Neff, the effective number of neutrino species in the lamda CDM Standard Model of cosmology, theoretically, should have a value of 3.046 if there are three neutrino flavors (under about 10 eV in mass) and there is no "dark radiation".
The measured value of Neff combining the most recent Planck satellite data and some other astronomy observations that it included in its analysis is 3.52 +0.48/-0.45, assuming that the tensor to scalar ratio, r, is zero. This result is roughly equally consistent at with the possibility of three neutrino species and with the possibility of four neutrino species.
Big Bang Nucleosynthesis data point to a consistent result of 3.5 +/- 0.2, again equally consistent with three neutrino species or with four (or with three species of neutrinos and a fractional neutrino species attributable for example to dark radiation).
The big question to date has been whether this stubborn mean value in excess of the expected 3.046 in study after study has been simply a product of experimental error, or if it instead denotes some other fundamental physical phenomena, such as a light sterile neutrino that could also explain the reactor anomaly in neutrino oscillations, or a light particle just on the brink of being too heavy to count as a neutrino that only counts fractionally, or dark radiation, any of which would constitute beyond the Standard Model physics.
The best fitting dark matter particle content to fit existing astronomy data regarding dark matter call for a single type of Dirac dark matter particle and a massive boson often called a "dark photon" that mediates a U(1) force between them (the dark photon terminology flows from the fact that this vector boson would behave essentially like photons in QED if photons were massive).
So, there are reasonably well motivated, conservative extensions of the Standard Model that could accommodate a fourth neutrino species or a dark radiation component (each apparently worth an Neff of about 0.227 (i.e. 7/8*(4/11)4/3). Two dark radiation components would be a very nice fit to the pre-BICEP2 experimental data.
BICEP2 has reported that r=0.20 +0.07/-0.05, which would imply a result of Neff=4.00 +/- 0.41. Another set of unpublished preliminary results (A. Lewis, http://cosmoco ee.info/ les/Antony Lewis/bicep planck.pdf (20 March 2014)), point to Neff=3.80 +/-0.35.
Given the tension between the BICEP2 estimate of r=.10-.34 in a 95% confidence interval, and r=0-0.11 in a 95% based on pre-BICEP2 data reported by BICEP2, a true value of r=0.10-.11 would be not inconsistent with the 95% confidence interval of either of the data points that are in tension with each other. Presumably, such an intermediate number would split the difference of the tensor to scalar ratio adjustment to Neff, bringing its value to about 3.66-3.76 with error bars of about +/- 0.4.
Note, however, that if r is not equal to zero, that the Neff associated with three neutrino species might not be 3.046 (I don't know enough to be sure).
The cosmos coffee forum link is illuminated by http://cosmocoffee.info/viewtopic.php?t=2302
On dark radiation and Neff.
Perhaps, you will be interested in the comment at http://blog.vixra.org/2014/03/20/how-certain-are-the-bicep2-findings/#comment-36510
The theory expressed in that comment seems awfully far out to me.
Dr. Philip Gibbs is a very reputable physicist, and his blog is viewed by thousands of capable physicists. Yet, none of them has said that that comment is far out, as there is nothing in this entire universe is more solidly rooted on the ground than the Alpha equation which is the pure function of only two numbers (64, 48).
A week ago, Greer Heard hosted a debate on ‘God and Cosmology’ with the participants of William Lane Craig, Tim Maudlin, James Sinclair, Sean Carroll and Alex Rosenberg. It is truly a ‘far out’ debate. Yet, the comment at (http://scientiasalon.wordpress.com/2014/04/20/philosophy-my-first-five-years/comment-page-1/#comment-1178 ) does bring that debate down to Earth.
Planck polarization data has Neff at 3.04 +/- 0.18.
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