Matter has been found yet, and it is important to build a theoretical model for dark matter that can produce interesting experimental insights. We perform a similar procedure for dark matter, but with no collision terms, obtaining two equations instead. The boltzmann equation is often used to calculate relic density of nonbaryonic dark matter. The boltzmann equation written in abstract form as df dt cf 2. Coupled dark matter must be treated separately see implementation in class ofdm. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up.
Velocity dependence of dark matter electron scattering. To do so, we use the interactions to write down a set of equations, known as boltzmann equations, that model the density of the dark matter in the early universe as it expands and see if the results match experimental measurements today. Numerical boltzmann equation solutions for secretly. Wimp dark matter and cosmology include the textbooks by dodelson 1. These dilatons affect the coupling of stringy matter to dparticle defects, which are generic in string theory.
Dark matter calculation and evaluation a summary a paper by. Theory of dark energy and dark matter 3 we proceed as follows. This analysis presents what could be the most fundamental particle and quanta of dark matter and dark energy. The freezeout, the boltzmann transport equation and the dark. Homogeneous boltzmann equation in quantum relativistic.
The existence of a vast amount of dark matter dm in the universe is supported by many. Boltzmann equation and dark matter freezeout notes. Defense against the dark arts university of california. Defense against the dark arts uci physics and astronomy. Boltzmann equation squared scattering amplitude phase space integrals. The boltzmann equation describes the evolution of the phasespace density fx,v of a dm particle in the halo. The collision terms in the boltzmann equation have several. Two different asymptotic techniques are used, boundarylayer theory, which makes use of asymptotic matching, and the delta expansion, which is a powerful technique for solving nonlinear differential equations. Asymptotic analysis of the boltzmann equation for dark matter. Yet another introduction to dark matter the particle physics approach. Asymptotic analysis of the boltzmann equation for dark. These equations are then solved numerically for the decaying dark matter scenario, wherein neutrinos with mass of order 30 ev radiatively decay producing photons which ionize the intergalactic medium. Entropy per baryon q radiationmatter equality q energy decoupling 2.
A compact solution for the photon spectrum is found in terms of the ionization ratio. Smjvjiin case of only one dark matter particle and nocoannihilating partners. Figure 5 2 from a novel dark matter mechanism to produce x. Tracking the number density of dark matter particles per unit entropy y n. It has a specific spectrum of wavelengths, inversely related to intensity that depend only on the bodys temperature, which is assumed for the sake of calculations and theory to be. Relevant particular cases such as bose, bosefermi, and photonelectron gases are. Asymptoticanalysis of theboltzmann equation for darkmatter. Production of dark matter in the early universe conclusion conclusion relic particle abundances can be calculated with the boltzmann equation abundance of cold relics depends almost only on annihilation cross section wimps are good dark matter candidates neutrinos as hot dark matter can be excluded because of low mass. Due to the presence of both nand n2 terms, the numeric solution to eq. The boltzmann equation describes the physics of thermal dark matter relic abundances in the presence of rolling dilatons. Numerical boltzmann equation solutions for secretly asymmetric. An alternate view of galaxies is as a system of particles in six dimensional phase space.
Pdf an introduction to the boltzmann distribution and the maxwell boltzmann distribution for the ideal gas. This coupling leads to an additional source term in the boltzmann equation. Philosophenweg 12 1 the boltzmann equation consider a stable particle. Jacobson department of physics, princeton university. Cold dark matter q baryonic plasma q photon number density matrix perturbation photon dimensionless intensity matrix photon boltzmann equations q photon source functions q photon pressure, density, anisotropic inertia q photon lineofsight solutions q neutrino number density perturbation 8n q neutrino dimensionless intensity j q neutrino. Thermal relics from the big bang, winter semester 200910 1. The dynamics of spacetime is governed by the einsteins equation from general relativity, and the dynamics of matter distribution is governed by boltzmann s equation. So you cant quite nail down the crosssection and mass. The tool to study these systematically is the boltzmann equation.
Thats three unknowns and only two equations the boltzmann equation and the observation of the dark matter density. Baym equations 10 under the assumption that the pro duction of dark matter do es not a. Dark matter makes up nearly 85% of the universes matter density 1. Measuring the dark matter equation of state and its. Boltzmann equation and dark matter freezeout notes dr. Pdf an introduction to the boltzmann distribution and the maxwellboltzmann distribution for the ideal gas.
But you can narrow down the possible values of crosssection and mass that a dark matter. Pdf quantum kinetic equations and dark matter abundances. This paper presents an asymptotic analysis of the boltzmann equations riccati differential equations that describe the physics of thermal dark matter relic. Boltzmann equation and use previous work on the time derivative and collision terms for photons, and work with zeroth and rstorder terms to nd the nal, fourierspace boltzmann equation. Valle abstract we consider some mathematical questions about boltzmann equations for quantum particles, relativistic or non relativistic. The distribution function f is a function of seven variables, so solving the collisionless boltzmann equation. The main idea is that particles were in thermal equilibrium with the early universe. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random. Thanks for contributing an answer to physics stack exchange. This equation is derived based on the ideal gas equation, boltzmann. The collisionless boltzmann equation we define a galaxy as a self gravitating system of stars and particles of dark matter barnes, 1996. The boltzmann equation in cosmology linkedin slideshare. Matthias krause, cid cosmological independent department, germany, 2007 objective in this paper, the calculation of dark matter is depicted in easy to understand graphics.
