The first detailed 3D maps of the galaxy distribution were made possible when spectrographs -- the machines used to measure galaxy redshifts -- were retrofitted with high-voltage image intensifiers. The spectrum of a galaxy that required a 2 to 3 hour exposure prior to 1970 took only a 10 to 15 minute exposure after that date, as long as an image intensifier was available. Of course, CCD technology has now carried things further, but the ability to measure galaxy spectra with an image intensifier was the first break-through in imaging technology.
In 1971, University of Arizona Prof. William Tifft recruited graduate student Stephen Gregory to assist him in measuring galaxy redshifts obtained with the new image intensifiers. For one of the first surveys, William Tifft selected a region centered on the beautiful Coma cluster of galaxies. Once their survey of galaxy redshifts was complete and they plotted a redshift map for Coma -- in the now-famous 3D pie-chart format -- Tifft and Gregory noticed a paucity of galaxies in the space between us and the Coma cluster. One other astronomer, Nicholas Mayall, had studied the Coma cluster in a similar fashion in the 1960's, but because he had too few galaxy redshifts and did not plot his results in a true 3D diagram, Mayall was unable to draw any remarkable conclusions.
The first diagram shown here is the original Tifft and Gregory 3D graph. In this depiction, the Earth and Sun are situated at the sharp vertex at the bottom of the diagram, and the extragalactic universe stretches out toward the top with the furthest edge of the diagram corresponding to a distance of about 80 Mpc (260 million light years). Each dot in this pie-shaped diagram represents a single galaxy whose redshift has been measured and therefore whose distance can be estimated (directly from Edwin Hubble's velocity-distance relationship). While all pie-diagrams are shown flattened onto the computer screen, they actually have depth (into and out of the computer screen) which cannot be shown on an ordinary display. Notice in the Tifft-Gregory pie-chart that the volume between the vertex and the line labeled 4000 is not uniformly filled with galaxies. Edwin Hubble and other cosmologists predicted that this volume would be uniformly filled with galaxies, but this is simply not true for the galaxies in the real universe.
Although Tifft and Gregory noted that there was a deficiency of galaxies in this region, when they published their results, they did not make too much of it and only briefly mentioned this point in a figure caption. Exactly why they chose to down-play this particular result is discussed in the technical discussion below.
By 1976 Stephen Gregory and I had both finished our doctoral studies in astronomy at the University of Arizona, and we were casting about for interesting research topics. We decided to create a 3D map of a much larger volume of space in a slice across the sky that stretched 21 degrees from the Coma cluster to the cluster Abell 1367. Selecting such a wide area for a redshift survey was a new concept at that time, since others who were measuring galaxy redshifts were concentrating on studies of well known rich clusters like those in the constellations of Coma Berenices and Hercules, not recognizing the true power of making large-scale 3D maps over large volumes of space.
Even before we collected the redshifts, Gregory and I made the following hypothesis: If the two galaxy clusters, Coma and Abell 1367, are members of the same supercluster, the 21 degree span between them should be filled with galaxies that bridge the gap between the two clusters. Gregory and I measured the redshifts at Kitt Peak National Observatory, made our 3D map, and immediately after drawing the diagram we were astonished to find that not only was our hypothesis confirmed regarding the bridge of galaxies connecting Coma and Abell 1367, but more importantly, the galaxy distribution within the entire 21 degree slice of the sky was very filamentary with large empty regions of space throughout the survey volume.
The second diagram shows the Gregory-Thompson 1978 results. The Coma cluster sits near the left hand side of the pie-chart and the cluster A1367 sits at the right hand side (both at a distance from Earth of 90 Mpc to 100 Mpc). Just like the Tifft and Gregory plot shown above, the Earth and Sun are situated at the vertex and extragalactic space stretches toward the top to a depth of approximately 133 Mpc (435 million light years). Each point in the diagram represents a single galaxy whose redshift was determined with an image-intensified spectrograph.
We analyzed our new map and described the superclusters and the vast empty regions we had discovered, and then we submitted a manuscript containing these results to the Astrophysical Journal. It was submitted in September 1977 and published in June 1978. In this manuscript, we introduced the word "voids" to describe for the first time the large empty regions seen in our 3D redshift map. Then we immediately went on to do other galaxy redshift surveys with other collaborators: Massimo Tarenghi, Guido Chincarini, Herb Rood, and of course, William Tifft. Each time a new 3D map was made, it confirmed our initial results. As described below a second group (Joeveer, Einasto, and Tago) published similar results in the November 1978 issue of the Monthly Notices of the Royal Astronomical Society.
