Friday, 18 January 2013

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.     

32 comments:

X said...

A bitch??? The result is nothing less than astonishing. Imagine if this had been known before the discovery of the 3rd generation! You would immediately learn that there was a 3rd generation without actually having to produce any of its particles. Now imagine if this had been known before you wasted a lot of time thinking about a 4th generation. You would immediately know that that was a huge waste of time. Without actually doing any of the hard work of looking for such particles! (You have to do the hard work of studying the sky, but thankfully somebody else did that for us. :-D) The result is amazing.

Anonymous said...

As an experimental neutrino physicist I find this to be good news. Too many dubious experimental results with marginal significance have received too much attention from over-excited people who point to Neff as a reason to be excited. There is plenty to do in neutrino physics without having to chase phantoms, and hopefully this distraction will now go away.

Anonymous said...

Hum .. if confirmed with increased significance, could these results exclude the existence of the axion ?

Jester said...

Not really. In the standard picture axions are cold dark matter. The bound from Neff applies only to axion-like particles that thermalize and become hot.

Anonymous said...

X, but we DO know that there is a third generation, so this result doesn't astonish us :). Also, even if this result had been known 10 years ago, 4th generation is just 2 (astro)sigma away from it.

tulpoeid said...

Anonymous, X is right because the point of view at which s/he's standing is preferential. Looking at the sky and knowing how many generations exist is as close to a miracle as one can get :)

Marni Dee Sheppeard said...

Well, that certainly kills a few 3+1, 3+2 papers.

none said...

A layperson doubt: Do those results have any effect on supersymmetric models?

[]s,

Roberto Takata

Jester said...

In general no. The bounds on Neff constrain very light particles (MeV or less). As for SUSY particles, theorists usually imagine them at the TeV scale.

Anonymous said...

There are rumors that the WMAP9 papers contain a bug in their Neff analysis. They are revising their Neff constraint to something more consistent with the more recent SPT and ACT results, i.e., Neff = 3.6 +/- 0.3. Keep your eyes open for the revised WMAP9 result.

andrew said...

"All these peaks and wiggles are predicted by the standard cosmological model, the so-called ΛCDM model (black line)."

Meanwhile, the Neff data simultaneously removes many of the main remaining dark matter candidates (since different experimental data suggests that cold dark matter produces more large scale structure in the universe than we observe, and that warm dark matter with keV scale particles would be a better fit. Yet, keV scale dark matter particles ought to produce a Neff of at least 4, which the numbers cited disfavor by about 4-1 (and a Neff of 5+ is disfavored by about 4.97 sigma). So, Marnie, hold onto the 3+1 papers for a bit, but ditch the 3+2 papers for sure.

Direct dark matter searches also strongly disfavor heavy WIMPS that wouldn't show up in Neff.

Thus, the same measurement simultaneously confirms CDM and denies it a mechanism.

Anonymous said...

It should also be pointed out that the new SPT data described in Story et al (1210.7231) and Hou et al (1212.6267) provides, in conjunction with WMAP7 data, the tightest current constraint on Neff: Neff = 3.62 +/- 0.48, or Neff = 3.71 +/- 0.35 when Hubble constant and BAO data are included (and there's no (known) bug in the SPT papers). The latter is 1.9-sigma higher than the standard value of 3.046. Even though these new SPT papers used WMAP7 data, the WMAP7 vs WMAP9 change is outweighed by the big improvement in the SPT data (which the WMAP9 paper didn't use). It will be interesting to see what Planck sees, with Planck-only errors forecasted to be sigma(Neff)~0.2.

Doddy said...

It's worth noting something Jester says in slightly more detail: Neff bounds come from the effect on CMB damping, but only if one fixes the low \ell stuff, like the angular diameter distance to last scattering. So, if you just blindly went onto LAMBDA's CAMB web app and upped Neff, the Silk damping actually increases. As for 3+1 models: it's still easy to accommodate a light sterile neutrino as these guys only thermalise through mixing and, again as Jester said, don't have to contribute anywhere near a "whole" neutrino species to the CMB.

Finally, WMAP+ACT on Neff is in marginal tension with WMAP+SPT, with the ACT combination being lower. Being full sky, Planck should clear this up. The new lower values of Neff come form enforcing consistency with standard BBN, so if you want more neutrinos you can always mess with BBN (!) or introduce late decays in the intermediate epochs.

Doddy said...

Andrew: tooting my own trumpet but that would seem to me to favour axions as part of the DM. They can be light and erase structure like WDM, but the non-thermal production means they never show up in Neff.

Zachariah said...

Would it be possible to explain in layman's terms how the detailed map of the CMB provides strong evidence for dark matter?

curious george said...

