Gauge-invariant variations in the redshift and cosmic background radiation anisotropies |
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Authors: | W R Stoeger G F R Ellis B G Schmidt |
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Institution: | (1) Vatican Observatory Group, 85721 Tucson, Arizona, USA;(2) International School of Advanced Studies, SISSA, Strada Costiera 11, I-34014 Trieste, Italy;(3) Department of Applied Mathematics, University of Cape Town, C.P. 7700 Rondebosch, South Africa;(4) Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, D-8046 Garching-bei-München, Germany |
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Abstract: | The gauge-invariance of the calculations determining anisotropics in the cosmic microwave background radiation (the Sachs-Wolfe effect) is re-examined. It is shown that the results obtained are gauge-invariant only if a physically-based definition of the surface of last scattering is implemented, in a context where perturbations of the surface of last scattering as well as of the space-time are taken into account. Any physical interpretation of the results based on their splitting into scalar , vector , and tensor parts, is unique only if non-local (unverifiable) conditions are imposed; locally, any such interpretation is non-unique. The physical meaning of the Sachs-Wolfe potentialB and associated redshift formula depends on implementing a very specific gauge, without a clear physical or geometric meaning; its implications do not extend to other, more usual, gauges. |
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