Gregory and I summarized our early redshift surveys in an article entitled "Voids and Superclusters in the Galaxy Distribution" published in the March 1982 issue of Scientific American. Displayed here are two images from this Scientific American article. The first image shows the title page and the second image shows a simulated 3D diagram where we display the void - supercluster structure as it was known as of early 1982. This 1982 article in Scientific American is significant in showing the rather mature view that Gregory and I had of the void and supercluster phenomenon in the early 1980's.
As is often the case with startling new discoveries, not all astronomers and cosmologists immediately accepted this new view of the large scale galaxy distribution. In fact, while both Stephen Gregory and I knew precisely what we had discovered, we were repeatedly criticized even into the early 1980's by several prominent theoretical cosmologists who found our results hard to understand given their assumptions about the universe and even earlier assumptions made by Hubble and the founders of modern cosmology. When one redshift survey after another (some of these by Gregory and me) repeatedly confirmed our discovery, finally the last hold-outs in theoretical cosmology accepted the reality of voids in the galaxy distribution. Today the large scale structure provides a key point of reference for astrophysicists who struggle to find an acceptable way to explain how the voids were created in the context of the hot Big Bang, cold dark matter and models of galaxy formation. In this regard, the large scale structure plays a role similar to that of the cosmic microwave background as one of the key touchstones for modern cosmology.
Speculation on the nature of the large-scale distribution of galaxies began with the first surveys of nebulae by Messier and Herschel in the late 18th century, and this speculation continued through the mid 1970's when -- in a remarkably short period of time -- several extensive redshift surveys of galaxies revealed the beautiful but complex web-like structure consisting of voids and galaxy superclusters. In this section I discuss a number of technical details of the first galaxy redshift surveys. Andrea Biviano (2000) gives an excellent technical review of the very early history of extragalactic astronomy dating from the work of William Herschel in the late 1700's and extending through 1983. Although Biviano (2000) discusses the history of the work on large-scale structure during a 250 year period, I provide here a description of only the rapid changes that occurred in our view of the universe during the 1970's and into the 1980's.
While many studies of the large-scale distribution of galaxies were made prior to the mid-1970's, virtually all of these studies were based on the apparent distribution of objects as we see them projected onto the sky, i.e. depth information was not part of the analysis. The lack of depth information crippled the early investigations and left the true nature of the large-scale structure in an unresolved muddle. The first person to find his way out of this problem was Prof. Gerard de Vaucouleurs. Throughout the 1950's he worked to determine the distribution of galaxies in the Local Supercluster, and by the late 1960's he began to move from studying the distribution of galaxies on the sky to studying their 3D distribution using the relatively small number of catalogued galaxy redshifts which, by then, he had placed in his (first) Reference Catalogue of Galaxies. Based on these early studies, Gerard de Vaucouleurs properly suggested that the spatial distribution of the local galaxy distribution -- out to a redshift of about 2000 km/s -- was quite irregular.
One might ask: Why didn't Gerard de Vaucouleurs discover voids during his studies of the Local supercluster? The answers are (1) that he did not have at his disposal the distances to enough galaxies outside the Local supercluster, and (2) his personal view or model of the universe was wrong. In 1970 Gerard de Vaucouleurs published an article in the journal Science (de Vaucouleurs 1970) in which he summarizes his knowledge of the 3D distribution of galaxies and presents all the evidence available at that time for large-scale irregularities in the galaxy distribution. Then he makes a leap in logic to claim that the universe as a whole must be inhomogeneous on the largest scales and suggests that hierarchical world models like those of Charlier (1908, 1922, 1925) replace conventionally accepted models of Big Bang cosmology. This paper demonstrates how uncertain the status of the large scale structure was just six years before the Gregory and Thompson paper was published in 1978.
It was in the early 1970's that the image intensifier tube was first introduced into observational astronomy. The best of these intensifiers were developed with funds from the Carnegie Foundation and were therefore called Carnegie image tubes. The University of Arizona's effort to build and test Carnegie image tubes was headed by Dr. Richard Cromwell. He, in concert with Prof. William G. Tifft and several others at the University of Arizona, tested these devices at the Steward Observatory 2.3-m telescope on Kitt Peak. When the Carnegie image tube camera was tested with a spectrograph on the 2.3-m telescope, it was immediately apparent that the redshift of an average galaxy (and hence an estimate of the galaxy's distance) could be obtained in a matter of 10 to 15 minutes of telescope time. This same redshift would have taken many hours to obtain with a simple photographic plate, the only other detector available in that era.
