How has our view of the universe changed in the last ~25 years, and do we have a reasonable sample?

In pictures, basically its gone from this:

Figure 1.The angular distribution of galaxies in the northern hemisphere.
Image from Peebles (1980)

To this:

Figure 2.The 3-D distribution of ~4000 galaxies in redshift space.
Image by M. Geller et al. Science 246

In words, we have gone from a two dimensional view of the universe to a three dimensional view.

OK, here's the longer version

Introduction

If one is to understand anything about the large scale structure of the universe, it is generally advisable to know where the galaxies that make up that structure are. Therefore, mapping and understanding the spatial galaxy distribution is a prerequisite for constructing a viable picture of the universe. This effort, in progress since galaxies were first seen, finally reached its first step with the Abell, Zwicky & Lick catalogs, eventually documenting the angular locations of 1 million galaxies. The second step, well underway, has been to determine the 3rd dimension, the distance to the galaxies via redshift surveys.

Abell, Zwicky & Lick

Before technology allowed astrophysicists to measure the redshifts of large numbers of galaxies in the early 80's, knowledge of the large scale structure of the universe was limited to only the angular distributions of galaxies, and a very uniform microwave background. In the late 50's, G. O. Abell collected several thousand angular positions of galaxies from the Palomar Sky Survey into a catalog. The catalog did not contain any information concerning the distance to the galaxies -- it was essentially a projection of the true galaxy distribution onto a sphere. Then in the 60's Fritz Zwicky, undoubtedly overseeing a large number of underpaid, sleep deprived graduate students, visually scanned around 1000 photographic plates from the same survey, obtaining positions of over 30000 galaxies in the northern sky. Finally, in the early 80's, S. Schectman built a catalog of 1 million galaxies in the northern sky from Lick Observatory astrographic survey.

A representation of the galaxy distribution obtained from this survey is shown above in figure 1. It is a box graph, where a larger box indicates a higher density of galaxies in that bin. Note that in the 2-D survey there appears to be a fairly uniform background of galaxies, with regions of higher density scattered throughout. Much effort was spent in determining how much of the universe was represented by this seemingly uniform "background" and how much was contained in the clusters. Eventually, in 1977, by comparing the distributions of paired galaxies with single galaxies, Soniera & Peebles found that there really wasn't a whole lot of evidence for this uniform background, a result now backed up by modern redshift data

Redshift Surveys

When redshifts were first being obtained starting in the 1920's, it would typically take a few days on a large telescope to collect enough photons to obtain the required spectrum. Once telescopes with enough light gathering power became available and spectroscopic detectors became sophisticated enough to allow many redshifts to be taken in a reasonable amount of time, people started using these instruments to make maps of the 3 dimensional locations of galaxies and galaxy clusters.

Figure 3 Another view of the 3-D distribution of ~4000 galaxies in redshift space.
Image by M. Geller et al. Science 246

The plot above (fig. 3) and the one near the top of this page (fig 2) are representations of some of the measured 3 dimensional galaxy positions in redshift space. The radial distance in these plots is the measured redshift (essentially indicating the distance from us) and the angular coordinates represent the angular position of the objects in the sky. Redshift measurements involve determining the spectrum of the object to be measured. Once that is known, recognizable spectral lines can be found, and their deviation from their normal positions used to find the object's redshift. The Hubble Law then allows one to turn that redshift into a radial distance from our galaxy. Even though measuring a redshift takes much lest time than it used to, strong competition for telescope time necessitates picking an appropriate strategy to maximize useful results in a minimum amount of time. Some of these are:

Pencil Beam/Targeted Surveys
Here one picks a specific object, or several small regions of space, typically just a bit larger than the average scale length of galaxy density fluctuations (4-8 h-1 Mpc) to get a sampling of the redshifts in a region. These sorts of surveys are best suited to measuring large redshifts, because they allow sampling of small regions for relatively long times.

Some examples include:

Slices
This extends the 1 dimensional approach of the pencil beams to a two dimensional angular sweep. It is a compromise between studying distant, high redshift objects, & measuring the spatial distribution of galaxies. Typically one picks a constant declenation and measures the redshifts of all galaxies with a magnitude greater than some specified value, within a specified range of right ascensions. These surveys are surprisingly good at examining large scale structure, just as a CAT scan is good at examining biological structure. For this reason voids are easily seen with this type of survey.

Wide Angle Studies
These are the obvious extensions of the 2 dimensional "slices" to map a volume in space rather than just a strip. The two plots above are examples of the results from a survey of this type, namely the CfA survey. Notice that they are essentially stacked slices. These types of surveys are the most ambitious, due to their high consumption of telescope time. However, by covering a large volume they greatly aid the understanding of large scale structure. (Assuming knowing more about the galaxy distribution helps you understand it, see below...)

Examples:

Do we have a reasonable sample?

