An extensive, growing body of work has been penned on cosmologies that include one or more sterile neutrinos. Early entries in the literature formulated a Boltzmann-like equation describing sterile-neutrino production in a way that bypasses the numerical tracking of high-frequency complex phases, and meticulous quantum-kinetic analyses shortly thereafter put the formula on firmer ground. A new and more direct derivation is given here, showing that the equation follows almost immediately from a quantum relaxation-time approximation and an expansion in the mixing angle. Besides reproducing the desired result, the relaxation ansatz captures to a high degree of accuracy the interlaced dynamics of oscillations, decoherence, and plasma repopulation. Successes and limitations of the semiclassical equation are illustrated numerically and are shown to reflect the accuracy of the approximations employed in the derivation. The inclusion of interactions among the sterile neutrinos is also briefly addressed.
Starting from operator equations of motion and making arguments based on a separation of time scales, a set of equations is derived which govern the non-equilibrium time evolution of a GeV-scale sterile neutrino density matrix and active lepton number densities at temperatures T > 130 GeV. The density matrix possesses generation and helicity indices; we demonstrate how helicity permits for a classification of various sources for leptogenesis. The coefficients parametrizing the equations are determined to leading order in Standard Model couplings, accounting for the LPM resummation of 1+n <-> 2…
We analyze the influence of decaying sterile neutrinos with the masses in the range 1-140 MeV on the primordial Helium-4 abundance, explicitly solving the Boltzmann equations for all particle species, taking into account neutrino flavour oscillations, and paying special attention to systematic uncertainties. We show that the Helium abundance depends only on the sterile neutrino lifetime and not on the way the active-sterile mixing is distributed between flavours, and derive an upper bound on the lifetime. We also demonstrate that the recent results of Izotov & Thuan [arXiv:1001.4440], who find…
We propose a new production mechanism for keV sterile neutrino Dark Matter. In our setting, we assume the existence of a scalar singlet particle which never entered thermal equilibrium in the early Universe, since it only couples to the Standard Model fields by a really small Higgs portal interaction. For suitable values of this coupling, the scalar can undergo the so-called freeze-in process, and in this way be efficiently produced in the early Universe. These scalars can then decay into keV sterile neutrinos and produce the correct Dark Matter abundance. While similar settings in which the s…
We present a formalism that allows the computation of the baryon asymmetry of the universe from first principles of statistical physics and quantum field theory that is applicable to certain types of beyond the Standard Model physics (such as the neutrino Minimal Standard Model -- $ν$MSM) and does not require the solution of Boltzmann or Kadanoff-Baym equations. The formalism works if a thermal bath of Standard Model particles is very weakly coupled to a new sector (sterile neutrinos in the $ν$MSM case) that is out-of-equilibrium. The key point that allows a computation without kinetic equatio…
By numerically solving the appropriate Boltzmann equations, we study the production of sterile neutrinos in models with low reheating temperatures. We take into account the production in oscillations as well as in direct decays and compute the sterile neutrino primordial spectrum, the effective number of neutrino species, and the sterile neutrino contribution to the mass density of the Universe as a function of the mixing and the reheating parameters. It is shown that sterile neutrinos with non-negligible mixing angles do not necessarily lead to $N_ν\sim 4$ and that sterile neutrinos may have …
For active-sterile mixing to be responsible for the full relic abundance of dark matter additional new physics is needed beyond the keV-scale sterile neutrino itself. The extra ingredient we consider here is the presence of self-interactions among the sterile neutrinos. We examine whether active-to-sterile conversion is amplified enough in this scenario that the observed abundance of dark matter can be obtained with a subconstraint mixing angle. This turns out never to be the case in the region we explore: either self-interactions have too small an impact and cannot escape bounds on the mass a…
We consider relatively heavy neutrinos $ν_H$, mostly contributing to a sterile state $ν_s$, with mass in the range 10 MeV $\lesssim m_s \lesssim m_π \sim 135$ MeV, which are thermally produced in the early universe in collisional processes involving active neutrinos, and freezing out after the QCD phase transition. If these neutrinos decay after the active neutrino decoupling, they generate extra neutrino radiation, but also contribute to entropy production. Thus, they alter the value of the effective number of neutrino species $N_{\rm eff}$ as for instance measured by the cosmic microwave bac…
We consider heavy sterile neutrinos $ν_s$, with mass in the range 10 MeV $\lesssim m_s \lesssim m_π \sim 135$ MeV, thermally produced in the early universe and freezing out after the QCD phase transition. The existence of these neutrinos may alter the value of the effective number of neutrino species $N_{\rm eff}$, measured by the cosmic microwave background (CMB), and the ${}^4$He production during the BBN. We provide a detailed account of the solution of the relevant Boltzmann equations and we identify the parameter space constrained by current Planck satellite data and forecast the paramete…
A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic fluids recently proposed in Ref. [1], is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast-wave on massive interstellar clouds. Close to second order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time-steps, are reported.