Once the image tube camera was available on the spectrograph, William Tifft was able to collect many, many galaxy spectra and he enlisted the support of others to assist him in measuring the spectra to extract the galaxy redshift information. Two people were first in becoming part of William Tifft's redshift team: graduate student Stephen A. Gregory and postdoctoral researcher Massimo Tarenghi. While Tifft and Gregory concentrated on redshift measurements in the Coma cluster of galaxies, Tifft and Tarenghi worked on the Hercules cluster. It turns out that Kitt Peak National Observatory (now National Optical Astronomy Observatory) also assembled several Carnegie image tubes and mounted them on the spectrographs of their large telescopes. Dr. Herbert J. Rood and Prof. Guido Chincarini were visiting astronomers at Kitt Peak in that era, and they became regular users of these image tube spectrographs. Herb Rood and Guido Chincarini were also very interested in studying the Coma cluster of galaxies. At the time of the very first redshift surveys, I was concentrating on studies of galaxy morphology in rich clusters. Instead of measuring galaxy redshifts, I worked on direct images of the same clusters: Coma, Hercules, and others. I was also a Ph.D. student of Prof. William Tifft and was therefore a part of this small community of extragalactic astronomers.
The galaxy redshift surveys in rich clusters progressed rapidly, but one big fly appeared in the ointment when, in 1972, William Tifft published a paper in the Astrophysical Journal (Tifft 1972) claiming to find discrete bands in a diagram in which galaxy redshift was plotted against galaxy magnitude for a sample of Coma cluster galaxies. On this basis, William Tifft began to suspect that galaxy redshifts were not of Doppler origin -- as all cosmologists believed -- and instead he began to speak of quantized redshifts and redshift segregation. Redshift segregation was the term William Tifft used when he began to see the very first structure in the 3D redshift survey diagrams. Discussions between the University of Arizona redshift survey group and the Rood and Chincarini group were fairly open (in fact Massimo Tarenghi and Guido Chincarini were friends), so Guido Chincarini and Herb Rood quickly became aware of William Tifft's redshift segregation and redshift quantization concepts. While William Tifft independently advocated this unusual interpretation as a parallel effort, the redshift surveys proceeded and the samples grew larger and larger, especially for the Coma cluster. Galaxy redshift survey papers on the Coma cluster were the first to appear: Chincarini and Rood (1975) and Tifft and Gregory (1976)
The diagram below shows the primary result of the Tifft and Gregory (1976) Coma cluster
redshift survey. In terms of the study of large-scale structure, it represents a
remarkable advance for two reasons. For the first time ever, the redshift survey
data are plotted in polar coordinates in a form that would later be called a
pie-plot, a wedge diagram, or a slice of the universe diagram. In such diagrams,
the galaxy declination coordinate is ignored (or more properly stated,
it is projected onto the plane of the diagram), the right ascension is used as the
angular polar coordinate, and the galaxy redshift (interpreted as distance) is used as the
radial coordinate. We are located at the apex of the diagram at redshift = 0.
The Tifft and Gregory wedge diagram
as shown below begins to provide the first hint of an inhomogeneity in the galaxy
distribution over scales of 50 Mpc to 100 Mpc. This apparent inhomogeneity is the second
remarkable feature of their paper. William Tifft and Stephen Gregory did not emphasize
the second point in their paper, however, and they only mention it in a figure caption.
It was not emphasized because (1) the survey area is rather small and there is only
the first hint of structure, and perhaps more significantly (2) William
Tifft had non-Doppler redshift ideas on his mind, and he was not ready to interpret the
diagram in a true 3D geometric fashion.
Guido Chincarini and Herb Rood had their own scheme for presenting their galaxy redshift
observations of the Coma cluster. In this scheme, taken directly from the early work of
Nicholas Mayall (1960), galaxy redshifts are plotted on the vertical axis while
the galaxy's radial position from the center of the cluster is plotted
on the horizontal axis. While there is some hint of spatial information in such
a plot, in a general sense it muddles the true 3D information. An example from
one of the best Chincarini and Rood papers is reproduced below. Although the
plot shows clumpy behavior in the redshift direction, in the radial direction the galaxy
distribution is relatively smooth. This led Chincarini and Rood (1976) to state -- in
their best paper before the discovery of voids -- that "the large sizes of clusters
and their fading into the low-density supercluster backgrounds leaves little if
any space between them." In other words, they saw no voids. They did note the
clumpy redshift distribution, but this they called a "segregation in redshifts"
directly borrowing the non-Doppler term suggested by William Tifft.