The data thats available now for understanding the topology of the universe is essentially a collection of 3-D data points with magnitudes greater than a certain limit (e.g. for the CfA survey this threshold was a magnitude of 15.5). This might be likened to using data greater than a specified elevation to understand the topology of the Earth. You would find the locations of all the mountain ranges, and possibly from that infer where continents are, but you would have no information about the oceans, etc. Applying this analogy to the galaxy distributions would make one wonder what exactly is in the voids (the large areas of black in the redshift plots above)? Could it be there are galaxies & dust there which are too dim to see? Whether there are or not would have important implications on what models one should use to describe the universe.

Well, for one thing, we can see through the voids, indicating there is not much to get in the way of light coming from the far side. Examinations of absorption lines from the sparse material that is in the voids, of light from objects on their far side, further indicate that most of the matter seems to be where the galaxies are. In other words, to follow the analogy, it seems there are only mountain ranges, in which case the galaxy distributions are reasonable indicators of the large scale structure of the universe.

Interpretations

Figure 4: A plot of the distribution of galaxies within 100Mpc of the
Milky Way. The real distribution has been smoothed with a
gaussian distribution of 15 Mpc. -- from Moore et al.

With the available redshift data, practically everyone agrees that the universe consists of a collection of voids and large clusters of galaxies. Unfortunately, that is all that seems to be agreed upon. There appear to be three main camps of opinions concerning what kind of structure is dominant in the universe:
Meatballs
Like the nickname says, this picture assumes the universe is a heirarchical collection of "solid" galaxy clusters and superclusters (the meatballs) sitting in a void background. This model is favored by proponents of Cold Dark Matter based galaxy evolution models since the small structures form first, then cluster together to form larger superclusters.
Swiss Cheese
This is the opposite of the meatball picture, where voids are imbedded in a background of galaxies. This is favored by proponents of Hot Dark Matter based models, where particles like massive neutrinos damp out the small scale matter fluctuations, and tend to produce large voids. Somehow there are sources of these particles which push material out to the edges, which collide to form the borders between the voids we see today. Some suggest these sources were gigantic explosions of some kind.
Sponges
This is a sort of compromise between the upper two pictures, where voids and clusters merge together in a sort of 3-d jigsaw effect.
Depending on one's determination, its seems to be possible to fit the galaxy distributions with any of these three pictures. If you smooth your data too much, you end up with meatballs. Smooth it too little or not at all, you might end up with swiss cheese. The problem seems to lie in the complete randomness of the real distributions.

More "Creative" Solutions

The difficulty in finding ways to represent the three dimensional galaxy maps seems to have encouraged the development of some very strange models. For example, in 1992, Xiaochun Luo & David N. Schramm presented a paper in Science suggesting the large scale structure of the universe can be fit with a fractal of dimension 1.2. It is unclear however what this means -- even to the authors:
The following questions arise when we discuss the possible fractal structures in the universe: How far does the fractal correlation extend? What can we learn from the fractal dimension D=1.2? What physical process can give rise to a fractal structure in the distribution of observable objects? At present these questions have ambiguous answers.
It is later suggested that if the fractal nature of the galaxy distributions is in fact true, that gravitational instabilty cannot fully describe the formation of galaxy clusters. Despite this however, it may be that determining a fractal dimension for the universe could have some use as a statistical test for comparing models to observations. In some sense, the fractal dimension tells how much of the three dimensional space a collection of points fills. Any successful model would probably have to fill the same amount of space.

Another person who at one time had his hand in the fractal bag, is J. Einasto. Recently, in a Nature article, his group has suggested the large scale structure of the universe is periodic, with a "lattice" constant of 120 Mpc. No mechanism for this is mentioned other than the suggestion that again, if this were true, mere gravitational instability could not explain the large scale structure of the universe. This paper's best (or maybe second best) use, however, is probably as an illustration of the dangers of allowing one's imagination and subjective opinions rule the interpretation of data. A rather frightening demonstration of this danger can be seen by clicking on this image, where you will see my subjective interpretaton of the same galaxy clusters.

Figure 5: The collection of superclusters used in Einasto et al. to
demonstrate the large scale periodicity of the universe. Click on it if you are brave.

As you can see, different people can see different things in data like this, which is why some objective means of representing this data is a prerequisite for developing any kind of sensible model. Currently none of the attempts at this seem to have worked, leading to a fair amount of confusion.

Non-conclusion

It is clear that there is no real consensus on what the large scale structure of the universe really is. Before the wide angle redshift surveys became available, it was pretty well accepted that based on the microwave background and the quasi-uniform angular distributions of galaxies that we lived in an essentially uniform universe. Both individual and clusters of galaxies are fairly evenly scattered in the celestial sphere. This impression completely fell apart once we started getting information on how far away these galaxies and clusters really are. The current state of affairs seems to be one of uncertainty whether the universe is made up of meatballs, sponges, swiss cheese, fractals, crystals, holy ducks, or weird clowns with balloons...

References