Well, there are inhomogeneities on all scales, but most of them are filtered out at scales larger than around 300 Mly or so. One rather direct way to measure this is just to take a large field of the sky with lots of galaxies, and start doing number counts of galaxies in each box at different size scales. Once you hit around 300Mly or so, those number counts become very nearly constant. Not actually constant, of course, but nearly so.skippy1729 said:Above what scale is the universe considered to be homogeneous? What sort of measure is used? I've looked at a few cosmology texts and they don't really discuss it much. Weinberg states 300 million LY. With 250 million LY diameter voids and 1370 million LY long filaments, 300 million LY seems like a very lumpy soup! Any references would be appreciated.
Skippy
Chalnoth said:Well, there are inhomogeneities on all scales, but most of them are filtered out at scales larger than around 300 Mly or so. One rather direct way to measure this is just to take a large field of the sky with lots of galaxies, and start doing number counts of galaxies in each box at different size scales. Once you hit around 300Mly or so, those number counts become very nearly constant. Not actually constant, of course, but nearly so.
Hmmm, sadly it was too long ago, and I'm unable to find the original reference. You may be right, it might have been an examination of isotropy and not homogeneity.skippy1729 said:I assume that you are talking about some sort of 3D box sorted by redshift distance. But unless the box dimensions are much larger than 300 Mly some will be dominated by voids and some by walls and filaments. If you are talking about dividing the sky into a 2D grid, uniformity will only imply isotropy which will not imply homogeneity without additional assumptions.
Do you have any references to actual calculations?
Skippy
harcel said:Actually, it also works in 3D. The scales you quote for voids and filaments are very rare exceptions, most are much smaller. Indeed, if you smooth the 3D density field on scales of ~300 MLyr you will find roughly the same total mass in all these volumes. The errors on that follow Poisson statistics, exactly what you expect for the shot noise in purely random fields.
The scale at which this homogeneity appears depends on the age of the universe. In the very early universe the mass distribution was already more homogeneous at much smaller scales. Larger scale fluctuations in the density field start to evolve non-linearly later. Google some of the terms here, and include terms like sigma-8 and collapse and you will find more info! Good luck!
The scale of homogeneity is a concept used in statistical analysis to determine if a particular sample or data set is representative of the entire population. It measures the extent to which the characteristics or variables being studied are evenly distributed across the sample.
The scale of homogeneity is important because it helps ensure the reliability and validity of statistical analyses. If a sample is not homogeneous, it may not accurately represent the population, leading to biased or inaccurate conclusions.
The scale of homogeneity is typically measured using statistical tests, such as the chi-square test or the F-test. These tests compare the expected frequencies of variables in a sample to the observed frequencies, and determine if there is a significant difference.
There are several factors that can affect the scale of homogeneity. These include the size of the sample, the characteristics of the population, and the type of data being analyzed. Additionally, sampling bias or errors in data collection can also impact the scale of homogeneity.
To improve the scale of homogeneity, researchers can use techniques such as stratified sampling or random sampling to ensure a more representative sample. Additionally, careful data collection and data cleaning methods can also help improve the scale of homogeneity.