We have proposed that above some unknown scale R the matter density falls off rapidly. What are the observational constraints on the value of R? I gather the amount of matter at redshift z (or distance r) is only poorly known.
H.V. Klapdor-Kleingrothaus, K. Zuber /Teilchenastrophysik, B.G. Teubner Gmbh, Stuttgart,1997
This paper, Hawkins et al. "The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe", may have what you want: http://arxiv.org/abs/astro-ph/0212375
It has an analysis of galactic density up to z ~ 0.2. Deeper studies of the density of galactic clusters including the dark matter component are in progress and in proposal, e.g. http://www.stsci.edu/jwst/overview/history/drm/drm1.pdf
Your question is about matter density, but here is something on the related subject of [normal] matter composition with redshift: http://ned.ipac.caltech.edu/level5/March03/McWilliam/McWilliam_contents.html
Thanks, Jay
It seems from your references that matter density is only probed out to a small fraction (< 1 %) of the radius of the observable universe. Do you agree?
Not really. There are estimates of DM contents also at higher redhifts. Good indications come from the Planck data: http://io9.com/the-planck-satellite-discovers-extra-dark-matter-in-the-458250688 which probes the universe as a whole and from observations of high redshift clusters. If you explain better what you really need I can try to help.
Well, there are the Hubble Deep Field, Hubble Ultra Deep Field, and Hubble Extreme Deep Field, but yes, the sampling is sparse for large redshifts.
For any sample, there will of course be an upper limit to the redshift, and some loss of sampling short of that upper limit. This paper on the HXDF, Beckwith et al: http://arxiv.org/pdf/astro-ph/0607632v1.pdf mentions that the density of very distant galaxies is a tenth of the local density, but that that is a lower limit because of the selection effects of identifying objects and establishing their redshift.
This paper gives a straightforward figure of number vs. redshift in the HDF, Gwyn and Hartwick: http://arxiv.org/pdf/astro-ph/9603149v1.pdf The large variability of galaxy density vs redshift shows that the deep measurements are narrow as well, and sample a Universe that is locally non-homogenous. The homogeneity and isotropy of the deepest measurement of all, the microwave background, gives some confidence that that variability is due to the narrow sample.
In other words, I think the Universe is isotropic and homogeneous on the largest scales, the canonical view.
A much wider but still very deep sample, but one with complex selection effects, is gamma-ray bursts. Here is the redshift distribution of Swift GRBs: http://raunvis.hi.is/~pja/GRBsample.html The GRB rate samples core-collapse supernovae of massive stars, which samples star-formation rate, which has something to do with matter density. Clearly the number of GRBs detected does not increase as the volume observed nor even vary as the star formation rate. However, the energy range and sensitivity of BAT on Swift is not enough to see all bursts at the largest redshifts.
This paper, Virgili et al: http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2011.19459.x/abstract attempts to relate the GRB rate to expected rates using Swift data. Their conclusion is that there are slightly more high-redshift GRBs than expected. This paper uses BATSE data, for which there were only a few direct redshift measurements, http://authors.library.caltech.edu/27129/1/DONaipcp03.pdf
Just in case, may be these papers will be useful:
arXiv:1311.4870 [pdf, ps, other]
The Sloan Digital Sky Survey quasar catalog: tenth data release
Isabelle Pâris, Patrick Petitjean, Éric Aubourg, Nicholas P. Ross, Adam D. Myers, Alina Streblyanska, Stephen Bailey, Patrick B. Hall, Michael A. Strauss, Scott F. Anderson, Dmitry Bizyaev, Arnaud Borde, Jon Brinkmann, Jo Bovy, William N. Brandt, Howard Brewington, Joel R. Brownstein, Benjamin A. Cook, Garrett Ebelke, Xiaohui Fan, Nurten Filiz Ak, Hayley Finley, Andreu Font-Ribera, Jian Ge, Fred Hamann, Shirley Ho, Linhua Jiang, Karen Kinemuchi, Elena Malanushenko, Viktor Malanushenko, Moses Marchante, Ian D. McGreer, Richard G. McMahon, Jordi Miralda-Escudé, Demitri Muna, Pasquier Noterdaeme, Daniel Oravetz, Nathalie Palanque-Delabrouille, Kaike Pan, Ismaël Perez-Fournon, Matthew Pieri, Rogério Riffel, David J. Schlegel, Donald P. Schneider, Audrey Simmons, Matteo Viel, et al. (4 additional authors not shown)
Comments: Accepted for publication in A&A. The catalog is available at this http URL (Note that there is a slight delay for the website to appear online)
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO)
Some information about z>10
arXiv:1311.3953 [pdf, ps, other]
Non-Equilibrium Populations of Hydrogen in High-Redshift Galaxies
Brian B. Pomerantz, Kayla Redmond, Vladimir Strelnitski
Comments: 11 pages, 7 figures, submitted to MNRAS
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO)
Some theory about z>100
arXiv:1311.3787 [pdf, ps, other]
Cosmic structure, averaging and dark energy
David L. Wiltshire
Comments: 55 pages, 15 figures. Based on 5 lectures presented at the 15th Brazilian School on Cosmology and Gravitation, Mangatariba, August 2012. To appear in the Proceedings, eds S. Perez Bergliaffa and M. Novello, 2013
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
arXiv:1311.3666 [pdf, ps, other]
Discovery of three z>6.5 quasars in the VISTA Kilo-degree Infrared Galaxy (VIKING) survey
B. P. Venemans (1), J. R. Findlay (2), W. J. Sutherland (3), G. De Rosa (4), R. G. McMahon (5,6), R. Simcoe (7), E. A. Gonzalez-Solares (5), K. Kuijken (8), J. R. Lewis (5) ((1) MPIA Heidelberg, (2) Durham University, (3) Queen Mary, London, (4) Ohio State University, (5) IoA Cambridge, (6) KICC Cambridge, (7) MIT, (8) Leiden Observatory)
Comments: 22 pages, 9 figures. ApJ in press
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO)
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