Cosmology Can Possibly Solve the Neutrino Hierarchy Problem.

There are three neutrino species in the standard model, hereafter refereed to as 1, 2, and 3, that we know have mass from atmospheric and solar neutrino oscillation experiments. Furthermore, data from these experiments put constraints on the mass-splittings between these three neutrinos.  From atmospheric experiments we know the mass differences between 2 and 3 is |M²₂₃| ~ 1.4x10^-3 eV² and from the solar neutrino experiments we know the mass splitting between 1 and 2 is M²₁₂ ~ 7.9x10^-5 eV².

So here is the problem: We know that the neutrinos have mass and we know what their mass splittings are but we don't know their hierarchy or in other words the order of their masses as shown in the figure to the right. For example, it could be that neutrino 3 is the most massive of the three... but it can also be the case that it is the least massive.  This is what I mean by the neutrino hierarchy problem I used in the title.

Cosmology To The Rescue!

Fortunately, there are cosmological measurements that can be made that may solve this issue in the future. In this post I will discuss a wonderful paper that pioneered these details was written by Jimenez et al.  The solution goes like this:

1.  CMB and large scale structure experiments give us a bound on the sum of the neutrino masses denoted as Σ = m₁+m₂+m₃.  The current bound is that  Σ  is between 0.05eV and 0.3eV.

2. After Σ is better constrained in the future, the mass splitting Δ = m₃ - m₁, importantly with sign!, can be be measured from the matter power spectrum of large scale structure for the given Σ.  The plot above shows how the matter power spectrum, P(k), is altered by the different values of Δ.  Once Δ is known with confidence, including sign, the problem is solved.



3. The plot above shows forecasts for how well we will be able to tell the difference between the normal inverted hierarchy given future experiments. (Normal being where m₃ is larger and invereted when it is smaller.)

4.  Furthermore, cosmolgy should be able to shed light on whether neutrinos are Dirac or Majorana particles. (If Majorana they are their own anti-particle and if Dirac they are not.) The below flow chart shows how this works.  First, double beta-decay experiments may be able to determine directly if neutrinos are their own anti-particle.  But if future experiments fail to see a signal, cosmology may help answer if this is because the signal is just too weak or whether it is because neutrinos really are Dirac. As you can see, if Σ is just right and if the hierarchy is inverted or degenerate, cosmology will be able to demonstrate neutrinos are in fact Dirac.

So in conclusion: It appears cosmology may be able to provide a wealth of insight into neutrino physics in the coming years.  Through cosmology we may solve the neutrino hierarchy problem and even possibly say whether or not neutrinos are Dirac.

Jimenez, R., Kitching, T., Peña-Garay, C., & Verde, L. (2010). Can we measure the neutrino mass hierarchy in the sky? Journal of Cosmology and Astroparticle Physics, 2010 (05), 35-35 DOI: 10.1088/1475-7516/2010/05/035