QUANTUM-FIELDS AT LOCAL EQUILIBRIUM AND DISTORTIONS OF THE COSMIC MICROWAVE BACKGROUND

The partition function for a free bosonic quantum field at local thermal equilibrium is calculated. The result is applied to a study of possible deviation from the Planck distribution of the cosmic microwave background radiation (CMB). We show that if the temperature is sufficiently smooth on short length scales as compared with a typical wavelength of the thermal photons, the deviation can be described in terms of an effective frequency dependent temperature. The model therefore predicts an increase of power for high frequencies. We argue that this prediction could be appropriate for anisotropies of the CMB at angular scales smaller than what the horizon at decoupling subtends on the sky today. © 1992.