Likelihood of a Galaxy Survey

The positions of galaxies can tell us a lot about the Universe and gravity. Measurements by the Planck satellite provide a precise picture of the temperature of a slice of the Universe around 13.77 billion years ago.

The temperature variation seen in the picture arises because of the variation of the amount of energy in that slice.

The simplest “statistical properties” that are onsidered are the amplitude of the flutuations and the sizes of the fluctuotions. In the above picture from Planck, these correspond to the range of temperatures spanned by the blue and red blobs, and the sizes of the blobs.

Since 13.77 billion years ago and today the energy variations seen in that picture have moved around due to the force of gravity. Using General Relativity (the model of gravity that seems to work given all experimental evidence) or any other theory of gravity, we can calculate (with some uncertainty) how those energy fluctuations evolve in time. If we assume that the statistical properties of that slice of the Universe seen by Planck also apply to the rest of the observalbe Universe, we can predict the statistical properties of the energy fluctuations of the more nearby Universe.

Regular matter makes up part of the energy seen by Planck (though most of the energy is in the form of Dark Matter). So the statistical properties of the distribution of galaxies are expected to be directly related those of the energy fluecations.

On average, distances between galaxies is uniformly increasing with time. It is convenient to think of the change in distance as a function of time as a velocity, so that galaxies are moving away from each other. This average motion is the cosmological expansion that is locally well described by the Hubble relation.

This motion due also due to the force of gravity. The average expansion of the Universe is explained by solving General Relativity inputting the spatial average of the energy constituants.

In a nutshell, given the statistcal properties of the temperature variations seen by Planck and a theory of gravity, we can predict the statistical properties of galaxues.