Constraining the cosmic radiation density due to lepton number with Big Bang Nucleosynthesis

TL;DR

This work tackles the problem of how primordial lepton asymmetries and neutrino flavor oscillations modify the radiation content at BBN, quantified by $N_{ m eff}$. It employs a full kinetic treatment with 3×3 flavor density matrices, solving $i\frac{d\rho_{f p}}{dt}=[\Omega_{f p},\rho_{f p}]+C[\rho_{f p},\bar{\rho}_{\bf p}]$ where $\Omega_{f p}$ includes vacuum, matter, and neutrino-neutrino interactions, and tracks the evolution from $T_\gamma\sim 10$ MeV to BBN. The evolving neutrino spectra are fitted by time-dependent $T_{\nu_\alpha}$ and $\xi_{\nu_\alpha}$ and fed into a modified $\,\mathtt{PArthENoPE}$ to compute deuterium and helium abundances, allowing the authors to derive 95% CL bounds on the total lepton asymmetry $\eta_\nu$ and the initial electron-neutrino asymmetry $\eta_{\nu_e}^{\rm in}$ across different values of $\theta_{13}$. The key findings show that large $\theta_{13}$ drives rapid flavor equilibration and yields $N_{ m eff}$ very close to the standard value $3.046$, while $\theta_{13}$ near zero permits $N_{ m eff}$ up to about $3.4$ and allows broader asymmetry ranges; upcoming Planck measurements of $N_{ m eff}$ will thus test these neutrino asymmetry scenarios.

Abstract

The cosmic energy density in the form of radiation before and during Big Bang Nucleosynthesis (BBN) is typically parameterized in terms of the effective number of neutrinos N_eff. This quantity, in case of no extra degrees of freedom, depends upon the chemical potential and the temperature characterizing the three active neutrino distributions, as well as by their possible non-thermal features. In the present analysis we determine the upper bounds that BBN places on N_eff from primordial neutrino--antineutrino asymmetries, with a careful treatment of the dynamics of neutrino oscillations. We consider quite a wide range for the total lepton number in the neutrino sector, eta_nu= eta_{nu_e}+eta_{nu_mu}+eta_{nu_tau} and the initial electron neutrino asymmetry eta_{nu_e}^in, solving the corresponding kinetic equations which rule the dynamics of neutrino (antineutrino) distributions in phase space due to collisions, pair processes and flavor oscillations. New bounds on both the total lepton number in the neutrino sector and the nu_e -bar{nu}_e asymmetry at the onset of BBN are obtained fully exploiting the time evolution of neutrino distributions, as well as the most recent determinations of primordial 2H/H density ratio and 4He mass fraction. Note that taking the baryon fraction as measured by WMAP, the 2H/H abundance plays a relevant role in constraining the allowed regions in the eta_nu -eta_{nu_e}^in plane. These bounds fix the maximum contribution of neutrinos with primordial asymmetries to N_eff as a function of the mixing parameter theta_13, and point out the upper bound N_eff < 3.4. Comparing these results with the forthcoming measurement of N_eff by the Planck satellite will likely provide insight on the nature of the radiation content of the universe.

Figures (9)

• Figure 1: Evolution of the flavor neutrino asymmetries when $\eta_\nu=-0.41$, and $\eta_{\nu_e}^{\rm in}=0.82$. The solid curves correspond to vanishing $\theta_{13}$ (outer black lines) and $\sin^2\theta_{13}=0.04$ (inner red lines). The total neutrino asymmetry is constant and equal to three times the value shown (blue dotted line).
• Figure 2: The final energy spectra of relic electron neutrinos and antineutrinos in arbitrary units for the same case of Figure \ref{['evol_lnu']} with vanishing $\theta_{13}$. Upper (lower) solid line stands for electron neutrino (antineutrino) calculated numerically (label "real"). Upper (lower) dotted line stands for electron neutrino (antineutrino) described by a Fermi/Dirac distribution just characterized by the same effective value of the electron neutrino degeneracy parameter.
• Figure 3: Evolution of the neutrino energy density for the same case as in Figure \ref{['evol_lnu']}. The vertical axis is marked with $N_{\rm eff}$, left before $e^+e^-$ annihilation, right afterwards. The solid curves correspond to vanishing $\theta_{13}$ (upper black line) and $\sin^2\theta_{13}=0.04$ (lower red line). The case without asymmetries is shown for comparison (blue dotted line).
• Figure 4: Evolution of the effective comoving temperatures and degeneracy parameters of electron (solid lines) and muon or tau (dashed lines) neutrinos for the same case as in Figure \ref{['evol_lnu']}. Both the case of vanishing $\theta_{13}$ (thick black lines) and $\sin^2\theta_{13}=0.04$ (thin red lines) are shown. The effective temperature for the case without asymmetries is shown in the upper panel for comparison (blue dotted line).
• Figure 5: The 95% C.L. contours from our BBN analysis in the $\eta_\nu-\eta_{\nu_e}^{\rm in}$ plane for $\theta_{13}=0$ (left) and $\sin^2 \theta_{13}=0.04$ (right). The two contours correspond to the different choices for the primordial $^4$He abundances of eqs. \ref{['he1']} (blue) and \ref{['he2']} (purple). The (red) dot-dashed line is the set of values of $\eta_\nu$ and $\eta_{\nu_e}^{\rm in}$ which, due to flavor oscillations, evolve towards a vanishing final value of electron neutrino asymmetry $\eta_{\nu_e}^{\rm fin}$. We also report as dashed lines the iso-contours for different values of $N_{\rm eff}$, the effective number of neutrinos after $e^+e^-$ annihilation stage.