We examine the bounds on resonantly-produced sterile neutrino dark matter from phase-space densities of Milky Way dwarf spheroidal galaxies (dSphs). The bounds result from a derivation of the dark matter coarse-grained phase-space density from the stellar kinematics, which allows us to explore bounds from some of the most compact dSphs without suffering the resolution limitation from N-body simulations that conventional methods have. We find that the strongest constraints come from very compact dSphs, such as Draco II and Segue 1. We additionally forecast the constraining power of a few dSph c…
Cosmic Structure Strikes Back: The Elimination of Vector-Mediated Nonstandard Interaction Models as a Mechanism for Sterile Neutrino Dark Matter Production
Novel neutrino self-interaction can open up viable parameter space for the relic abundance of sterile-neutrino dark matter (S$ν$DM). In this work, we constrain the relic target using core-collapse supernova which features the same fundamental process and a similar environment to the early universe era when S$ν$DM is dominantly produced. We present a detailed calculation of the effects of a massive scalar mediated neutrino self-interaction on the supernova cooling rate, including the derivation of the thermal potential in the presence of non-zero chemical potentials from plasma species. Our res…
Sterile neutrinos with masses in the keV range are considered to be a viable candidate for warm dark matter. The rate of their production through active-sterile neutrino transitions peaks, however, at temperatures of the order of the QCD scale, which makes it difficult to estimate their relic abundance quantitatively, even if the mass of the sterile neutrino and its mixing angle were known. We derive here a relation, valid to all orders in the strong coupling constant, which expresses the production rate in terms of the spectral function associated with active neutrinos. The latter can in turn…
We derive the non-equilibrium single-particle momentum distribution function of a hadron resonance gas. We then study the effects that this newly derived expression can have in the freeze-out description of fluid-dynamical models of heavy ion collisions and compare it with the method traditionally employed, the 14-moment approximation.
We perform a detailed and illustrative study of the production of keV sterile neutrino Dark Matter (DM) by decays of singlet scalars in the early Universe. In the current study we focus on providing a clear and general overview of this production mechanism. For the first time we study all regimes possible on the level of momentum distribution functions, which we obtain by solving a system of Boltzmann equations. These quantities contain the full information about the production process, which allows us to not only track the evolution of the DM generation but to also take into account all bound…
We consider the possibility of simultaneously addressing the baryon asymmetry of the Universe, the dark matter problem and the neutrino mass generation in minimal extensions of the Standard Model via sterile fermions with (small) total lepton number violation. Within the framework of Inverse and Linear Seesaw models, the small lepton number violating parameters set the mass scale of the active neutrinos, the efficiency of leptogenesis through a small mass splitting between pairs of sterile fermions as well as the mass scale of a sterile neutrino dark matter candidate. We provide an improved pa…
We derive the Boltzmann equation and the collision kernel for massive spin-1/2 particles, using the Wigner-function formalism and employing an expansion in powers of $\hbar$. The phase space is enlarged to include a variable related to the spin degrees of freedom. This allows to reduce the transport equations of the independent components of the Wigner function to one scalar equation. To next-to-leading order in $\hbar$, we find that the collision kernel contains both local and nonlocal terms. We show that off-shell contributions cancel in the Boltzmann equation. Our framework can be used to s…
We review the derivation of the Boltzmann equation and its cosmological applications in this paper. The derivation of the Boltzmann equation, especially the collision term, is discussed in detail in the language of the quantum field theory without any assumption of the finite temperature system. We also discuss the integrated Boltzmann equation with the deal of the temperature parameter as an extension of the standard equation. Among a number of its cosmological applications, we mainly target two familiar examples, the dynamics of the dark matter abundance through the freeze-out/in process and…
Sterile neutrino dark matter in conformal Majoron models
Laboratório de Instrumentação e Física Experimental de Partículas (LIP), Universidade do Minho（葡萄牙米尼奥大学实验粒子物理与仪器实验室）；Department of Physics and Astronomy, University of Hawaii at Manoa（夏威夷大学马诺阿分校物理与天文学系）；Departamento de Física, Escola de Ciências, Universidade do Minho（葡萄牙米尼奥大学理学院物理学系）；Department of Physics, Lund University（瑞典隆德大学物理系）；Departamento de Física da Universidade de Aveiro（葡萄牙阿威罗大学物理系）
In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissi…
With the advent of new and more sensitive direct detection experiments, scope for a thermal WIMP explanation of dark matter (DM) has become extremely constricted. The non-observation of thermal WIMP in these experiments has put a strong upper bound on WIMP-nucleon scattering cross section and within a few years it is likely to touch the neutrino floor. Hence in all probability, DM may have some non-thermal origin. In this work we explore in detail this possibility of a non-thermal sterile neutrino DM within the framework of U(1)$_{\rm B-L}$ model. The U(1)$_{\rm B-L}$ model on the other hand i…
We solve coupled momentum-dependent Boltzmann equations for the phase space distribution of cosmic relic particles, without resorting to approximations of assuming kinetic equilibrium or neglecting backscattering or elastic interactions. Our method is amendable to precision numerical computations. To test it, we consider two benchmark models where the momentum dependence of dark matter distribution function is potentially important: a real singlet scalar extension near the Higgs resonance and a sterile neutrino dark matter model with a singlet scalar mediator. The singlet scalar example shows …
Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dy…
In this paper, we analyze in a mathematically rigorous fashion the validity of the Boltzmann transport equation within quantum field theory. We work within the specific model of a hermitian, scalar field with polynomial self-interaction in two-dimensional Minkowski space. Our main results are as follows: Firstly, that one can obtain a non-perturbative, exact integro-differential equation for the number densities, which we called the pre-Boltzmann equation. We secondly take the long-time-dilute-medium limit of this equation, to obtain a simpler equation. This limiting equation is qualitatively …
The clustering properties of sterile neutrinos are studied within an extension of the minimal standard model, where these are produced via the decay of a gauge singlet scalar. The distribution function after decoupling is strongly out of equilibrium. (DM) abundance and phase space density constraints from (dSphs) constrain the mass in the $\mathrm{keV}$ range consistent with a gauge singlet with mass and vacuum expectation value $\sim 100,\mathrm{GeV}$ decoupling at this temperature. The (DM) transfer function and power spectrum are obtained from the solution of the non-relativistic Boltzmann-…
We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics of the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new unpublished results. For the first-order equation, we explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame, i.e., the Landau-Lifshitz one. It is argued that the frame on which the flow of the relativistic hydrodynamic…
We present a derivation of a Boltzmann equation for the QCD plasma, starting from the quantum field equations. The derivation is based on a gauge covariant gradient expansion which takes consistently into account all possible dependences on the gauge coupling assumed to be small. We point out a limitation of the gradient expansion arising when the range of the interactions becomes comparable with that of the space-time inhomogeneities of the system. The method is first applied to the case of scalar electrodynamics, and then to the description of long wavelength colour fluctuations in the QCD p…
We derive the second-order hydrodynamic equation for reactive multi-component systems from the relativistic Boltzmann equation. In the reactive system, particles can change their species under the restriction of the imposed conservation laws during the collision process. Our derivation is based on the renormalization group (RG) method, in which the Boltzmann equation is solved in an organized perturbation method as faithfully as possible and possible secular terms are resummed away by a suitable setting of the initial value of the distribution function. The microscopic formulae of the relaxati…
We derive generic relativistic hydrodynamical equations with dissipative effects from the underlying Boltzmann equation in a mechanical and systematic way on the basis of so called the renormalization-group (RG) method. A macroscopic frame vector is introduced to specify the frame on which the macroscopic dynamics is described. Our method is so mechanical with only few ansatz that our method give a microscopic foundation of the available hydrodynamical equations, and also can be applied to make a reduction of the kinetic equations other than the simple Boltzmann equation.
We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.
The data on atmospheric neutrinos can be explained assuming the existence of oscillations between muon neutrinos and light sterile neutrinos with mixing close to maximal, and Delta_m^2 approximately equal to 3 E-3 (eV^2). This interpretation of the data is in potential conflict with the successes of big bang nucleosynthesis (BBN), since oscillations can result in a too large contribution of the sterile state to the energy density of the universe at the epoch of nucleosynthesis. The possibility to evade these cosmological constraints has been recently the object of some controversy. In this wor…
We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely man…
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff-Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradien…
We review and extend to include the gauge fields our derivation of the semiclassical limit of the collisionless quantum transport equations for the fermions in presence of a CP-violating bubble wall at a first order electroweak phase transition. We show how the (gradient correction modified) Lorenz-force appears both in the Schwinger-Keldysh approach and in the semiclassical WKB-treatment. In the latter approach the inclusion of gauge fields removes the apparent phase reparametrization dependence of the intermediate calculations. We also discuss setting up the fluid equations for practical cal…
Using the iterative solution of Boltzmann equation in the relaxation-time approximation, the derivation of a third-order evolution equation for shear stress tensor is presented. To this end we first derive the expression for viscous corrections to the phase-space distribution function, $f(x,p)$, up to second-order in derivative expansion. The expression for $δf(x,p)$ obtained in this method does not lead to violation of the experimentally observed $1/\sqrt{m_T}$ scaling of the femtoscopic radii, as opposed to the widely used Grad's 14-moment approximation. Subsequently, we present the derivati…
We report on a work in progress, whose goal is a systematic field theoretical derivation of the quantum transport equations for baryon production in the electroweak plasma at a first order phase transition in the limit of slowly varying background fields (thick wall limit). We start with the Schwinger-Dyson equations for the two point Green function written in the closed time contour (CTC) formalism. The quantum Boltzmann equations for the density matrix arise when the SD-equations are expanded to the first order in the gradients in the on-shell limit. In this paper we consider only scalar fie…