Ironically, the Chincarini and Rood data covered a wide area of the sky (stretching
16 degrees to the west of Coma), so they had collected much of the redshift data
sample that was needed to see the voids in this region of space,
but they failed to display the data in a way that would make the large-scale
structure apparent. Their papers made it very clear that they were interpreting
the radial extent of the data in their diagram as the spherical extent of
the Coma supercluster, whereas a 3D diagram would show that the majority of their
Coma supercluster galaxies reside in what is now called the Great Wall, a linear
feature that happens to run perpendicular to the line of sight.
By the time the first Coma cluster redshift surveys appeared in press, both Stephen Gregory and I had completed our Ph.D. work and were ready to pursue other research topics. We were both very cognizant of the unsettled debate regarding the existence or nature of galaxy superclusters. Gerard de Vaucouleurs was not the only prominent extragalactic astronomer who was discussing this problem. The two most competitive astronomers to weigh in for this debate were Professor Fritz Zwicky and Professor George Abell. Fritz Zwicky argued vehemently against the existence of superclusters while George Abell was an outspoken supporter of superclusters. Of course, their views were strongly molded by the way they each had defined galaxy clusters in their respective cluster catalogs.
Given that redshift surveys could be used to map the 3D distribution of
galaxies -- and hence map the superclusters -- Gregory and I decided to make a direct
test to see whether
superclusters exist. As our first target we chose the Coma / A1367 region
of the sky, a natural choice because many redshifts in and around the Coma cluster
had already been measured. When we submitted our request for telescope time, we
stated our hypothesis very clearly: if Coma and A1367 belong to the same
supercluster, they should be connected by a bridge of galaxies indicative of an
over-density of galaxies
in that region of space. We were granted the telescope time to measure
galaxy redshifts, and in the era when Chincarini and Rood were publishing their
Mayall plots, we had the clearly stated aim of mapping the 3D galaxy distribution
in a swath of sky that stretched 21 degrees to the west of Coma. (Chincarini and
Rood had already gone 16 degrees.) Once the galaxy redshifts were measured and we made
the appropriate 3D pie-plot (or wedge diagram), we not only got an immediate answer to
our question regarding the bridge of galaxies connecting Coma and A1367, but we saw the
void phenomenon for the first time. Our wedge diagram is shown below.
We were astounded by the clearly defined void / supercluster structure that was visible in our Coma/A1367 redshift plot, and we proceeded to write a manuscript for the Astrophysical Journal that very carefully and completely described not only phenomenologically what we saw but provided in very carefully worded sections the best interpretation we could devise. For example, in a quotation from section IV. of the published paper, we said the following:
"It is an important challenge for any cosmological model to explain the origin of these vast, apparently empty regions of space. There are two possibilities: (1) the regions are truly empty, or (2) the mass in these regions is in some form other than bright galaxies. In the first case, severe constraints will be placed on theories of galaxy formation because it requires a careful (and perhaps impossible) choice of both omega (present mass density/closure density) and the spectrum of initial irregularities in order to grow such large density irregularities. If the second case is correct, then matter might be present in the form of faint galaxies, and an explanation would have to be sought for the peculiar nature of the luminosity function. ..."
After many months of revisions -- and struggles over the precise choice of words -- the final version of our manuscript was finished during the summer of 1977, which Stephen Gregory and I spent together in Tucson. We submitted the manuscript to the Astrophysical Journal for review, and it arrived at the journal on September 7, 1977. As it turns out, this was none too soon because, unknown to us, another group of astronomers in Estonia was also making large-scale 3D maps of the galaxy distribution based on the relatively patchy redshift data that had already accumulated in catalogs. In fact, a scientific meeting had been organized in Tartu, Estonia, for September 12-16, a meeting that was called "The Large Scale Structure of the Universe". Throughout the previous year, the meeting organizers -- Prof. Malcolm Longair and Dr. Jaan Einasto -- had arranged with those observational astronomers and theoretical cosmologists who were working on the large- scale structure of the universe to make presentations at the meeting. Ironically, in correspondence with these organizers, our participation in this meeting had been denied in favor of more senior scientists. While neither Stephen Gregory nor I were invited to this meeting, several other members of the Arizona redshift group were invited: William Tifft, Massimo Tarenghi, Herb Rood, and Guido Chincarini. This is excusable only in one regard: Stephen Gregory and I realized the potential impact of our discovery, so we had refused to discuss our new results even with our closest astronomy colleagues until the manuscript was ready to be submitted. So neither Malcolm Longair nor Jaan Einasto could have known what we had discovered.
