Tuesday, May 12, 2015

Summary of the Case of ~ 7keV Sterile Neutrinos as Dark Matter

Update 8/15/2017

I just wrote a new post. I still think that dark matter is sterile neutrinos. However, I'm leaning now towards their masses being on the order of 10^10 GeV  (ten to the ten GeV), i.e.
For more information on the predictions of Type I Seesaw models, see this Jan 2017 arxiv manuscript by Stephen F. King. This model appears to be quite predictive as far as being able to predict the angles for neutrino mixing as well as the CP violation term, delta. The CP violation term is very nearly equal to -90 degrees, which means near maximal CP violation.

Original Post
A resonantly-produced-sterile-neutrino-minimal-extension to the SM is entirely consistent with all known particle physics and astrophysics data sets. Such  a SM-extension means that there could only be a small number of adjustments required to the StandardModel of Particle Physics (SM) in order for the SM to explain all astrophysics data sets, i.e. to explain dark matter, dark energy and inflation. What could such a RP-sterile-neutrino-SM-extension model look like:

(1) There are no new particle-classes to be discovered (other than nailing down the mass of the light, active neutrinos and the heavier, sterile neutrinos)

(2) Not counting spin degeneracy: There were likely 24 massless particles before the electro-weak transition. After this transition, some of the particles acquire mass, and the symmetry is broken into:
1 photon, 3 gauge bosons (W+ / W- / Z ) and 8 gluons   (12 Integer spin bosons in total)  
6 quarks, 6 leptons, i.e. electron / neutrinos   (12 Non-integer spin fermions in total)

Note that 24 is the number of symmetry operators in the permutation symmetry group S(4) and the classes within the S(4) symmetry group have sizes 1,3,8 (even permutations) and 6,6 (odd permutations.)  This is likely not a coincidence. Given that there are 4 (known) forces of nature and 4 (known) dimensions of spacetime, the S(4) symmetry group is likely to appear in nature. (See Hagedorn et al. 2006)

(3) Higgs scalar field is the inflaton field required to produce a universe with: (a) near zero curvature (i.e. flat after inflation), (b) Gaussian primordial fluctuations, (c) scalar tilt of ~0.965 for the fluctuations, (d) a near-zero running of the scalar tilt, (e) small, but near zero tensor fluctuations, and (f) no monopoles/knots.

(4) The sum of the rest mass of the squared of the SM bosons is equal to the sum of the rest mass of the squared of the SM fermions, and that the sum of these two is equal to rest mass squared equivalent energy of the Higgs Field. In other words, during the electro-weak transition in which some particles acquire mass via the Higgs mechanism, half of the rest mass squared energy does towards bosons (H, W, Z) and half goes to fermions (e, ve,  u, d, etc...). If this is the case, then there are constraints on the mass of any sterile neutrinos. In order to not effect this "sum of rest mass squared" calculation, the rest mass of any sterile neutrinos must be less than ~10 GeV. A keV sterile neutrino would have no effect on this "sum of rest mass squared" calculation.

So, it is entirely possible that there is no new physics (outside of the neutrino sector), provided that (a) the Higgs scalar field is the inflaton field, (b) sterile neutrinos are the dark matter particles, and (c) light active neutrinos are the cause of what we call dark energy. In the rest of this post, I summarize the case for ~7 keV resonantly-produced, sterile neutrinos as the main dark matter candidate. Note: some of these points, related to (b), can be found in the following papers by de Vega 2014 and Popa et al 2015.

(1) Small-scale crisis of Cold Dark Matter
It has been know for a long time that Cold Dark Matter (CDM) theories work fairly well at large scales, but fail when trying to model matter distributions at the galaxy / sub-galaxy scale. For example, CDM theories over predict the density of sub-halos and over-predict the amount of dark matter within galaxies. The problem is that the free-stream length of a 100 GeV dark matter particle is on the order of 0.1 parsec. This means that there should be dark matter clumps throughout galaxies. However, there is no evidence for such clumps, and in fact, the rotation curves of galaxies suggest that the dark matter forms a diffuse halo. Any hope that CDM theories could be modified with interactions terms to save the day have been thwarted by experimental constrains on dark matter self-interactions and dark matter-nucleon interactions.
In order to prevent the small-scale crisis of CDM theories, the mass of the dark matter particle must be lowered to ~ the keV scale. The exact rest mass is difficult to determine because the free-streaming length scale cut off of a dark matter particle depends on both the rest mass and the thermal velocity of the dark matter. The "free-streaming length scale cut off" increases with increasing dark matter temperature and decreases with dark matter rest mass.
For thermal relics, the rest mass that best fits data for galaxy sub-counts and galaxy mass distribution is ~ 2 keV. Note that for such a fermion particle, as modeled by de Vega 2014, the particle is quantum degenerate, which prevents the dark matter from clumping together at scales less than the size of the Milky Way.

