How many neutrinos in the sky?

Just before Christmas, the WMAP collaboration posted the 9-years update of their Cosmic Microwave Background results. Before going into details it's worth to stop for a second and admire the picture that I pasted here. Thanks to the observations of the WMAP satellite (black) and the terrestrial telescopes SPT (blue) and ACT (orange) we know the spectrum of the CMB fluctuations down to the scales of 0.1 degree. All these peaks and wiggles are predicted by the standard cosmological model, the so-called ΛCDM model (black line). In particular, the positions and the relative sizes of the peaks  provide the strongest argument to date for the existence of dark matter in the Universe: a non-relativistic matter component that, unlike baryons, does not interact with photons. At present, the alternatives to dark matter cannot even dream of quantitatively explaining the observed features of the CMB.

That late in the game one would not expect any spectacular turns of the action. Indeed, compared to the 7-years WMAP data, the update typically brings a 20-30% reduction of already tiny errors on the composition of the Universe. There is however one number that changed visibly. The effective number of relativistic degrees of freedom at the time of CMB decoupling, the so-called Neff parameter, is now Neff = 3.26 ± 0.35, compared to Neff = 4.34 ± 0.87 quoted in the 7-years analysis.  For the fans and groupies of this observable it was like finding a lump of coal under the christmas tree...

So, what is this mysterious Neff parameter? According to the standard cosmological model, at the temperatures above 10 000 Kelvin the energy density of the universe was dominated by a plasma made of neutrinos (40%) and photons (60%). The photons today make the  CMB  about which we know everything.  The neutrinos should also be around, but for the moment we cannot  study them directly. However we can indirectly infer their presence in the early universe via other observables. First of all, the neutrinos affect the energy density stored in radiation:  

which controls the expansion of the Universe during the epoch of radiation domination. The standard model predicts Neff equal to the number of known neutrinos species, that is Neff = 3  (in reality 3.05, due to finite temperature and decoupling effects). Thus, by measuring how quickly the early Universe was expanding, we can determine Neff.  If we find Neff ≈ 3  we confirm the standard model and close the store.  On the other hand, if we measured that Neff is significantly larger than 3, that would mean a discovery of  additional light  degrees of freedom in the early plasma that are unaccounted for in the standard model. Note that these new hypothetical  particles don't have to be similar to neutrinos, in particular they could be bosons, and/or have a different temperature (in which case they would correspond to non-integer increase of  Neff ). All that is required from them is that they are weakly interacting and light enough to be relativistic at the time of CMB decoupling.   Theorists have dreamed up many viable candidates that could show up in Neff : additional light neutrinos species, axions, dark photons, etc.

One way to measure Neff  is via nucleosynthesis (in principle it's not the same observable as in that case one measures the number of relativistic degrees of freedom at a much earlier epoch, but in most models Neff at the time of nucleosynthesis and CMB decoupling are similar). Here the physics is rather straightforward.   The larger Neff, the faster the universe expands, and the earlier the weak interactions transforming neutrons into protons fall out of equilibrium. Almost all the neutrons that survive the thermal bath end up bound into helium atoms, thus by measuring the amount of helium-4 in the universe one can infer Neff. A recent analysis of the nucleosynthesis constraints on Neff  is summarized in the plot. The upper panel shows the standard model prediction (red band) of the primordial helium mass fraction Yp as a function of Neff, confronted with experimental constraints. (Notice that different observations of the helium abundance are not quite consistent with each other, but that's normal in astrophysics;  the rule of thumb is that 3 sigma uncertainty in astrophysics is equivalent to 2 sigma in conventional physics).  Neff ≈ 4 seems to be preferred, although, given the uncertainties, any  Neff between 3 and 5 is consistent with the data.

The interest of particle physicists in Neff  come from the fact that, until recently, the CMB data also pointed at Neff≈4 with a comparable error.  The impact of Neff  on the CMB is much more contrived, and there are many separate effects one needs to take into account. For example, larger Neff delays the moment of matter-radiation equality, which affects the relative strength and positions of the peaks. Furthermore, Neff affects how the perturbations grow during the radiation era, which may show up in the CMB spectrum  at l ≥ 100. Finally, the larger Neff,  the larger is the effect of Silk damping at l ≥ 1000. Each single observable has a large degeneracy with other input parameters (matter density, Hubble constant, etc.) but, once the CMB spectrum is measured over a large range of angular scales, these degeneracies are broken and stringent constraints on Neff can be derived. That is what happened recently, thanks to the high-l CMB measurements from the ACT and SPT telescopes, and some  input from other astrophysical observations. The net result is that from the CMB data alone one finds  Neff = 3.89 ± 0.67, while using in addition an input from Baryon Acoustic Oscillations and Hubble constant measurements brings it down Neff = 3.26 ± 0.35.  All in all, the measured effective number of relativistic degrees of freedom in the early Universe can be well accounted for by the three boring neutrinos of the standard model. Well, life's a bitch.  The next update on Neff is expected in March when Planck releases its cosmological results,  but the rumor is that it will do nothing to cheer us up.

Update: as pointed out by a commenter, there's a rumor that the WMAP-9 analysis has a bug, and when it's corrected Neff increases significantly. So don't throw your sterile neutrinos models into a fire yet. 
Update #2: the bug was fixed in v2. The new number is Neff = 3.84 ± 0.40, consistent within 2 sigma with the standard model, but leaving some room for hope.