Reconciling BICEP2 and Planck results with right-handed Dirac neutrinos
  in the fundamental representation of grand unified E_6
  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'
gauge boson) lead to decoupling of right-handed neutrino just above the QCD
cross over transition: 175 MeV < T_{\nu_R}^{dec} < 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'} < 7.5 TeV. The model is fully predictive and can be confronted with
future data from LHC14.
