In 1984, I heard Hans Bethe give a talk in which he suggested the dark matter might be neutrinos. This sounded outlandish – from what I had just been taught about the Standard Model, neutrinos were massless. Worse, I had been given the clear impression that it would screw everything up if they did have mass. This was the pervasive attitude, even though the solar neutrino problem was known at the time. This did not compute! so many of us were inclined to ignore it. But, I thought, in the unlikely event it turned out that neutrinos did have mass, surely that would be the answer to the dark matter problem.

Flash forward a few decades, and sure enough, neutrinos do have mass. Oscillations between flavors of neutrinos have been observed in both solar and atmospheric neutrinos. This implies non-zero mass eigenstates. We don’t yet know the absolute value of the neutrino mass, but the oscillations do constrain the separation between mass states (Δmν,212 = 7.53×10−5 eV2 for solar neutrinos, and Δmν,312 = 2.44×10−3 eV2 for atmospheric neutrinos).

Though the absolute values of the neutrino mass eigenstates are not yet known, there are upper limits. These don’t allow enough mass to explain the cosmological missing mass problem. The relic density of neutrinos is

Ωνh2 = ∑mν/(93.5 eV)

In order to make up the dark matter density (Ω ≈ 1/4), we need ∑mν ≈ 12 eV. The experimental upper limit on the electron neutrino mass is mν < 2 eV. There are three neutrino mass eigenstates, and the difference in mass between them is tiny, so ∑mν < 6 eV. Neutrinos could conceivably add up to more mass than baryons, but they cannot add up to be the dark matter.

In recent years, I have started to hear the assertion that we have already detected dark matter, with neutrinos given as the example. They are particles with mass that only interact with us through the weak nuclear force and gravity. In this respect, they are like WIMPs.

Here the equivalence ends. Neutrinos are Standard Model particles that have been known for decades. WIMPs are hypothetical particles that reside in a hypothetical supersymmetric sector beyond the Standard Model. Conflating the two to imply that WIMPs are just as natural as neutrinos is a false equivalency.

That said, massive neutrinos might be one of the few ways in which hierarchical cosmogony, as we currently understand it, is falsifiable. Whatever the dark matter is, we need it to be dynamically cold. This property is necessary for it to clump into dark matter halos that seed galaxy formation. Too much hot (relativistic) dark matter (neutrinos) suppresses structure formation. A nascent dark matter halo is nary a speed bump to a neutrino moving near the speed of light: if those fast neutrinos carry too much mass, they erase structure before it can form.

One of the great successes of ΛCDM is its explanation of structure formation: the growth of large scale structure from the small fluctuations in the density field at early times. This is usually quantified by the power spectrum – in the CMB at z > 1000 and from the spatial distribution of galaxies at z = 0. This all works well provided the dominant dark mass is dynamically cold, and there isn’t too much hot dark matter fighting it.

The power spectrum from the CMB (low frequency/large scales) and the galaxy distribution (high frequency/”small” scales). Adapted from Whittle.

How much is too much? The power spectrum puts strong limits on the amount of hot dark matter that is tolerable. The upper limit is ∑mν < 0.12 eV. This is an order of magnitude stronger than direct experimental constraints.

Usually, it is assumed that the experimental limit will eventually come down to the structure formation limit. That does seem likely, but it is also conceivable that the neutrino mass has some intermediate value, say mν ≈ 1 eV. Such a result, were it to be obtained experimentally, would falsify the current CDM cosmogony.

Such a result seems unlikely, of course. Shooting for a narrow window such as the gap between the current cosmological and experimental limits is like drawing to an inside straight. It can happen, but it is unwise to bet the farm on it.

It should be noted that a circa 1 eV neutrino would have some desirable properties in an MONDian universe. MOND can form large scale structure, much like CDM, but it does so faster. This is good for clearing out the voids and getting structure in place early, but it tends to overproduce structure by z = 0. An admixture of neutrinos might help with that. A neutrino with an appreciable mass would also help with the residual mass discrepancy MOND suffers in clusters of galaxies.

If experiments measure a neutrino mass in excess of the cosmological limit, it would be powerful motivation to consider MOND-like theories as a driver of structure formation. If instead the neutrino does prove to be tiny, ΛCDM will have survived another test. That wouldn’t falsify MOND (or really have any bearing on it), but it would remove one potential “out” for the galaxy cluster problem.

Tiny though they be, neutrinos got mass! And it matters!

5 thoughts on “Neutrinos got mass!

  1. If the only dark matter existing in the universe is in the form of neutrinos then virtually all angular momentum will be held by baryons (normal matter) at all observable scales and red shifts. In the LCDM model most of the angular momentum, at all observable ages of the universe (at all red shifts) will be held by dark matter.

    Do you know of work done on differences in how a MOND universe would evolve and the standard LCDM universe, particularly in terms of angular momentum and its distribution across galaxies and perhaps even across galaxy clusters?

    In a universe consisting mostly of dark matter will zero net angular momentum of baryonic be conserved as rigorously in the observations (at various scales) compared with if baryonic matter alone existed?


  2. In LCDM, galaxies are thought to gain their angular momentum by torques applied when their halos are near maximum expansion. Presumably the baryons and dark matter are well mixed at this time, so share a fraction of angular momentum in proportion to their mass (17% for baryons). The distribution of angular momentum observed in the baryonic component of galaxies does not trace the original distribution as indicated by simulations, so it is necessary to build models that expel low angular momentum baryons or otherwise redistribute it among the light and dark matter. Since most of the angular momentum is held in the dark matter, it is hard to say much more.

    In MOND, the angular momentum is directly calculable since what you see is what you get. I imagine objects acquire their angular momentum in a similar manner – protogalaxies torque each other as they decouple from the Hubble expansion. There is less mass to torque, and MOND has a longer range for such things since it is effectively 1/r rather than 1/r^2. Bob Sanders looked into this long ago, e.g., arXiv:0712.2576 and astro-ph/9710335.


  3. Interesting. Usually the large scale structure constraints are said to require a neutrino smaller than this, so it is a new one to invoke this king of mass to soothe these tensions.
    One of the predictions I made when working on the CMB (1999,2000,2004) was that there would appear to be more power at high multipoles because lensing is enhanced by early structure formation in MOND. The tension Planck sees could be interpreted as corroboration of that. However, I don’t pretend to understand the CMB acoustic power spectrum beyond L > 600 in MOND, so I don’t really know what to make of this.
    It would be nice if LCDM could settle on an acceptable bound on the neutrino mass.


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