(2) Constraints from Lyman-Alpha (allow a non-thermal 7 keV sterile neutrino)
A standard 2 keV thermal relic sterile neutrino is ruled out by recent measurements of the Lyman-Alpha forest by Viel et. al.. 2013. They find that the dark matter particle (as a thermal relic) should be >3.3 keV, and the best fit is on the order of 33 keV. Interestingly, a cold, resonantly produced sterile neutrino of rest mass of 7 keV can act like a ~14 keV rest mass thermal relic at large scales (>0.1 Mpc) and can act like a 2.5 keV thermal relic at the small scale (<0 .1="" a="" fig.1.="" href="http://arxiv.org/pdf/1304.0759v3.pdf" in="" mpc="" nbsp="" of="" s="" seen="">de Vega 2014
, a cold, non-equilibrium 1 keV mass sterile neutrino can act like a ~4 keV rest mass thermal relic at large scale and ~1 keV thermal relic at small-scale. The key thing here is that if the sterile neutrino is cold, then at large-scale it acts as if it has the rest mass of a heavier thermal relic, but at small-scale, because of quantum degeneracy, it acts like a lighter rest mass. Hence a ~7 keV cold sterile neutrino can act like ~14 keV thermal relic at large scale, while acting like a ~2.5 keV thermal relic at the small scale. This is exactly the type of particle that is required to recognile large-scale constraints on rest mass (m_thermal > 3.3 keV from Lyman Alpha) against small-scale constraints (m_thermal ~ 2 keV.)
(3) Early Star Formation and Re-ionization
2015 results from Planck now suggest that the reionization optical depth (tau) is significantly lower than previous estimates from WMAP and Planck 2013 results. The 2015 Planck results are now consistent with experimental values from Finkelstein et al. 2014, which quote an optical depth (tau) of 0.063+/-0.013. CDM theories typically predict values on the order of 0.9+/-0.1. So, CDM theories overestimate the reionization optical depth, whereas warm dark matter particles ~2-3 keV thermal relics can now correctly estimate the value of the the reionization optical depth.

The reason for the higher value of optical depth is that CDM theories predict that star formation will occur earlier than in the WDM theories. This is because the lighter rest mass of the WDM particles prevents small-scale clumping until later in the universe's history. While this is still only a limited amount of data collected so far on early star formation, the data available fits better to WDM theories than to CDM theories  (for the same reasons that WDM theries now better explain the value of reionization optical depth than do CDM theories.) For more information, see Shultz et al. 2014:
The High-z Universe Confronts Warm Dark Matter: GalaxyCounts, Reionization and the Nature of Dark Matter

(4) Neff is likely slightly higher than 3.04 (Likely requiring some combination of WDM and/or Lepton Asymmetry)
Planck plus BAO + ext + Yp suggests a value of Neff on the order of 0.1 - 0.5, especially if you only use recent BBN data on helium fraction (there has been a trend towards higher helium fraction, Yp, over the last few decades.)
As detailed here, Heavens et al. estimate that Neff = 0.49 +/- 0.32, using only recent measurements of the acoustic scale. As the authors state that this value of Neff is essentially model independent. This means that we could have late-time scale conversion of dark matter into dark energy, and this would have no effect on the estimate of Neff. Basically, the early time physics needs this higher value of Neff in order to make the right-sized acoustic scale.
So, in summary, when you combine all sources of data, the value of Neff is likely in the range of 3.0 to 3.5.

The inclusion of a sterile neutrino can effect Neff  for two different reasons: (1) the lower the mass / temperature ratio of the dark matter particle, the more the particle contributes to the "radiation" energy as opposed to "matter" energy in the universe. Hence, this makes Neff appear to be slightly higher than 3.04. For example, a 7 keV sterile neutrino alone could increase Neff by ~0.03. (2) If the sterile neutrino is made via the Shi-Fuller mechanism, then there must be a lepton asymmetry. Under such conditions, there will be either more neutrinos or anti-neutrinos than expected.
Popa et al 2015 found that a 7 keV RP-sterile neutrino is consistent with CMB + BAO + SN + lensing datasets, and in fact, it helps improve the overall fit to the data by slightly increasing Neff (by ~0.1.)

(6) There is good reason to believe that dark matter is converting into dark energy. (See Salvatelli et al.) This means that we are likely looking for a dark matter particle that is not stable. A particle that is capable of decaying into dark energy is preferred to one that does not decay into dark energy. A sterile neutrino that decays into light, active neutrinos can effectively act like both dark matter & dark energy. At first, the sterile neutrinos acts like dark matter, but if it can covert to a light active neutrino within the center of black holes or neutron stars, then we have a mechanism of producing neutrinos. These neutrinos will have lots of entropy and/or degeneracy pressure that prevents them from gravitationally collapsing. For example, Fermi repulsion of the neutrinos can make sure that the neutrinos can't be confined. If a sterile neutrino can convert into light active neutrinos inside the center of blackholes or neutron stars, then this can help to explain why there is a "late-time" conversion of dark matter into dark energy.
The conversion of dark matter into dark energy helps ease the tension between Planck CMB estimates of cold dark matter & power density of fluctuations and RSD/SZ cluster estimates of cold dark matter & power density of fluctuations. (See Fig 2 of Salvatelli et al.)
(Also, see a previous post on this topic.)


There appears to be a possible detection of a 7.1 keV decaying sterile neutrino by Bulbul et al. 2014 and by Boyarsky et al. (See a previous post on this topic.) The signal-to-noise is still in dispute, so we will have to wait a little bit longer before Bulbul et al. or Boyarsky et al. can made a firm, experimental claim.

(8) If there is any coupling to the Higgs Boson, the dark matter particle must also be light or else it would have been found already at the LHC. The LHC is starting to constrain possible MSSM dark matter particles. For example, see B´elanger et al. 2013 or Cao et al. 2014. There is still a small parameter space left for SUSY GeV dark matter, but it is closing quickly.

(9) If there is equal splitting of "Mass Squared" between Fermions and Bosons suggests that the dark matter particle should be light (i.e., less than ~10 GeV) in order not to push the balance towards fermions.

In summary, all astrophysical data sets (both large and small scale) are suggesting that dark matter has a rest mass in the 2-10 keV range that is produced resonantly due to a small, but non-zero lepton asymmetry.

Side note: There is still appears to Lithium problem. A sterile neutrino and a small lepton asymmetry does not seem to solve the lithium problem. We will have to look elsewhere to resolve this issue.

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