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Reconciling BICEP2 and Planck results with right-handed Dirac neutrinos in the fundamental representation of grand unified E_6

Luis A. Anchordoqui, Haim Goldberg, Xing Huang, Brian J. Vlcek

TL;DR

The paper addresses the tension between the BICEP2 inference of a large tensor-to-scalar ratio $r$ and Planck temperature data by invoking extra light relativistic degrees of freedom, specifically three right-handed Dirac neutrinos arising in the fundamental ${\bf 27}$ of $E_6$. These neutrinos interact via a TeV-scale $Z'$ gauge boson, yielding milli-weak couplings that cause their decoupling to occur near the QCD crossover, thereby suppressing their contribution to $N_{\rm eff}$ to $N_{\rm eff} \approx 3.86 \pm 0.25$ with $\Delta N_\nu \approx 0.81 \pm 0.25$. The authors map the decoupling temperature to the effective degrees of freedom using lattice-informed $g_s(T)$, and confront the resulting cosmology with collider constraints to find a predictive region $\overline g \simeq 0.46$ and $M_{Z'}$ in the TeV range that is accessible to LHC14. The work provides a concrete, testable link between cosmological observations and TeV-scale new physics, proposing a clear path to falsify the scenario with upcoming collider data. Overall, the approach offers a coherent mechanism to accommodate the observed $N_{\rm eff}$ while remaining consistent with CMB, BBN, and accelerator constraints, and it highlights a tangible LHC target for a $Z'$ gauge boson.

Abstract

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_{ν_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 1σ) 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.

Reconciling BICEP2 and Planck results with right-handed Dirac neutrinos in the fundamental representation of grand unified E_6

TL;DR

The paper addresses the tension between the BICEP2 inference of a large tensor-to-scalar ratio and Planck temperature data by invoking extra light relativistic degrees of freedom, specifically three right-handed Dirac neutrinos arising in the fundamental of . These neutrinos interact via a TeV-scale gauge boson, yielding milli-weak couplings that cause their decoupling to occur near the QCD crossover, thereby suppressing their contribution to to with . The authors map the decoupling temperature to the effective degrees of freedom using lattice-informed , and confront the resulting cosmology with collider constraints to find a predictive region and in the TeV range that is accessible to LHC14. The work provides a concrete, testable link between cosmological observations and TeV-scale new physics, proposing a clear path to falsify the scenario with upcoming collider data. Overall, the approach offers a coherent mechanism to accommodate the observed while remaining consistent with CMB, BBN, and accelerator constraints, and it highlights a tangible LHC target for a gauge boson.

Abstract

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_{ν_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 1σ) 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.

Paper Structure

This paper contains 6 sections, 28 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Constraints on Cosmological Parameters from CMB data
  3. Right-Handed Neutrinos with Milli-Weak Interactions
  4. Theoretical Considerations
  5. Confronting Neutrino Cosmology with LHC Data
  6. Conclusions

Figures (4)

  • Figure 1: Left. Marginalized joint 68% CL and 95% CL regions for ($r,n_s$) using Planck + WMAP + BAO with (blue) and without (purple) a running spectral index. The green contours show the BICEP2 $68\%$ and $95\%$ confidence regions for $(r,n_s)$, with $\alpha_s \neq 0$. The burgundy areas indicate the 68% and 95% CL allowed regions from the 9-parameter fit. The solid line shows the expected relation between $r$ and $n_s$, for a $V(\phi) \propto \phi$ inflationary potential. Right. 68% and 95% CL contours for ($h,r$). The 9-parameter fit predicts a value of $h$ in concordance with observations by Planck and HST.
  • Figure 2: 68% and 95% confidence regions for the 9-parameter fit (burgundy). Also shown are the 68% and 95% confidence regions for $\Lambda$CDM + $N_{\rm eff}$, using Planck + WMAP (purple), Planck + WMAP + BAO (blue) data. The horizontal lines indicate the 95% CL upper limits on $\sum m_\nu$.
  • Figure 3: Left. The parametrization of the entropy density given in Eq. (\ref{['soverT']}) (dashed line) superposed on the result from high statistics lattice simulations Bazavov:2009zn (solid line). Right. Comparison of $g_s (T)$ obtained using Eq. (\ref{['gdet']}) (dashed line) and the phenomenological estimate of Laine:2006cpSteigman:2012nb (solid line).
  • Figure 4: The (yellow) shaded area shows the $68\%$ confidence region allowed from decoupling requirements to accommodate $\Delta N = 0.81 \pm 0.25$, The horizontal line dictates the effective coupling $\overline g$ for $Z'_\chi$; the cross-hatched part of the line reflects the LHC experimental limits on the mass of the gauge boson. We have taken ${\cal K} =0.5$ (left) and ${\cal K} = 2.5$ (right).