We perform a detailed study of the weak interactions of standard model neutrinos with the primordial plasma and their effect on the resonant production of sterile neutrino dark matter. Motivated by issues in cosmological structure formation on small
scales, and reported X-ray signals that could be due to sterile neutrino decay, we consider $7$ keV-scale sterile neutrinos. Oscillation-driven production of such sterile neutrinos occurs at temperatures $T gtrsim 100$ MeV, where we study two significant effects of weakly charged species in the primordial plasma: (1) the redistribution of an input lepton asymmetry; (2) the opacity for active neutrinos. We calculate the redistribution analytically above and below the quark-hadron transition, and match with lattice QCD calculations through the transition. We estimate opacities due to tree level processes involving leptons and quarks above the quark-hadron transition, and the most important mesons below the transition. We report final sterile neutrino dark matter phase space densities that are significantly influenced by these effects, and yet relatively robust to remaining uncertainties in the nature of the quark-hadron transition. We also provide transfer functions for cosmological density fluctuations with cutoffs at $k simeq 10 h {rm Mpc}^{-1}$, that are relevant to galactic structure formation.
We propose a method of measuring extremely weak magnetic fields in the intergalactic medium prior to and during the epoch of cosmic reionization. The method utilizes the Larmor precession of spin-polarized neutral hydrogen in the triplet state of the
hyperfine transition. This precession leads to a systematic change in the brightness temperature fluctuations of the 21-cm line from the high-redshift universe, and thus the statistics of these fluctuations encode information about the magnetic field the atoms are immersed in. The method is most suited to probing fields that are coherent on large scales; in this paper, we consider a homogenous magnetic field over the scale of the 21-cm fluctuations. Due to the long lifetime of the triplet state of the 21-cm transition, this technique is naturally sensitive to extremely weak field strengths, of order $10^{-19}$ G at a reference redshift of $sim 20$ (or $10^{-21}$ G if scaled to the present day). Therefore, this might open up the possibility of probing primordial magnetic fields just prior to reionization. If the magnetic fields are much stronger, it is still possible to use this method to infer their direction, and place a lower limit on their strength. In this paper (Paper I in a series on this effect), we perform detailed calculations of the microphysics behind this effect, and take into account all the processes that affect the hyperfine transition, including radiative decays, collisions, and optical pumping by Lyman-$alpha$ photons. We conclude with an analytic formula for the brightness temperature of linear-regime fluctuations in the presence of a magnetic field, and discuss its limiting behavior for weak and strong fields.
In this paper, we study small-scale fluctuations (baryon pressure sound waves) in the baryon fluid during recombination. In particular, we look at their evolution in the presence of relative velocities between baryons and photons on large scales ($k
sim 10^{-1} {rm Mpc}^{-1}$), which are naturally present during the era of decoupling. Previous work concluded that the fluctuations grow due to an instability of sound waves in a recombining plasma, but that the growth factor is small for typical cosmological models. These analyses model recombination in an inhomogenous universe as a perturbation to the parameters of the homogenous solution. We show that for relevant wavenumbers $kgtrsim 10^3 {rm Mpc}^{-1}$ the dynamics are significantly altered by the transport of both ionizing continuum ($h u>13.6$ eV) and Lyman-$alpha$ photons between crests and troughs of the density perturbations. We solve the radiative transfer of photons in both these frequency ranges and incorporate the results in a perturbed three-level atom model. We conclude that the instability persists at intermediate scales. We use the results to estimate a distribution of growth rates in $10^{7}$ random realizations of large-scale relative velocities. Our results indicate that there is no appreciable growth; out of these $10^7$ realizations, the maximum growth factor we find is less than $approx 1.2$ at wavenumbers of $k approx 10^{3} {rm Mpc}^{-1}$. The instabilitys low growth factors are due to the relatively short duration of the recombination epoch during which the electrons and photons are coupled.
It has recently been suggested that the tidal deformation of a neutron star excites daughter p- and g-modes to large amplitudes via a quasi-static instability. This would remove energy from the tidal bulge, resulting in dissipation and possibly affec
ting the phase evolution of inspiralling binary neutron stars and hence the extraction of binary parameters from gravitational wave observations. This instability appears to arise because of a large three-mode interaction among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We show that additional four-mode interactions enter into the analysis at the same order as the three-mode terms previously considered. We compute these four-mode couplings by finding a volume-preserving coordinate transformation that relates the energy of a tidally deformed star to that of a radially perturbed spherical star. Using this method, we relate the four-mode coupling to three-mode couplings and show that there is a near-exact cancellation between the destabilizing effect of the three-mode interactions and the stabilizing effect of the four-mode interaction. We then show that the equilibrium tide is stable against the quasi-static decay into daughter p- and g-modes to leading order. The leading deviation from the quasi-static approximation due to orbital motion of the binary is considered; while it may slightly spoil the near-cancellation, any resulting instability timescale is at least of order the gravitational-wave inspiral time. We conclude that the p-/g-mode coupling does not lead to a quasi-static instability, and does not impact the phase evolution of gravitational waves from binary neutron stars.
