradiction with standard cosmology, so when in doubt, of course we choose standard cosmology, right?