But you can narrow down the possible values of crosssection and mass that a dark matter particle might have. The collisionless boltzmann equation defines a galaxy as a selfgravitating system of stars and particles of dark matter. Dark matter is required to explain the stability of galaxies and the rate of formation of largescale structures. In appendix b, we will describe in detail the derivation, from the definition of the. More precisely, the average dark matter content of the universe is about 0. Because the derivation for the nonrelativistic dark matter agent is at the heart of these lecture notes, we will also. This paper proposes an equation of state of dark energy and dark matter as one unified entity. We would like to understand if the model could be a realistic theory for dark matter. For the discussion of approximate solutions to this equation, it is convenient to distinguish according to the freezeout temperature. Dark matter dynamics in the early universe by lin fei submitted to the department of physics on may, 2011, in partial fulfillment of the requirements for the degree of bachelor of science in physics abstract we study a new form of dark matter interaction which may significantly affect the thermal relic abundance of dark matter. This analysis presents what could be the most fundamental particle and quanta of dark matter and dark. Boltzmann equation with mathematica victor christianto abstract the boltzmann equation is often used to calculate relic density of nonbaryonic dark matter. By combining kinematical and gravitational lensing data it is possible to test the widely adopted assumption of pressureless dark matter. The theoryside highlight of the dark matter renaissance is the boltzmann equation.
To calculate the dark matter relic abundance one must solve eq. Pdf boltzmann equation for nonequilibrium particles and. There are many solutions for boltzmann equation in the form of software packages, such as maddm. The freezeout, the boltzmann transport equation and the dark matter bigbang nucleosynthesis recombination brief thermal history of the universe cosmology. Such test is based on general relativity results, the weak. There are much more going on in the early universe than just. The results are then logically tested, discussed, and compared. The dark matter yield as a function of temperature. Let us look at the limiting case of cold matter, i.
Dark matter, higgs bosons, supersymmetry and all that. There are much more going on in the early universe than. In an expanding universe, the total energy of nonrelativistic matter remains constant, with its density decreasing as the volume increases. Introduction calculations conclusions outline 1 introduction dark matter particles candidates for dark matter 2 calculations the boltzmann equation abundances 3 conclusions 2 22 emanuele biolcati dark matter and its particle interpretations. What people will usually say about dm is that it is cold and collisionless, cold dark matter cdm, or collisionless cold dark matter ccdm. Topics covered include potential theory, orbit theory, collisionless boltzmann equation, jeans equations, disk stability, violent relaxation, phase. So far tested only through gravity every local mass concentration gravitational potential orbits and velocities of stars and galaxies measurement of gravitational potential and therefore of local matter distribution. They find an extra term that accounts for the effects of. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. This course describes the physics of collisionless, gravitational nbody systems stellar systems and dark matter halos. Relic abundances and the boltzmann equation abstract. The equation of state for ordinary nonrelativistic matter e.
In section 5, we will solve the boltzmanns equation with only the catalytic reaction both numerically and analytically. First, we have shown in ma and wang, 2014a a new cosmology theorem that our universe is a three dimensional sphere and is static, assuming the einstein general relativity and the cosmological principle that our universe is homogeneous and isotropic. Dark matter was rst proposed in 1933 by fritz zwicky to account for the radial velocity dispersion of galaxies in the coma cluster 11 english reprint 12 which were suggestive of the presence of nonluminous matter. Asymptotic analysis of the boltzmann equation for dark matter relics article pdf available in journal of mathematical physics 5310 march 2012 with 42 reads how we measure reads. Velocity dependence of dark matter electron scattering tess w. Blackbody radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, emitted by a black body an idealized opaque, nonreflective body. Pdf asymptotic ysis of the boltzmann equation for dark. Pdf asymptotic analysis of the boltzmann equation for. U1 b, u1 l 2 an asymmetry is generated in the early universe, n. Numerical boltzmann equation solutions for secretly asymmetric dark matter scenarios christopher dessert phy 379h honors tutorial course department of physics the university of texas at austin undergraduate honors thesis supervising professor. Dark energy is required to rationalise the striking fact that the expansion of the universe started to accelerate recently meaning a few billion years ago. The existence of such massive clusters in the early universe agrees with a cosmological model in which clusters form in a merge of many subclusters in a universe dominated by cold dark matter.
The interactions are complicated and the resulting equations are impossible to solve by hand. This equation is derived based on the ideal gas equation, boltzmann constant, einstein energymass principle and based on the assumption that dark energy and dark matter behave as a perfect fluid. Neutrino protonelectron photon dark matter metriccompton scattering coulomb scattering modern cosmology by dodelson, 2003 10. I discuss the validity of the quantum boltzmann equation for the cal culation of. He prescribes a scheme that is straightforward in principle but di. Pdf asymptotic analysis of the boltzmann equation for dark. Dec 09, 2019 the dark matter yield as a function of temperature. Homogeneous boltzmann equation in quantum relativistic kinetic theory. Asymmetric dark matter an alternative framework is asymmetric dark matter adm, 1 dm carries a conserved quantum number, e. To do so, we use the interactions to write down a set of equations, known as boltzmann equations, that model the density of the dark matter in the early universe as.
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