Why do only neutrinos of all massive particles contribute to a radiation energy density? Is this independent of what a neutrino mass might be?

Jester said...

Zachariah, in more laymen's terms, here's a short explanation I'm borrowing from Cosmic Variance: "...In the early universe, dark matter just collapses under the pull of gravity, while ordinary matter also feels pressure, and therefore oscillates. As a result, the two components are out of phase in the even-numbered peaks in the CMB spectrum. In English: dark matter pushes up the first and third peak in the CMB spectrum, while suppressing the second and fourth peak. That would be extremely hard to mimic in a theory without dark matter..."

Jester said...

George, what makes neutrinos special is that they decoupled from the rest of the thermal plasma when they were still relativistic, around T~MeV. That would be true for any neutrino masses below MeV (and we know the masses are below eV).

Anonymous said...

(Different Anonymous) to George, Andrew, Jester: there are some confusions above about mass scales.

Basically N_eff is the energy density in anything which was relativistic in the few e-foldings before the CMB era, excluding photons; and measured in units of one very light neutrino.

So, keV-scale warm dark matter does not count because it went non-relativistic way before the CMB era. Warm DM is indistinguishable from cold DM as far as the microwave background is concerned, but does affect very small-scale structure i.e. dwarf galaxies due to free-streaming at much earlier times.

Neutrinos at < 0.2eV are almost identical to massless ones in the CMB, though they are non-relativistic today and have subtle effects on large-scale structure.

Anything at ~ 1 eV is an intermediate case because it goes non-relativistic just before the CMB era, so the effects are more complicated than just a change in N_eff (but popular CMB codes can handle that). This is disfavoured anyway by large-scale structure.

Jester said...

Right, what I said above was confusing: only particles below eV mass will contribute to Neff measured in the CMB.

Foster Boondoggle said...

Doesn't the existence of neutrino masses double Neff, even though the right-handed nu's don't couple to anything? Their existence doubles the number of relativistic d.o.f.

Doesn't that mean Neff should be 6? Or is that factor of 2 already incorporated into the LCDM and nucleosynthesis calculations?

Anonymous said...

The bug-fixed WMAP9 papers have appeared on the arxiv, and, as the rumors suggested, the Neff constraint that uses BAO data went up: the new WMAP9+CMB+H0+BAO constraint is Neff = 3.84 +/- 0.40, 2-sigma higher than the standard value of 3.046. This constraint is consistent with and slightly broader than the SPT+WMAP7+H0+BAO constraint of Neff = 3.71 +/- 0.35 presented in 1212.6267.

Jester said...

Thanks!

Jester said...

Foster, the usual assumption is that the right-handed sterile neutrinos are very heavy, in which case Neff=3 (only light particles contribute to Neff). But it is possible that some of these sterile neutrino are light and get populated in the early universe, which may explain why Neff is measured somewhat higher than 3.

Thomas Dent said...

No attempt by WMAP to admit fault or explain the 'slight alteration', though. What are they playing at?

Anonymous said...

Neff~ 3.16 +- 0.4 from CMB lensing...

abbyyorker said...

I could have sworn that light neutrino bounds were also made by ee collider luminosity, and that they suggested 3 generations years ago.

Anonymous said...

@abbyyorker, yes LEP used the invisible width of the Z to beautifully constrain Nnu~3.0+epsilon, but that only applies to particles coupling to the Z. The constraints from cosmology are ~30X less precise but more generic (thereby constraining axions, light sterile neutrinos, etc.).

Anonymous said...

A new CMB data combination is in Calabrese et al.

They find mild tension between ACT + SPT on the ell > 1500 tail: from the CMB power spectrum alone they find Neff:
2.90 +/- 0.53 (WMAP9 + ACT)
3.75 +/- 0.47 (WMAP9 + SPT)
3.34 +/- 0.4 (WMAP9 + ACT + SPT)

Adding in also the 4-point function from CMB lensing , they get 3.24 +/- 0.39.

This is all CMB without BAO+HO, which probably tend to pull Neff slightly upwards.
So, basically the preference between ~ 3 or 4 is fuzzy, but 5 looks strongly disfavoured. As noted elsewhere, Planck should give a substantial improvement (but if the true value were 3.5 it may not settle the question).

Anonymous said...

What a 3.5 value would imply in terms of particle content of Dark Matter? Is there a kind of Dark Matter that seems already prefered by this data (e.g. axions, etc)?

Anonymous said...

What this new data can say about the NuMSM devised by Shaposhnikov?

Jester said...

Rather than discussing interpretations of Neff=3.5 it's better to wait 3 more weeks for the Planck results, as they will seriously change the experimental situation.