Relic Abundance of Dark Matter Particles: New Formulation and New Result of Abundance Calculation †

A new theoretical framework for computation of the relic abundance of cold dark matter particles such as LSP is presented and some generic features of new results are discussed. The most important is a generalization of the Boltzmann equation to include off-shell effects and its thermal average over cosmic medium. It is shown that at very low temperatures, much below the mass of annihilating particles, equilibrium abundance is suppressed only by powers of temperature instead of the exponential Boltzmann factor. This change gives a larger relic abundance when heavy particles freeze out at these low temperatures. 1 Introduction The well-known problem in cosmology, the dark matter problem, requires some sort of new heavy stable particles which have decoupled from the rest of the universe at an early epoch. The conventional estimate of the relic abundance [1] of dark matter particles that have escaped from pair annihilation is based on the Boltzmann equation for the annihilating particle for which the rate is thermally averaged over the rest of light particles in cosmic medium. The freeze-out temperature of pair annihilation may roughly be estimated by equating the inverse pair annihilation rate to the Hubble rate, and the relic abundance is determined by the thermal number density at that freeze-out temperature [2], which is exponentially suppressed at low temperatures.