Lepton asymmetry, neutrino spectral distortions, and big bang nucleosynthesis

PHYSICAL REVIEW D 95, 063503 (2017) Lepton asymmetry, neutrino spectral distortions, and big bang nucleosynthesis E. Grohs, 1 George M. Fuller, 2 C. T. Kishimoto, 2,3 and Mark W. Paris 4 Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA Department of Physics, University of California, San Diego, La Jolla, California 92093, USA Department of Physics and Biophysics, University of San Diego, San Diego, California 92110, USA Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA (Received 9 December 2016; published 3 March 2017) We calculate Boltzmann neutrino energy transport with self-consistently coupled nuclear reactions through the weak-decoupling-nucleosynthesis epoch in an early universe with significant lepton numbers. We find that the presence of lepton asymmetry enhances processes which give rise to nonthermal neutrino spectral distortions. Our results reveal how asymmetries in energy and entropy density uniquely evolve for different transport processes and neutrino flavors. The enhanced distortions in the neutrino spectra alter the expected big bang nucleosynthesis light element abundance yields relative to those in the standard Fermi-Dirac neutrino distribution cases. These yields, sensitive to the shapes of the neutrino energy spectra, are also sensitive to the phasing of the growth of distortions and entropy flow with time/scale factor. We analyze these issues and speculate on new sensitivity limits of deuterium and helium to lepton number. DOI: 10.1103/PhysRevD.95. 063503 I. INTRODUCTION In this paper we use the BURST neutrino-transport code [1] to calculate the baseline effects of out-of-equilibrium neutrino scattering on nucleosynthesis in an early universe with a nonzero lepton number, i.e., an asymmetry in the numbers of neutrinos and antineutrinos. Our baseline includes a strong, electromagnetic, and weak nuclear reaction network; modifications to the equation of state for the primeval plasma; and a Boltzmann neutrino energy transport network. We do not include neutrino flavor oscillations in this work. Our intent is to provide a coupled Boltzmann transport and nuclear reaction calculation to which future oscillation calculations can be compared. In fact, the outstanding issues in achieving ultimate precision in big bang nucleosynthesis (BBN) simulations will revolve around oscillations and plasma physics effects. These issues exist in both the zero and nonzero lepton-number cases, but are more acute in the presence of an asymmetry. We self-consistently follow the evolution of the neutrino phase-space occupation numbers through the weak- decoupling-nucleosynthesis epoch. There are many studies of the effects of lepton numbers on light element, BBN abundance yields. Early work [2,3] briefly explored the changes in the helium-4 ( 4 He) abundance in the presence of large neutrino degeneracies. Later work considered how lepton numbers could influence the 4 He yield [4,5] through neutrino oscillations. In addition, other works employed lepton numbers to constrain the cosmic microwave back- ground (CMB) radiation energy density [6,7] or the sum of the light neutrino masses [8]. References [9,10] simulta- neously investigated BBN abundances and CMB quantities using lepton numbers. The most recent work has used the primordial abundances to constrain lepton numbers which have been invoked to produce sterile neutrinos through matter-enhanced Mikheyev-Smirnow-Wolfenstein reso- nances [11–13]. Currently, our best constraints on these lepton numbers come from comparing the observationally inferred primordial abundances of either 4 He or deuterium (D) with the predicted yields of 4 He and D calculated in these models. Previous BBN calculations with neutrino asymmetry have made the assumption that the neutrino energy dis- tribution functions have thermal, Fermi-Dirac (FD) shaped forms. In fact, we know that neutrino scattering with electrons, positrons, and other neutrinos and electron- positron annihilation produce nonthermal distortions in these energy distributions, with concomitant effects on BBN abundance yields [1]. Though the nucleosynthesis changes induced with self-consistent transport are small, they nevertheless may be important in the context of high precision cosmology. Anticipated Stage-IV CMB measure- ments [14,15] of primordial helium and the relativistic energy density fraction at photon decoupling, coupled with the expected high precision deuterium measurements made with future 30-m class telescopes [16–20] will provide new probes of the relic neutrino history. In the standard cosmology with zero lepton numbers, neutrino oscillations act to interchange the populations of electron neutrinos and antineutrinos (ν e , ν ¯ e ) with those of muon and tau species (ν μ , ν ¯ μ , ν τ , ν ¯ τ ) [21]. Once we posit that there are asymmetries in the numbers of neutrinos and antineutrinos in one or more neutrino flavors, then neutrino © 2017 American Physical Society