Sterile neutrino as dark matter particle?
Sterile neutrino is one of the many candidates explaining dark matter. Sterility means that would have no electroweak or color interactions. Lightest SUSY particle is another candidate and there are many others. There is also entire zoo of WIMPS which are weakly interacting and massive.
There are some experiments proposing that the decays of sterile neutrino explain the un-identified line at about 3.5-3.6 keV in the X-ray spectrum of galaxy clusters. The mechanism of decay producing photons remains to me unclear: personally I find this kind of decay infeasible because of the defining properties of sterile neutrino. There is however rather strong evidence that sterile neutrinos do not exist. The number of neutrinos deduced from cosmic microwave background according to standard cosmology is in good approximation equal to 3, not 4.
The experimental finding (if true) could be explained in many manners. My personal proposal for anomalous X rays is based on a new kind of nuclear physics at energy range of keV (MeV is the energy range of ordinary nuclear physics and 1000 times higher). The energy scale would be that for exotic states "almost-predicted" by TGD: they would look electromagnetically/chemically just like ordinary isotopes of nuclei but would have slightly different masses. The X rays radiation from Sun could excite these states and imply annually varying anomalies in nuclear decay rates since the distance to Sun is varying. This has been observed.
Suppose that sterile neutrino exists and is dark? How this would affect cosmology. Usually all particles - including the dark ones - are assumed to couple to gravitons with strength proportional to their mass. This would exclude sterile neutrinos.
Dark matter in TGD Universe
In TGD Universe dark matter corresponds to phases of ordinary matter with non-standard value of Planck constant heff=n× h.
- The most natural assumption is that only particles with same value of Planck constant heff=n× h appear in the same vertex. Since graviton and other elementary particles have similar anatomy in TGD Universe, this would naturally apply also to gravitons and would distinguish between TGD dark matter and the usual dark stuff.
Gravitational constant is proportional to the CP2 length scale R squared: this gives G= k R2/X, where X has dimensions of Planck constant. Should one take X=h, the minimal value of heff or should one take X=heff (k is a numerical constant). In the latter case the gravitational constant would be weaker than for ordinary matter. Another, more plausible option is that one uses X=gK2 where gK2 is the square of Kähler coupling having dimensions of h.
- What about classical gauge fields and gravitational fields? Here the direct touching of space-time sheets would induce interaction and the given test particle would experience the forces assignable to the space-time sheets that it touches and one would experience the effective linear superposition of fields in good approximation. This leads to a view about how GRT space-time emerges from TGD: one can think that GRT space-time is obtained by slashing the space-time time sheets to single slightly curved region of M4 space-time: various effective fields are sums of those associated with the sheets.
Could phases with different value of heff have classical interactions mediated by touching. To formulate this concretely, a concrete view about what large heff = n×h means at the level of space-time geometry and topology and the most general assumption is that classical fields mediate the interaction.
The physical picture is following. Large heff gives rise to long range quantal correlations and fluctuations naturally assignable to quantum - and perhaps even ordinary criticality. Criticality means non-determinism and this means that the two 3-surfaces at the light-like boundaries of causal diamonds are connected by large number of space-time surfaces with n-sheets co-inciding at ends. Each sheet can be deformed by conformal gauge symmetries and n is the number of conformal equivalence classes for these connecting surfaces.
Technically speaking, space-time can be regarded as a singular n-fold covering space. I see no obvious rule preventing the multi-sheeted covering from touching ordinary space-time sheets or the other ones with different values of n. Whether all sheets can touch the test particle simultaneously or not is not quite clear. If not, then the interaction could be weaker.
The conclusion might be following.
- Interactions between ordinary and dark phases of matter with different Planck constants would be due to the transitions transforming particles with different Planck constant to each other. The rate for these transitions could be rather low but TGD inspired model for biomatter as ordinary matter controlled by dark matter requires these.
- Phases with different values of heff can interact also via exchange of gravitons but the interaction strength is expected to be proportional to the transition amplitude between different values of heff. Classical gravitational forces act between dark and ordinary matter and the simplest guess is that the interaction strengths are same as for the exchange of gravitons suffering heff changing phase transition.
- In this framework - just one possible scenario - one would have large number of weakly interacting cosmologies and CMB would only tell about one particular cosmology. Multiverse would be realized but the laws of physics would be same for various sub-verses apart from the different value of Planck constant. Living matter would be basic example about the interaction of sub-verses.
The counterpart of sterile neutrino in TGD as generator of N=2 SUSY?
TGD cannot remain outsider as far as the fate of sterile neutrino is considered. The right- handed neutrino νR predicted by TGD is indeed "sterile" in that it does not couple to electro-weak gauge potentials. νR can however mix with left-handed neutrino since induced gamma matrices contain both M4 and CP2 parts and the latter mix different M4 chiralities. Neutrinos are massive so that mixing seems to occur. The chirality mixing caused by the induced gamma matrices is purely TGD based mechanism of massivation and reflects directly the fact that space-times are assumed to be 4-surfaces.
The least broken part of supersymmetry in TGD relies on right-handed neutrino.
- One takes ordinary particle and adds right-handed neutrino or antineutrino or both to get superpartners.
- Is SUSY broken or exact? If SUSY is not broken, the resulting state must be dark (large heff) just because it is not observed! Could SUSY partners be dark matter that is sparticles with heff>h? SUSY breaking would mean only different heff, not mass!
- Or do spartners have heff=h so that SUSY must be broken and spartners have large masses. For this option I encounter a problem similar to that in SUSYs What is the p-adic mass scale for the superpartners, which would obey same mass formula but with different and higher p-adic mass scale (smaller prime p). It should be probably heavier than LHC scale. Note however that TGD SUSY is different from standard one practically excluded at LHC energies.
- These two options are extremes: also their hybrid is possible. p-Adic mass scale and heff could be different for particles and their spartners.
Could antimatter be dark matter in TGD sense?
The experimental absence of dark matter is one of the poorly understood aspects of cosmology.
- One natural looking explanation in TGD framework is that antimatter is at different space-time sheets at different regions of M4 so that the approximate GRT space-time obtained by squishing the sheets to single one contains only matter or antimatter. The central regions of large voids with size of 108 lys are possible candidates in this respect. This kind of regions would have been created as an outcome of annihilation of particles and antiparticles during early cosmology. A slight difference in their densities induced by CP breaking could lead to the separation of matter and antimatter in recent day Universe.
- Could antimatter be dark matter with different Planck constants and remain very weakly interacting. Dark and visible matter would see each other only via emission of various gauge bosons and gravitons suffering heff changing phase transition during propagation. As proposed, this could apply also to gravitons.
- Also a hybrid of these views can be considered. The transformation rates of particles and antiparticles to their dark variants were different in the early universe so that the densities were slightly different before the annihilation began and left only ordinary matter and dark antimatter. The heff changing phase transition should be CP breaking for this option.
This would allow to localize CP breaking to a mixing like phenomenon. Interestingly, also the CKM mixing of quarks and leptons breaks CP: in TGD framework it corresponds to topological mixing of the topological of partonic 2-surfaces.