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4.2. Nonstandard Expansion Rate: S neq 1 (Delta Nnu neq 0)

The excellent agreement between the SBBN-predicted baryon density inferred from the primordial-D abundance and that derived from the CBR and large scale structure (Spergel et al. 2003), and also the agreement between predicted and observed D and 3He suggest that the tension with 4He, if not observational or astrophysical in origin, may be a sign of new physics. As noted earlier, YP is sensitive to the early-Universe expansion rate (while D, 3He, and 7Li are less so). A faster expansion (S > 1, Delta Nnu ;> 0) leads to a higher predicted primordial abundance of 4He, and vice versa for S < 1 (Delta Nnu < 0). In Figure 12 is shown the same YP versus yD band as for SBBN in Figure 10, along with the corresponding bands for the nonstandard cases of a faster expansion (Delta Nnu = 4) and a slower expansion (Delta Nnu = 2). It can be seen that the data "prefer" a slower than standard early-Universe expansion rate. If both eta and Delta Nnu are allowed to be free, it is possible (not surprisingly) to accommodate the adopted primordial abundances of D and 4He (see Fig. 2). Given the similar effects of Delta Nnu neq 0 on the BBN-predicted D, 3He, and 7Li abundances, while it is possible to maintain the good agreement (from SBBN) for 3He, the tension between 7Li and D cannot be relieved. In Figure 13 are shown the 1-, 2-, and 3-sigma BBN contours in the eta - Delta Nnu plane derived from the adopted values of yD and YP. Although the best-fit point is at Delta Nnu = -0.7 (and eta10 = 5.7), it is clear that SBBN (Nnu = 3) is acceptable.

Figure 12

Figure 12. As in Figure 10 for Nnu = 2, 3, 4, which correspond to S = 0.915, 1, 1.078.

Figure 13

Figure 13. The 1-, 2-, and 3-sigma contours in the eta - Delta Nnu plane for BBN and the adopted D and 4He abundances.

The CBR temperature anisotropy spectrum and polarization are also sensitive to the early-Universe expansion rate (see, e.g., Barger et al. 2003a, and references therein). There is excellent overlap between the eta - Delta Nnu confidence contours from BBN as shown in Figure 13 and from the CBR (Barger et al. 2003a). In Figure 14 are shown the confidence contours in the eta - Delta Nnu plane for a joint BBN - CBR fit (Barger et al. 2003a). Again, while the best fit value for Delta Nnu is negative (driven largely by the adopted value for YP), Delta Nnu = 0 is quite acceptable.

Figure 14

Figure 14. The 1- and 2-sigma contours in the eta - Delta Nnu plane for the joint BBN - CBR (WMAP) fit (Barger et al. 2003a).

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