Chronos said:
All observational evidense to date strongly suggests galaxies and matter are evenly dispersed throughout the universe. WMAP is the best evidence to date.
WMAP shows that the cosmic background radiation is evenly distributed; and this is our earliest view of the gas which then later became stars and galaxies and astronomers.
WMAP also shows the "ripples", which are seeds of structure, or the
lack of even distribution on the scale of galaxies, which has been mentioned previously. So yes, WMAP is good evidence for large scale homogeneity... with the important quibble that it is
not an even distribution on the scale of galaxies at all! Galaxies themselves are not evenly distributed at all... they are clustered, and the clusters are clustered. But if you go to larger scales, you do have homogeneity.
One of the interesting questions in deep space astronomy is to identify the largest scales of inhomogeneity. Give the extreme smoothness of cosmic background radiation, we expect a bound on the size of structures. There's been time for material to clump into the filaments and walls and voids which have been mentioned, but it's limited time. So there would be a problem if structure was found on sufficiently large scales.
The observations on that point are not all cut and dried! Models for how matter clumps together also have to take into account the effects of dark matter, which also clumps. There have been occasional reports of apparent early structure which is on scales larger than would be expected, but I am not entirely sure of the status of these at present.
One topic I looked at some years ago was the "Francis Filament", which was at that time considered to be something of a problem by at least some researchers.
See also an old thread on the subject, [thread=147473]Explaining the structure of Galaxy "Filaments"[/thread].
Cheers -- sylas