We solved the Quantum Kinetic Equations (QKEs) for an active-sterile neutrino system in the early universe. While on the surface this may seem to be an overly simplistic system, other linear two-state systems can be mapped onto the active-sterile system. In the early universe, we find that solutions to the QKEs are well described by an adiabatic approximation where the off-diagonal terms of the density operator are constant on short (oscillation and/or scattering) timescales, but may slowly evolve on long (expansion) timescales. This "quantum kinetic equilibrium" attains as the quantum development of phase balances with the kinetic destruction of phase. In this work, we introduce and assess this equilibrium ansatz as the neutrino states evolve in the early universe with a non-zero lepton number, engendering level crossings that result in scattering-induced active-sterile neutrino transformation.
Several lectures for non-experts on equilibrium and non-equilibrium kinetics in expanding universe are presented. An establishment of thermal equilibrium in the ealry universe as well as mechanisms leading to deviations from the equilibrium are discussed. In the first lecture an elementary introduction to cosmology is presented. Next, kinetic equation in Friedman-Robertson-Walker mertric is considered. Properties of its solutions for different types of particles, in particular, for photons of cosmic microwave background radiation, neutrinos, and massive particles, which could be cold dark matt…
It has been researched the kinetics of the thermal equilibrium's establishment in an early Universe under the assumption of the recovery of interaction scaling of elementary particles in range of superhigh energies. The case of the thermal equilibrium's weak initial violation and basic cosmological consequences of the thermal equilibrium's violation have been researched.
Sasankan et al, have recently claimed that there are significant deviations in the phase-space distributions of the kinetic energies of nuclei from the Maxwell-Boltzmann form usually assumed in BBN, and further, that these deviations lead to big changes in the predicted light-element abundances. Solving the relativistic Boltzmann equation perturbatively, we explicitly show that these deviations are not 20% as claimed, but rather are about 10^-17 in size and hence cannot significantly alter the predicted light-element abundances. We discuss and compute two related effects: O(0.1%) corrections t…
An influence of initial distribution nonequilibrium parameters on thermodynamical equilibrium recovery processes in early Universe under the assumption of elementary particles' scaling of interactions in range of superhigh energies is researched.
We introduce DRAKE, a numerical precision tool for predicting the dark matter relic abundance also in situations where the standard assumption of kinetic equilibrium during the freeze-out process may not be satisfied. DRAKE comes with a set of three dedicated Boltzmann equation solvers that implement, respectively, the traditionally adopted equation for the dark matter number density, fluid-like equations that couple the evolution of number density and velocity dispersion, and a full numerical evolution of the phase-space distribution. We review the general motivation for these approaches and,…
Flat directions in generic supersymmetric theories can change the thermal history of the Universe. A novel scenario was proposed earlier where the vacuum expectation value of the flat directions induces large masses for all the gauge bosons and gauginos. This delays the thermalization of the Universe after inflation and solves the gravitino problem. In this article we perform a detailed calculation of the above scenario. We include the appropriate initial state particle distribution functions, consider the conditions for the feasibility of the non-thermal scenario, and investigate phase space …
We derive solutions to the Schwinger-Dyson equations on the Closed-Time-Path for a scalar field in the limit where backreaction is neglected. In Wigner space, the two-point Wightman functions have the curious property that the equilibrium component has a finite width, while the out-of equilibrium component has zero width. This feature is confirmed in a numerical simulation for scalar field theory with quartic interactions. When substituting these solutions into the collision term, we observe that an expansion including terms of all orders in gradients leads to an effective finite-width. Beside…
In terms of fundamental principles of quantum theory of interacting particles and relativistic kinetic theory there was carried out an analysis of the main principle of standard cosmological scenario - the initial existence of local thermodynamical equilibrium. It has been shown, that condition of the existence of local thermodynamical equilibrium in Universe is determined essentially by means of function of total cross-section of particles' interaction from the kinematic invariant and in case of scaling's recovery in range of superhigh energies it is initially broken.
A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic ab…
We develop further a kinetic theory of strings and derive a transport equation for a network of cosmic strings with Nambu-Goto evolution, interactions and background gravitational effects taken into account. We prove an H-theorem and obtain necessary and sufficient conditions for a thermodynamic equilibrium. At the lowest order the equilibrium is estimated by the von Mises-Fisher distributions parametrized by mean directions and dispersions of the right- and left-moving tangent vectors. Under assumption of a local equilibrium we derive a complete set of hydrodynamic equations that govern the e…
Non-equilibrium Green's functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early time pre-equilibrium stage of high-energy heavy ion collisions. Besides their practical relevance they also provide a meaningful way to address the question when and to what extent a hydrodynamic description of the system becomes applicable. Within the kinetic theory framework we derive a new method to calculate time dependent non-equilibrium Green's functions describing the evolution of energy and momentum perturbations on top of an evolving far-from-equilibrium …
We introduce the quantum-field-theory (QFT) derivation of chiral kinetic theory (CKT) from the Wigner-function approach, which manifests side jumps and non-scalar distribution functions associated with Lorentz covariance and incorporates both background fields and collisions. The formalism is utilized to investigate second-order responses of chiral fluids near local equilibrium. Such non-equilibrium anomalous transport is dissipative and affected by interactions. Contributions from both quantum corrections in anomalous hydrodynamic equations (EOM) of motion and those from the CKT and Wigner fu…
We study the far-off-equilibrium dynamics of a Bjorken expanding non-conformal system within kinetic theory and hydrodynamics. We show that, in contrast to the conformal case, neither shear nor bulk viscous pressure relax quickly to a non-equilibrium attractor. In kinetic theory an early-time, far-from-equilibrium attractor exists for the scaled longitudinal pressure, driven by the rapid longitudinal expansion of the medium. Second-order dissipative hydrodynamics fails to accurately describe this attractor, but a modified anisotropic hydrodynamic formulation reproduces it and provides excellen…
We formulate a kinetic theory of self-interacting meson fields with an aim to describe the freezeout stage of the space-time evolution of matter in ultrarelativistic nuclear collisions. Kinetic equations are obtained from the Heisenberg equation of motion for a single component real scalar quantum field taking the mean field approximation for the non-linear interaction. The mesonic mean field obeys the classical non-linear Klein-Gordon equation with a modification due to the coupling to mesonic quasi-particle excitations which are expressed in terms of the Wigner functions of the quantum fluct…
Recently there has been significant interest in the macroscopic manifestation of chiral anomaly in many-body systems of chiral fermions. A notable example is the Chiral Magnetic Effect (CME). Enthusiastic efforts have been made to search for the CME in the quark-gluon plasma created in heavy ion collisions. A crucial challenge is that the extremely strong magnetic field in such collisions may last only for a brief moment and the CME current may have to occur at so early a stage that the quark-gluon matter is still far from thermal equilibrium. This thus requires modeling of the CME in an out-o…
We develop a macroscopic description of the space-time evolution of the energy-momentum tensor during the pre-equilibrium stage of a high-energy heavy-ion collision. Based on a weak coupling effective kinetic description of the microscopic equilibration process (à la "bottom-up"), we calculate the non-equilibrium evolution of the local background energy-momentum tensor as well as the non-equilibrium linear response to transverse energy and momentum perturbations for realistic boost-invariant initial conditions for heavy ion collisions. We demonstrate how this framework can be used on an event-…
We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar field particles with quartic (tree level) self-interactions ($λϕ^4$) in Friedmann-Lemaitre-Robertson-Walker spacetime. Using a new covariant generating function for the moments of the Boltzmann distribution function, we analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator. We show how the covariant generating function can be also used to find the exact equations for the moments in the full nonlinear regime. Differ…
