Cosmic background radiation has been observed to deviate from the Planck law expected from a blackbody at $\sim 2.7$ K at frequencies below $\sim 3$ GHz. We discuss the abundance of the low-energy photons from the perspective of nonequilibrium statistical mechanics. We propose a mechanism of stochastic frequency diffusion, the counterpart to stochastic acceleration for charged particles in a turbulent plasma, to modify the standard Kompaneets equation. The resulting violation of the Einstein relation allows us to take advantage of low-frequency localization and finally leads to photon cooling. The modified equation predicts a frequency distribution in agreement with the absolute temperature measurements of the cosmic background radiation down to about 20 MHz, for which we offer an updated compilation. In that sense, the so-called space roar we observe today is interpreted as a nonequilibrium echo of the early universe and more specifically of nonequilibrium conditions in the primordial plasma.

• Received 26 August 2019
• Accepted 3 February 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.013210

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society