Mathematics – Logic
Scientific paper
Feb 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phrvd..49.1845s&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 49, Issue 4, 15 February 1994, pp.1845-1853
Mathematics
Logic
16
Observational Cosmology, Fundamental Problems And General Formalism, Relativity And Gravitation, Background Radiations
Scientific paper
The use of observational coordinates allows the formulation of redshift in a general cosmological space-time in a simple form, (1+z)=A0dw/dτ, where A0 is a normalization constant, w is the observational time coordinate, and τ is the proper time along the fundamental flow lines. This in turn allows easy calculation of the anisotropy of the cosmic microwave background radiation (CMBR) due to the Sachs-Wolfe (SW) effect. We reproduce the usual dominant first-order effect δTR/TR=1/3(δbB-δbA), where δb is the density contrast of baryons on the last scattering surface; as implied by this equation, the observationally significant result is the difference of δb in two different directions A and B on the plane of the sky. In order to obtain the actual result, one also needs to study perturbations of the temperature on the background last-scattering surface and on its first-order counterpart. In addition to the usual dominant term in the SW effect, we obtain a second term when the pressure p is significant at last scattering; this term depends on the difference in the pressure at the points of emission A and B on the last-scattering surface, and enters the CMBR anisotropy with a sign opposite to that of the usual term. For the adiabatic case, this pressure term can reduce the SW effect by up to 87% in a low-density universe. When p=0 at the last scattering surface, the usual SW result is obtained. Our results are gauge invariant to first order. Other explicit contributions to the Sachs-Wolfe anisotropy in the observational-coordinate calculation are clearly higher order. We discuss the interpretation of these results and compare them to other calculations of the large-scale cosmic microwave background anisotropy.
Ellis George F. R.
Stoeger William R.
Xu Chong-ming
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