The CBR temperature fluctuation anisotropy spectrum is sensitive to the early-Universe radiation density (_{R}) as well as to the overall expansion rate. The early Universe is radiation dominated so that _{R} 1 + 0.135 N_{} (see Eq. 6 and recall that H^{2}). The late Universe is matter dominated (MD) (_{M} _{M} h^{2}) and the crossover from RD to MD, important for the growth of fluctuations and for the age/size of the Universe at recombination, occurs for a redshift
(8) |
If the matter content is kept fixed while the radiation content is increased, corresponding to a faster than standard expansion rate, matter-radiation equality is delayed, modifying the growth of fluctuations prior to recombination and, also, the Universe is younger at recombination and has a smaller sound horizon, shifting the angular location of the acoustic peaks. The degeneracy between the radiation density ( N_{} or S) and _{M} is broken by the requirement that _{M} + _{} = 1 and the HST Key Project determination of the Hubble parameter (see [Barger et al. (2003a)] for details and further references). In Figure 10 are shown the 1 and 2 contours in the N_{} - plane from the CBR (WMAP) data; note the very different N_{} scales and ranges in Figures 9 and 10. As is the case for BBN (see Section 7), the CBR favors a slightly slower than standard expansion. However, while the "best" fit value for the expansion rate factor is at S < 1 ( N_{} < 0), the CBR likelihood distribution of N_{} values is very shallow and the WMAP data are fully consistent with S = 1 ( N_{} = 0).
Figure 10. The 1 and 2 contours in the - N_{} plane from the CBR (WMAP) data. The best fit point (_{10} = 6.3, N_{} = -0.25) is indicated by the cross. |
Comparing Figures 9 and 10, it is clear that for this variant of the standard cosmology there is excellent overlap between the - N_{} confidence contours from BBN and those from the CBR (see Barger et al. 2003a). This variant of SBBN (S 1) is consistent with the CBR. In Figure 11 (from Barger et al. 2003a) are shown the confidence contours in the - N_{} plane for a joint BBN - CBR fit. Again, while the best fit value for N_{} is negative (driven largely by the adopted value for Y_{P}), N_{} = 0 (S = 1) is quite acceptable.
Figure 11. As for Figure 10, but for the joint BBN - CBR fit. The best fit point (_{10} = 6.0, N_{} = -0.75) is indicated by the cross. |