Model Testing and Parameter Estimation 193The South Pole-based BICEP2 telescope [8] has observed the presence of the pri-
mordial퐶B퓁 component in a fit to the theoretical B-mode power spectrum. This is
reported as a tensor to scalar ratio
푟= 0. 20 +−^00 ..^0705 , (8.48)which disfavors푟=0ataconfidenceof7. 0 휎. This result is so remarkable that it
certainly needs confirmation. If confirmed, its most likely interpretation is, that the
B-mode polarization signals gravitational waves from the time of inflation, and that
inflation indeed has occurred.
Density Parameters. The density parameters from all the large experiments com-
bined are [6]
훺mℎ^2 = 0. 1385 ± 0. 0025 ,훺bℎ^2 = 0. 02205 ± 0. 00028. (8.49)The Hubble constant,퐻 0 , and the matter density parameter,훺 0 , are only tightly con-
strained in the combination훺mℎ^2. In the table of Planck+WP results with 68% limits,
one finds that the Universe is consistent with being spatially flat,훺 0 =훺m+훺휆=1.
From the combination of all large experiments [8–15]
퐻 0 =^100 ℎ=^69.^6 ±^0.^7 ,훺m=^0.^286 ±^0.^008. (8.50)
From this one can derive the density parameters for baryons (b) and for
non-baryonic dark matter (c)
훺b= 0. 052 훺c= 0. 234 , (8.51)where we have not evaluated the errors because of model-dependent correlations.
If the Universe is not exactly flat, the vacuum energy is of the order of훺푘=훺 0 − 1 =
− 0. 003 ± 0 .003.
In Figure 8.6 the confidence regions in훺m,훺휆space are plotted for the combined
PanSTARRS1 supernova data [13], Planck CMB data [6], baryonic oscillation BAO
data [14] and퐻 0 data [6].
It is a remarkable success of the FLRW concordance model that the baryonic den-
sity at time 380kyr as evidenced by the CMB is in excellent agreement with the BBN
evidence in Euqation (6.99) from about 20 min after the Big Bang. As explained in Sec-
tion 6.4, the BBN value depends only on the expansion rate and the nuclear reaction
cross-sections, and not at all on the details of the FLRW model.
In Equation 6.95 we quoted the value for the ratio푌 4 of^4 He mass to total mass
(^1) H+ (^4) He from BBN data,푌BBN
4 =^0.^2565 ±^0 .0060. A more precise value can be found
from CMB data,푌 4 CMB= 0. 2477 ± 0 .0001 [6]. A universe with no helium is now ruled
out by CMB at very high confidence—it would produce too much small scale power.
This provides test of the BBN epoch.
Current limits on the total neutrino mass
∑
푚휈is of the order of<0.66eV (con-
fidence level CL=95%), but strongly model dependent. Combining this with Equa-
tion (8.16), we obtain the휈mass density parameter
훺휈< 0. 012. (8.52)