We eventually shared our findings with our former thesis advisor, William Tifft, and at the meeting in Tartu, Estonia, he presented a paper (authored by Tifft & Gregory) which briefly discussed the findings of our new paper and listed it in the references to his conference paper as Gregory and Thompson (1978) in press. It is most interesting to read the discussion that followed William Tifft's presentation in the conference proceedings (Longair & Einasto 1978). At the same time that several astronomers at the meeting began to realize what the redshift wedge diagrams were showing in terms of the large-scale structure, the theoretical cosmologists were making excuses as to why the data might be faulty. William Tifft himself made it clear that he was interpreting the unusual redshift distributions -- not only those from the Coma redshift survey of Tifft and Gregory (1975) but also the new Coma / A1367 redshift survey of Gregory & Thompson (1978) -- in terms of quantized redshift effects.
More significantly, at the Tartu meeting, Mihkel Joeveer and Jaan Einasto presented a
paper entitled "Has the Universe the Cell Structure?" in which they, too, report giant
empty regions in 3D plots of the galaxy distribution, and at one point in their
they say: "The mean diameter of big holes as well as superclusters is ~100 Mpc."
It should be stated very clearly that Mihkel Joeveer and Jaan Einasto based their
analysis on galaxy redshifts that they found in catalogs. Because of this fact,
their results were less definitive. For all anyone knew, their maps
might have been deficient due to non-uniformities in the data (cases where the
observations just happened to be absent in certain regions of the sky making it
look as though there was a giant void
here or there), whereas the Arizona redshift surveys all had a strict requirement that
the redshift samples were to be magnitude-limited. All the same, the Joveer and
Einasto results were on the mark, and one of their first pie or wedge diagrams
is reproduced below.
The Joeveer & Einasto analysis and the Gregory & Thompson analysis were both first discussed publicly in Tartu September 12-16, 1977 (Longair and Einasto 1978). Both final analyses were published in refereed journals and had somewhat similar time-lines. The Gregory & Thompson paper appeared in its final from in the June 15, 1978 issue of the Astrophysical Journal. Since our paper was submitted before the Tartu meeting and we did not attend, the paper contains no references to that meeting. Joeveer and Einasto added a third author -- Erik Tago -- to their final published paper, and this three-author paper appeared in the November 1978 issue of Monthly Notices of the Royal Astronomical Society. They do include references to the Tartu meeting presentations, including that of William Tifft. It is important to note that the primary criticism of the early redshift surveys -- criticisms that both Stephen Gregory and I faced over and over again in a five year period following the publication of our Coma / A1367 survey -- was based on the question as to whether the redshift samples were uniformly defined and complete. In this regard, the Gregory & Thompson (1978) results were clearly more substantial. In addition, the Gregory & Thompson paper was the first to be published in a refereed journal by more than four months, and we had not heard of the Estonia group's work.
Those observational astronomers who were closely associated with the redshift survey work immediately grasped the significance of this new void-supercluster view of the large-scale structure. This included Guido Chincarini, Herbert Rood, and Massimo Tarenghi, and very soon other astronomers moved into the field. Relatively soon after the Gregory & Thompson work was published, Ricardo Giovanelli -- a friend of Guido Chincarini and a staff member at Aricebo Radio Observatory -- and his wife, Martha Haynes, began a redshift survey in the beautiful Perseus-Pisces supercluster region, a survey based on galaxy redshifts from the 21-cm emission line of hydrogen. Just as quickly I was contacted by Trinh Thuan and Tom Bania, and we formed a team to do the same sort of work as visiting astronomers at Aricebo. It soon became clear that Giovanelli and Haynes had a great advantage in making 21-cm redshift observations because of their respective staff positions with Aricebo Observatory and Cornell University (Cornell University operates Aricebo Observatory). So within 18 months after we began, the Bania, Thuan, and Thompson 21-cm survey work on the Perseus-Pisces region came to a halt.
