Abstract
In the standard Friedmann cosmology the black-body radiation spectrum is usually taken (without explicit proof as far as we know) to have the same familiarT 4-form that it has in a flat space. With explicit use of the equation of motion of a quantized massless field propagating in a curved background Robertson-Walker metric we show (for the readily tractable scalar field case) that the assumption is in fact true for an open Universe. For a closed Universe, we find that there is an in principle modification to theT 4-law. Unfortunately, the correction turns out to be too small to be experimentally detectable. In passing, we also obtain a simple derivation for the cosmological red shift of frequencies.
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Reference
Mannheim, P. D. and Kazanas, D.: 1985, ‘Energy-Momentum Tensor of Fields in the Standard Cosmology’, University of Connecticut, Preprint.
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Deng, Y., Mannheim, P.D. Black-body radiation in a curved Robertson-Walker background. Astrophys Space Sci 135, 261–269 (1987). https://doi.org/10.1007/BF00641561
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DOI: https://doi.org/10.1007/BF00641561