Asymptotic analysis of the Boltzmann equation for dark matter relic abundance

Abstract

A solution to the Boltzmann equation governing the thermal relic abundance of cold dark matter is constructed by matched asymptotic approximations. The approximation of the relic density is an asymptotic series valid when the abundance does not deviate significantly from its equilibrium value until small temperatures. Resonance and threshold effects are taken into account at leading order and found to be negligible unless the annihilation cross section is negligible at threshold. Comparisons are made to previously attempted constructions and to the freeze out approximation commonly employed in the literature. Extensions to higher order matching is outlined, and implications for solving related systems are discussed. We compare our results to a numerical determination of the relic abundance using a benchmark model and find a fantastic agreement. The method developed also serves as a solution to a wide class of problems containing an infinite order turning point.

arXiv comment15 pages, 6 figures

References in corpus (16)

• Supersymmetric Dark Matter
• The Cosmological Parameters 2006
• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• micrOMEGAs3.1 : a program for calculating dark matter observables
• Neutralino Relic Density including Coannihilations
• Sterile Neutrino Dark Matter
• The Megamaser Cosmology Project. XIII. Combined Hubble constant constraints
• Axions as Dark Matter Particles
• An Improved Distance to NGC 4258 and its Implications for the Hubble Constant
• A SHARP view of H0LiCOW: $H_0$ from three time-delay gravitational lens systems with adaptive optics imaging
• STRIDES: a 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408-5354
• DarkSUSY 6 : An Advanced Tool to Compute Dark Matter Properties Numerically
• A new measurement of the Hubble constant and matter content of the Universe using extragalactic background light $\gamma$-ray attenuation
• Cosmology With Low-Redshift Observations: No Signal For New Physics
• Asymptotic Analysis of the Boltzmann Equation for Dark Matter Relics