Angular Momentum of the Cosmic Background Radiation

Abstract

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 $F(\ensuremath{\nu})=\mathrm{const}\ensuremath{\nu}{\ensuremath{\gamma}}^{\ensuremath{-}1}\mathrm{ln}[\frac{(1\ensuremath{-}{e}^{\ensuremath{-}\ensuremath{\beta}\ensuremath{\nu}\ensuremath{-}\ensuremath{\gamma}{\ensuremath{\nu}}^{2}})}{(1\ensuremath{-}{e}^{\ensuremath{-}\ensuremath{\beta}\ensuremath{\nu}})}],$ where $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ 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.