Is there an inert neutrino there?

There is a very interesting posting by Jester in Resonaances with title How many neutrinos in the sky?. Jester tells about the recent 9 years WMAP data and compares it with earlier 7 years data. In the earlier data the effective number of neutrino types was N_eff= 4.34 +/- 0.87 and in the recent data it is N_eff= 3.26 +/- 0.35. WMAP alone would give N_eff = 3.89 +/- 0.67 also in the recent data but also other data are used to pose constraings on N_eff.

To be precise, N_eff could include instead of fourth neutrino species also some other weakly interacting particle. The only criterion for contributing to N_eff is that the particle is in thermal equilibrium with other massless particles and thus contributes to the density of matter considerably during the radiation dominated epoch.

Jester also refers to the constraints on N_eff from nucleosynthesis, which show that N_eff∼ 4 us slightly favored although the entire range [3,5] is consistent with data.

It seems that the effective number of neutrinos could be 4 instead of 3 although latest WMAP data combined with some other measurements favor 3.

Addition:Later however a corrected version of the eprint appeared telling that the original estimate of N_eff contained a mistake and the correct estimate is N_eff=3.84+/- 0.40.

What could N_eff=4 mean in TGD framework?

1. One poses to the modes of the modified Dirac equation the following condition: electric charge is conserved in the sense that the time evolution by modified Dirac equation does not mix a mode with a well-defined em charge with those with different em charge. The implication is that all modes except pure right handed neutrino are restricted at string world sheets. The first guess is that string world sheets are minimal surfaces of space-time surface (rather than those of imbedding space). One can also consider minimal surfaces of imbedding space but with effective metric defined by the anti-commutators of the modified gamma matrices. This would give direct physical meaning for this somewhat mysterious effective metric.
   

   For the neutrino modes localized at string world sheets mixing of left and right handed modes takes place and they become massive. If only 3 lowest genera for partonic 2-surfaces are light, one has 3 neutrinos of this kind. The same applies to all other fermion species. The argument for why this could be the case relies on simple observation: the genera g=0,1,2 have the property that they allow for all values of conformal moduli Z₂ as a conformal symmetry (hyper-ellipticity). For g>2 this is not the case. The guess is that this additional conformal symmetry is the reason for lightness of the three lowest genera.
   
   

2. Only purely right-handed neutrino is completely delocalized in 4-volume so that one cannot assign to it genus of the partonic 2-surfaces as a topological quantum number and it effectively gives rise to a fourth neutrino very much analogous to what is called sterile neutrino. Delocalized right-handed neutrinos couple only to gravitation and in case of massless extremals this forces them to have four-momentum parallel to that of ME: only massless modes are possible. Very probably this holds true for all preferred extremals to which one can assign massless longitudinal momentum direction which can vary with spatial position.
   
   
3. The coupling of ν_R is to gravitation alone and all electroweak and color couplings are absent. According to standard wisdom delocalized right-handed neutrinos cannot be in thermal equilibrium with other particles. This according to standard wisdom. But what about TGD?
   

   One should be very careful here: delocalized right-handed neutrinos is proposed to give rise to SUSY (not N=1 requiring Majorana fermions) and their dynamics is that of passive spectator who follows the leader. The simplest guess is that the dynamics of right handed neutrinos at the level of amplitudes is completely trivial and thus trivially supersymmetric. There are however correlations between four-momenta.
   
   

   1. The four-momentum of ν_R is parallel to the light-like momentum direction assignable to the massless extremal (or more general preferred extremal). This direct coupling to the geometry is a special feature of the modified Dirac operator and thus of sub-manifold gravity.
      
      
   2. On the other hand, the sum of massless four-momenta of two parallel pieces of preferred extremals is the - in general massive - four-momentum of the elementary particle defined by the wormhole contact structure connecting the space-time sheets (which are glued along their boundaries together since this is seems to be the only manner to get rid of boundary conditions requiring vacuum extremal property near the boundary). Could this direct coupling of the four-momentum direction of right-handed neutrino to geometry and four-momentum directions of other fermions be enough for the right handed neutrinos to be counted as a fourth neutrino species in thermal equilibrium? This might be the case!
      

   One cannot of course exclude the coupling of 2-D neutrino at string world sheets to 4-D purely right handed neutrinos analogous to the coupling inducing a mixing of sterile neutrino with ordinary neutrinos. Also this could help to achieve the thermal equilibrium with 2-D neutrino species.

Addition: The recent (22.3. 2013) data from Planck satellite give updated view about cosmic microwave background. The data give N_eff=3.3 +/- .5 and do not favour inert neutrino. For a nice summary see Resonaances.

For background see the chapter http://tgdtheory.com/public_html/paddark/paddark.html#susychap of "p-Adic length scale hypothesis and dark matter hierarchy".