Angular Momentum of the Cosmic Background Radiation

The effect of a nontrivial conserved isotropic total angular momentum $M^2={m_x}^2+{m_y}^2+{m_z}^2$ on the equilibrium distribution of energy in a photon gas is examined. It is shown that the correspondingly modified Planck law takes the form $F\left(\nu \right)=\mathrm{const}\nu {\gamma }^{-1\mathrm{}}\ln \left[\frac{(1-e^{-\beta \nu -\gamma {\nu }^2})}{(1-e^{-\beta \nu })}\right],$ where $\beta$ and $\gamma$ are parameters determined by the energy and angular momentum. This law provides a good fit to the spectrum of the cosmic background radiation observed by Woody and Richards.