Updated BBN bounds on the cosmological lepton asymmetry for non-zero theta13

TL;DR

This work updates Big Bang Nucleosynthesis (BBN) bounds on the cosmological lepton asymmetry by incorporating recent indications of non-zero $\theta_{13}$ and exploring both normal and inverted neutrino mass hierarchies. The authors solve three-flavour neutrino evolution with density-matrix formalism, including oscillations, collisions, and matter effects, to determine how initial flavour asymmetries redistribute before BBN and affect the effective number of relativistic species, $N_{ m eff}$. The neutrino distributions are then used as input to the BBN code \\texttt{PArthENoPE} to compute primordial abundances and compare with observations of deuterium and helium, yielding 95% CL bounds on the total lepton asymmetry $\eta_\nu$ and on $N_{ m eff}$. They find that large $\theta_{13}$ drives near-equal flavour partitioning ($\eta_{\nu_e}\approx\eta_{\nu_\mu}\approx\eta_{\nu_\tau}\approx\eta_\nu/3$), tightening $\eta_\nu$ bounds and capping $N_{ m eff}$ around $3.1$, while very small $\theta_{13}$ in the normal hierarchy permits larger asymmetries and $N_{ m eff}$ up to about $3.43$. These results imply that future reactor experiments confirming $\sin^2\theta_{13}\gtrsim 0.03$ would constrain the lepton asymmetry to be a subdominant contributor to radiation density, with Planck sensitivity unlikely to detect larger contributions in that scenario. BBN thus remains the strongest probe of cosmological lepton number, complementary to CMB measurements.

Abstract

We discuss the bounds on the cosmological lepton number from Big Bang Nucleosynthesis (BBN), in light of recent evidences for a large value of the neutrino mixing angle theta13. The largest asymmetries for electron and muon or tau neutrinos compatible with 4He and 2H primordial yields are computed versus the neutrino mass hierarchy and mixing angles. The flavour oscillation dynamics is traced till the beginning of BBN and neutrino distributions after decoupling are numerically computed. The latter contains in general, non thermal distortion due to the onset of flavour oscillations driven by solar squared mass difference in the temperature range where neutrino scatterings become inefficient to enforce thermodynamical equilibrium. Depending on the value of theta13, this translates into a larger value for the effective number of neutrinos, N_eff. Upper bounds on this parameter are discussed for both neutrino mass hierarchies. Values for N_eff which are large enough to be detectable by the Planck experiment are found only for the (presently disfavoured) range sin^2(theta13)<0.01.

Figures (5)

• Figure 1: Evolution of the flavor neutrino asymmetries when $\eta_{\nu_e}^{\rm in}=-0.82$ and zero total asymmetry. The outer solid curves correspond to vanishing $\theta_{13}$ (black lines), while the inner ones (red lines) were calculated in the NH for two values of $\sin^2\theta_{13}$: from left to right, $0.04$ and $0.02$. The same two values of $\sin^2\theta_{13}$ apply to the cases shown as blue dotted lines, but in the IH.
• Figure 2: Final contribution of neutrinos to the total radiation energy density, parametrized with $N_{\rm eff}$, as a function of the total neutrino asymmetry for a particular value of the initial electron neutrino asymmetry ($\eta_{\nu_e}^{\rm in}=-0.82$). From top to bottom, the various lines correspond, respectively, to the following cases: no neutrino oscillations ($\eta_{\nu_e}$ conserved), $\theta_{13}=0$, and $\sin^2\theta_{13}=0.04$ for normal (red solid line) and inverted (blue dotted line) neutrino mass hierarchy.
• Figure 3: 95% C.L. contours from our BBN analysis in the $\eta_\nu-\eta_{\nu_e}^{\rm in}$ plane for several values of $\sin^2\theta_{13}$: 0 (black solid line), 0.04 and NH (red solid line), 0.04 and IH (blue dotted line). The case of no neutrino flavour oscillations is shown for comparison as the black dashed contour.
• Figure 4: The shadowed region corresponds to the values of the total neutrino asymmetry compatible with BBN at 95% C.L., as a function of $\theta_{13}$ and the neutrino mass hierarchy.
• Figure 5: Largest values of $N_{\rm{eff}}$ from primordial neutrino asymmetries compatible with BBN at 95% C.L., as a function of $\theta_{13}$ and the neutrino mass hierarchy.