In the mean time, optical redshift surveys continued to be published at a rapid pace. The first survey to appear after the Gregory & Thompson (1978) analysis of Coma / A1367 was a study of the very interesting Hercules supercluster, a region that includes A2147, A2151, and A 2152. This effort was headed by Dr. Massimo Tarenghi and included my participation and that of Guido Chincarini, Herb Rood, and William Tifft. Although the original plan for the Hercules study was to produce a single large paper, in the end the study was divided into two papers because of disagreements that arose with the reviewers of the paper, as well as with the various collaborators, about how to handle William Tifft's insistence that the paper include a discussion of non-Doppler redshift effects. In the end, the first paper (Tarenghi et al. 1979) contained primarily the basic redshift data, while the second paper (Tarenghi et al. 1980) was the forum for discussing the conventional 3D supercluster interpretation. William Tifft chose to remove his name from the second paper.
Stephen Gregory and I continued to work with William Tifft to complete a magnitude-limited redshift sample in the Perseus supercluster region. This is one of the areas that Joeveer, Einasto and Tago had studied first. Our aim in re-doing this work was to define a magnitude-limited survey of galaxy redshifts that would be immune from the criticism that incomplete redshift samples were misleading. The Perseus supercluster study was also published in the Astrophysical Journal (Gregory et al. 1981). Simultaneously, Guido Chincarini, Herb Rood and I completed yet another redshift survey and successfully detected a very long filament of galaxies connecting the Hercules group of clusters (A2147, A2151, A2152) to the A2197 & A2199 cluster pair (Chincarini et al. 1981). Sometime later, Gregory and I published a detailed study of the A2197 & A2199 galaxy cluster system (Gregory & Thompson 1984) which showed yet another example of the void & supercluster network.
In an effort to share with a general audience our new view of the large-scale galaxy distribution, Gregory and I wrote a paper for Scientific American, a paper that was given the title "Superclusters and Voids in the Galaxy Distribution". The original manuscript for this paper was in the hands of Scientific American as early as June, 1980, but the editors held it for publication in the March 1982 issue of this magazine (Gregory and Thompson 1982).
The precedence of the Gregory and Thompson (1978) paper is generally acknowledged today by astronomers and cosmologists (see Bahcall 1993 and Strauss 2004) despite the fact that several other groups who worked in this field in the 1980's chose to promote their own research in the public press and on television news shows as being "first in this" or "first in that". To be more specific, there were world-wide media blitzes featuring "The Million Cubic Megaparsec Void in Bootes" by Kirshner et al. (1981) and the "CfA Slice of the Universe" by de Lapparent, Geller and Huchra (1986). In the public press nothing was mentioned to indicate that the 1980's research was a confirmation of discoveries that had been reported previously in the 1970's. Those who wish to read more details about this matter can find the book entitled "The Universe at Midnight" by Ken Crosswell (2001) which contains interviews from several key redshift survey participants. The main outcome of the 1980's publicity campaigns -- and the convoluted way in which the Gregory and Thompson work was referenced in these two papers -- was to drain citations from the Gregory and Thompson (1978) paper and spread them among the papers published by the new research groups of the 1980's. This does nothing to change the fact that voids and their relationship to superclusters was first defined in 1978 by Gregory and Thompson.
Today the characteristics of the large scale distribution of galaxies are being used to constrain the concordance model of cosmology. These studies combine a power spectrum analysis of the irregularities in the cosmic microwave background (CMB) radiation with a power spectrum analysis of the large scale galaxy distribution -- plus other "priors" -- to beautifully constrain fundamental parameters such as the mean mass density of the universe, the baryon density, the dark energy (cosmological constant), etc. Foremost among these studies is that by Spergel et al. (2003) who analyized the WMAP power spectrum of the CMB in combination with an analysis of the 2dF galaxy redshift survey. More recently, the results of the SDSS galaxy redshift survey have become available, and Tegmark et al. (2004a, 2004b) report refinements to the standard model of cosmology after relaxing some "priors" and applying constraints from both the SDSS power spectra and the WMAP data. Among the more interesting results of Tegmark et al. (2003a) is the fact that hard constraints can be placed on the mass of neutrinos because the shape of the power spectrum of the large scale galaxy distribution depends on the total mass density in neutrinos. For sure these studies are work-in-progress: the analysis of the extensive SDSS galaxy redshift survey is just getting underway.
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