The tensor-to-scalar ratio ( r = 0.20 ^ { +0.07 } _ { -0.05 } ) inferred from the excess B-mode power observed by the Background Imaging of Cosmic Extragalactic Polarization ( BICEP2 ) experiment is almost twice as large as the 95 % CL upper limits derived from temperature measurements of the WMAP ( r < 0.13 ) and Planck ( r < 0.11 ) space missions .
Very recently , it was suggested that additional relativistic degrees of freedom beyond the three active neutrinos and photons can help to relieve this tension : the data favor an effective number of light neutrino species N _ { eff } = 3.86 \pm 0.25 .
Since the BICEP2 ratio implies the energy scale of inflation ( V _ { * } ^ { 1 / 4 } \sim 2 \times 10 ^ { 16 } ~ { } { GeV } ) is comparable to the grand unification scale , in this paper we investigate whether we can accommodate the required N _ { eff } with three right-handed ( partners of the left-handed standard model ) neutrinos living in the fundamental representation of a grand unified exceptional E _ { 6 } group .
We show that the superweak interactions of these Dirac states ( through their coupling to a TeV-scale Z ^ { \prime } gauge boson ) lead to decoupling of right-handed neutrino just above the QCD cross over transition : 175 ~ { } { MeV } \lesssim T _ { \nu _ { R } } ^ { dec } \lesssim 250 ~ { } { MeV } .
For decoupling in this transition region , the contribution of the three right-handed neutrinos to N _ { eff } is suppressed by heating of the left-handed neutrinos ( and photons ) .
Consistency ( within 1 \sigma ) with the favored N _ { eff } is achieved for 4.5 ~ { } { TeV } < M _ { Z ^ { \prime } } < 7.5 ~ { } { TeV } .
The model is fully predictive and can be confronted with future data from LHC14 .