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 analysis of the boltzmann equation for. This analysis presents what could be the most fundamental particle and quanta of dark matter and dark energy. There are much more going on in the early universe than just. Asymptotic analysis of the boltzmann equation for dark matter. Measuring the dark matter equation of state and its. Why is the dark matter freeze out temperature t sim frac m. The interactions are complicated and the resulting equations are impossible to solve by hand. Defense against the dark arts uci physics and astronomy.
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. Due to the presence of both nand n2 terms, the numeric solution to eq. The boltzmann equation is often used to calculate relic density of nonbaryonic dark matter. Pdf asymptotic analysis of the boltzmann equation for dark. The tool to study these systematically is the boltzmann equation. Wimp dark matter and cosmology include the textbooks by dodelson 1. Matthias krause, cid cosmological independent department, germany, 2007 objective in this paper, the calculation of dark matter is depicted in easy to understand graphics. Boltzmann equation and dark matter freezeout notes dr. The freezeout, the boltzmann transport equation and the dark. Sources and detection of dark matterenergy in the universe.
Thermal relics from the big bang, winter semester 200910 1. Thanks for contributing an answer to physics stack exchange. Numerical boltzmann equation solutions for secretly. Asymmetric dark matter an alternative framework is asymmetric dark matter adm, 1 dm carries a conserved quantum number, e. For the discussion of approximate solutions to this equation, it is convenient to distinguish according to the freezeout temperature.
There are many solutions for boltzmann equation in the form of software packages, such as maddm. The dark matter yield as a function of temperature. Philosophenweg 12 1 the boltzmann equation consider a stable particle. So you cant quite nail down the crosssection and mass. Let us look at the limiting case of cold matter, i. Jacobson department of physics, princeton university. 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. Homogeneous boltzmann equation in quantum relativistic. In appendix b, we will describe in detail the derivation, from the definition of the. By combining kinematical and gravitational lensing data it is possible to test the widely adopted assumption of pressureless dark matter. The boltzmann equation written in abstract form as df dt cf 2. The equation of state for ordinary nonrelativistic matter 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 it expands and see if the results match experimental measurements today.
Pdf an introduction to the boltzmann distribution and the maxwellboltzmann distribution for the ideal gas. U1 b, u1 l 2 an asymmetry is generated in the early universe, n. Defense against the dark arts university of california. 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. Numerical boltzmann equation solutions for secretly asymmetric. 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. Entropy per baryon q radiationmatter equality q energy decoupling 2.
Relevant particular cases such as bose, bosefermi, and photonelectron gases are. This analysis presents what could be the most fundamental particle and quanta of dark matter and dark. Figure 5 2 from a novel dark matter mechanism to produce x. We would like to understand if the model could be a realistic theory for dark matter. Homogeneous boltzmann equation in quantum relativistic kinetic theory. 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. Boltzmann equation with mathematica victor christianto abstract the boltzmann equation is often used to calculate relic density of nonbaryonic dark matter.
The distribution function f is a function of seven variables, so solving the collisionless boltzmann equation. Relic abundances and the boltzmann equation abstract. Dark matter makes up nearly 85% of the universes matter density 1. They find an extra term that accounts for the effects of. The freezeout, the boltzmann transport equation and the. The main idea is that particles were in thermal equilibrium with the early universe. The boltzmann equation in cosmology linkedin slideshare. Boltzmann equation squared scattering amplitude phase space integrals. This paper proposes an equation of state of dark energy and dark matter as one unified entity. 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. Asymptoticanalysis of theboltzmann equation for darkmatter. The freezeout, the boltzmann transport equation and the dark matter bigbang nucleosynthesis recombination brief thermal history of the universe cosmology.
Topics covered include potential theory, orbit theory, collisionless boltzmann equation, jeans equations, disk stability, violent relaxation, phase. 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. The boltzmann equation describes the evolution of the phasespace density fx,v of a dm particle in the halo. The collisionless boltzmann equation we define a galaxy as a self gravitating system of stars and particles of dark matter barnes, 1996. This course describes the physics of collisionless, gravitational nbody systems stellar systems and dark matter halos. I discuss the validity of the quantum boltzmann equation for the cal culation of. 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. 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. Pdf asymptotic ysis of the boltzmann equation for dark. The newtonian equations of motion for such a system may be written as. 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. Neutrino protonelectron photon dark matter metriccompton scattering coulomb scattering modern cosmology by dodelson, 2003 10. Baym equations 10 under the assumption that the pro duction of dark matter do es not a. In section 5, we will solve the boltzmanns equation with only the catalytic reaction both numerically and analytically.
Physics stack exchange is a question and answer site for active researchers, academics and students of physics. 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. 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. The standard model of cosmology, or the big bang theory in more colloquial language, can be summed up in a single statement.
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. Dark matter, higgs bosons, supersymmetry and all that. This paper presents an asymptotic analysis of the boltzmann equations riccati differential equations that describe the physics of thermal dark matter relic. 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. The boltzmann equation describes the physics of thermal dark matter relic abundances in the presence of rolling dilatons. Theory of dark energy and dark matter 3 we proceed as follows. 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. More precisely, the average dark matter content of the universe is about 0. Dec 09, 2019 the dark matter yield as a function of temperature. An alternate view of galaxies is as a system of particles in six dimensional phase space. Boltzmann equation and dark matter freezeout notes. Tracking the number density of dark matter particles per unit entropy y n. The theoryside highlight of the dark matter renaissance is the boltzmann equation. Thats three unknowns and only two equations the boltzmann equation and the observation of the dark matter density.
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. But you can narrow down the possible values of crosssection and mass that a dark matter. Asymptotic analysis of the boltzmann equation for dark. Yet another introduction to dark matter the particle physics approach. Pdf an introduction to the boltzmann distribution and the maxwell boltzmann distribution for the ideal gas.
Because the derivation for the nonrelativistic dark matter agent is at the heart of these lecture notes, we will also. A compact solution for the photon spectrum is found in terms of the ionization ratio. In an expanding universe, the total energy of nonrelativistic matter remains constant, with its density decreasing as the volume increases. This equation is derived based on the ideal gas equation, boltzmann. The existence of a vast amount of dark matter dm in the universe is supported by many. Pdf quantum kinetic equations and dark matter abundances. The results are then logically tested, discussed, and compared. What people will usually say about dm is that it is cold and collisionless, cold dark matter cdm, or collisionless cold dark matter ccdm. The collisionless boltzmann equation defines a galaxy as a selfgravitating system of stars and particles of dark matter. The collision terms in the boltzmann equation have several.
He prescribes a scheme that is straightforward in principle but di. To calculate the dark matter relic abundance one must solve eq. Dark matter is required to explain the stability of galaxies and the rate of formation of largescale structures. Dark matter calculation and evaluation a summary a paper by. Velocity dependence of dark matter electron scattering.
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. Matter has been found yet, and it is important to build a theoretical model for dark matter that can produce interesting experimental insights. Smjvjiin case of only one dark matter particle and nocoannihilating partners. But you can narrow down the possible values of crosssection and mass that a dark matter particle might have.
We perform a similar procedure for dark matter, but with no collision terms, obtaining two equations instead. Coupled dark matter must be treated separately see implementation in class ofdm. Pdf boltzmann equation for nonequilibrium particles and. These dilatons affect the coupling of stringy matter to dparticle defects, which are generic in string theory. 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. The boltzmann equation or boltzmann transport equation bte describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by ludwig boltzmann in 1872. There are much more going on in the early universe than.
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