Thinking About Large-Scale Structure

In article , "Robert L.
Oldershaw" writes:

on this, and none have found detectable clumping beyond 100-200 Mpc.
The result is (small) upper limits on large spatial scales. That's not
to say that there are rare extreme cases. Homogeneity is a statistical
statement, which implies there will be extremes in the tail of the
statistical distribution.

Well Craig, the putative "turnover" has already been shifted outside
your 100-200 Mpc limit you cited above.

How about the entire Cosmic Web? Is this not clumping on a VERY large
scale?

I think that this is a misunderstanding. The cosmic web itself IS
clumping on a large scale, but is not in disagreement with large-scale
inhomogeneity. Take a cube of the cosmic web a few hundred Mpc on a
side. Take another, non-overlapping cube. Are they statistically
similar? If so, then we have large-scale homogeneity.

If structures with sizes in the 500-1000 Mpc range were found to be
common, would you begin to doubt the whole concept of cosmological
"homogeneity", or would you recommend moving the goalposts again?

We can't know what exists where we haven't looked. So, if such
structures are detected, we have a new lower limit. This is not what is
usually termed "moving the goalposts", though. Concluding that there is
no homogeneity on ANY scale, when our vision is limited to some maximum
scale, seems an invalid extrapolation, though.

In article ,
"Robert L. Oldershaw" writes:
Are we really confident that we can claim that "there is very little
detectable clumpiness"..."beyond a few hundred Mpc"?

That's a fair question, but there are a couple of things to realize.
First of all, "very little" needs to be _quantitative_. Nobody
claims there is strictly zero clumpiness -- even the microwave
background is clumpy, though at a tiny level. The other thing to
realize is that the answer is inherently statistical.

The question of clumpiness is usually addressed in terms of "cosmic
variance." I offered one reference back on Feb 5. Two more recent
ones are at
http://adsabs.harvard.edu/abs/2010MNRAS.407.2131D
and
http://adsabs.harvard.edu/abs/2011ApJ...731..113M

The first of the above references indicates that inhomogeneity is
about 10% at size scales of 300 Mpc. Inhomogeneity decreases with
scale up to that value. Size of 600 Mpc corresponds to about 17
degrees on the sky at redshift z=1, and there are no single fields
(at least to my knowledge) deep enough to reach z=1 and that
large. (There should be some coming, however, and perhaps already
published.) However, 600 Mpc in redshift space is Delta z = 0.14, so
information on that scale is available from redshift surveys. There
is also information from measuring fields separated on the sky by
many degrees of arc. In fact, separated fields differ in number
counts by factors consistent with cosmic variance estimates.
Nevertheless, I'm not sure a modest increase (say from the expected
5% to 15-20%) is directly ruled out. Anything more than that would
almost certainly have been seen.

Once again, the (2008) cosmic variance calculator is at
http://casa.colorado.edu/~trenti/CosmicVariance.html

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

On Monday, March 21, 2016 at 4:24:21 AM UTC-4, Phillip Helbig (undress to reply) wrote:

I think that this is a misunderstanding. The cosmic web itself IS
clumping on a large scale, but is not in disagreement with large-scale
inhomogeneity. Take a cube of the cosmic web a few hundred Mpc on a
side. Take another, non-overlapping cube. Are they statistically
similar? If so, then we have large-scale homogeneity.

To me this might uncharitably referred as a sleight-of-hand method of
achieving "homogeneity". A more charitable way to describe your method
would be to characterize it as achieving "homogeneity" by inventive
use of definitions.


If structures with sizes in the 500-1000 Mpc range were found to be
common, would you begin to doubt the whole concept of cosmological
"homogeneity", or would you recommend moving the goalposts again?

We can't know what exists where we haven't looked. So, if such
structures are detected, we have a new lower limit. This is not what is
usually termed "moving the goalposts", though. Concluding that there is
no homogeneity on ANY scale, when our vision is limited to some maximum
scale, seems an invalid extrapolation, though.

But we have looked on 500-1000 Mpc scales and found systems of such
size. Since this approaches the limits of our observational
capabilities the results are still open to question, but we have
looked and found.

Do you imply that the "new lower Limit" for the turnover can be
indefinitely shifted to higher values, as needed to avoid
falsification? Forever?

Regarding your last sentence: but does that not also imply that
concluding that there must be "homogeneity" on SOME scale, when our
vision is limited to some maximum scale, seems an invalid
extrapolation, though?

RLO http://www3.amherst.edu/~rloldershaw

On Monday, March 21, 2016 at 4:25:24 AM UTC-4, Steve Willner wrote:

That's a fair question, but there are a couple of things to realize.
First of all, "very little" needs to be _quantitative_. Nobody
claims there is strictly zero clumpiness -- even the microwave
background is clumpy, though at a tiny level. The other thing to
realize is that the answer is inherently statistical.


Many thanks for this very informative post. If people routinely used
the phrase "statistical homogeneity" instead of the term "homogeneity"
a lot of confusion and misunderstanding could be avoided. Just to be
clear and candid, I do not for an instant buy the argument that the
use of the term "homogeneity" means or implies
"statistical/approximate homogeneity".

In science, I regard such distinctions as very important for obvious
reasons.

[Mod. note: reformatted -- mjh]

In article , "Robert L. Oldershaw" writes:
On Monday, March 21, 2016 at 4:25:24 AM UTC-4, Steve Willner wrote:

That's a fair question, but there are a couple of things to realize.
First of all, "very little" needs to be _quantitative_. Nobody
claims there is strictly zero clumpiness -- even the microwave
background is clumpy, though at a tiny level. The other thing to
realize is that the answer is inherently statistical.


Many thanks for this very informative post. If people routinely used
the phrase "statistical homogeneity" instead of the term "homogeneity"
a lot of confusion and misunderstanding could be avoided. Just to be
clear and candid, I do not for an instant buy the argument that the
use of the term "homogeneity" means or implies
"statistical/approximate homogeneity".

In science, I regard such distinctions as very important for obvious
reasons.

Note that essentially everyone except you means "statistical
homogeneity". Complete homogeneity implies a completely featureless
universe. Are you claiming that you were confused because you think
that this is what everyone meant?