## A center everywhere

In a few posts now, I’ve introduced the shell theorem and derived some differential equations for the scale factor. One feature of these derivations is that, although they begin with a coordinate system with some given origin, and some given proper distance to some specific mass (say, a galaxy), in the end, the details of the proper distance, the sample mass, and even the origin of coordinates all disappear. This is consistent with an assumed symmetry of the problem; namely, that on a grand cosmological scale the density of stuff is uniform everywhere. In this way, it doesn’t...

Read More## Noise and structure

In a previous post, I contrasted the distribution of matter in the universe at scales above and below a clustering distance, , of about 0.002 times the Hubble distance (about 14 billion light years). I mentioned that at scales below that distance, the two-point correlation function, defined as the joint probability of finding galaxies in volumes and at a distance , varies as a power law with an exponent . I want to expand on this idea in the present post. To change the focus slightly, let us imagine that we are given a sequence of numbers extracted from a Gaussian probability distribution,...

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