Asymptotic Analysis of the Boltzmann Equation for Dark Matter Relics in the presence of a Running Dilaton and Space-Time Defects

TL;DR

This paper analyzes how dilaton fields and space-time defects influence dark matter relic abundances through the Boltzmann equation, providing asymptotic solutions and implications for collider searches.

Contribution

It introduces a novel asymptotic analysis of the Boltzmann equation incorporating dilaton effects and space-time defects in string cosmology.

Findings

Derived detailed asymptotic relic abundances for various dilaton values

Identified the impact of dilatons on dark matter coupling to space-time defects

Discussed implications for supersymmetric dark matter detection at colliders

Abstract

The interplay of dilatonic effects in dilaton cosmology and stochastic quantum space-time defects within the framework of string/brane cosmologies is examined. The Boltzmann equation describes the physics of thermal dark-matter-relic abundances in the presence of rolling dilatons. These dilatons affect the coupling of stringy matter to D-particle defects, which are generic in string theory. This coupling leads to an additional source term in the Boltzmann equation. The techniques of asymptotic matching and boundary-layer theory, which were recently applied by two of the authors (CMB and SS) to a Boltzmann equation, are used here to find the detailed asymptotic relic abundances for all ranges of the expectation value of the dilaton field. The phenomenological implications for the search of supersymmetric dark matter in current colliders, such as the LHC, are discussed.