Astroparticle Physics

10.6 Detailed BBN 225prediction for D/H depends quite sensitively on the baryondensity, the measured D/H provides the most accurate determinationof η. The measured value from (10.27), namely,n d /n p = (3.40 ± 0.25) × 10 −5 , gives the range of allowedη values, which are shown by the vertical band in Fig. 10.5.This corresponds tosensitive D/H ratioη = (5.1 ± 0.5) × 10 −10 . (10.28)The boxes in Fig. 10.5 indicate the measured abundancesof 4 He and 7 Li (from slightly different analyses than thosementioned above). The size of the boxes shows the measurementuncertainty. These measurements agree remarkablywell with the predictions, especially when one considersthat the values span almost 10 orders of magnitude.The value of η = n b /n γ determines the baryon density,since the photon density is well-known from the measuredCMB temperature, T = 2.725 K, through (9.11) to be n γ =2ζ(3)T 3 /π 2 . Therefore, the value of η can be converted intoa prediction for the energy density of baryons divided by thecritical density,baryon-to-photon ratioΩ b = ϱ bϱ c. (10.29)The critical density is given by (8.33) as ϱ c = 3H 2 0 /8πG.The baryons today are non-relativistic, so their energy densityis simply the number of nucleons per unit volume timesthe mass of a nucleon, i.e., ϱ b = n b m N ,wherem N ≈0.94 GeV. Putting these ingredients together gives Ω b determinationΩ b = 3.67 × 10 7 × ηh −2 , (10.30)where h is defined by H 0 = 100 h km s −1 Mpc −1 .Usingh = 0.71 +0.04−0.03and η from (10.28) gives baryon fractionof the universeΩ b = 0.038 ± 0.005 , (10.31)where the uncertainty originates both from that of the Hubbleconstant and also from that of η. Recently η and Ω b havebeen measured to higher acuracy using the temperature variationsin the cosmic microwave background radiation, leadingto Ω b = 0.044 ± 0.004; this will be followed up inChap. 11 (see also Table 11.1). The values from the BBNand CMB studies are consistent with each other and, takentogether, provide a convincing confirmation of the Big Bangmodel.