Relic Abundance of WIMPs in Non-standard Cosmological Scenarios

Abstract

In this thesis we study the relic density $n_{\chi}$ of non--relativistic long--lived or stable particles $\chi$ in various non--standard cosmological scenarios. First, we discuss the relic density in the non--standard cosmological scenario in which the temperature is too low for the particles $\chi$ to achieve full chemical equilibrium. We also investigated the case where $\chi$ particles are non--thermally produced from the decay of heavier particles in addition to the usual thermal production. In low temperature scenario, we calculate the relic abundance starting from arbitrary initial temperatures $T_0$ of the radiation--dominated epoch and derive approximate solutions for the temperature dependence of the relic density which can accurately reproduces numerical results when full thermal equilibrium is not achieved. If full equilibrium is reached, our ansatz no longer reproduces the correct temperature dependence of the $\chi$ number density. However, we can contrive a semi--analytic formula which gives the correct final relic density, to an accuracy of about 3\% or better, for all cross sections and initial temperatures. We also derive the lower bound on the initial temperature $T_0$, assuming that the relic particle accounts for the dark matter energy density in the universe. The observed cold dark matter abundance constrains the initial temperature $T_0 \geq m_\chi/23 $, where $m_\chi$ is the mass of $\chi$. Second, we discuss the $\chi$ density in the scenario where the the Hubble parameter is modified. Even in this case, an approximate formula similar to the standard one is found to be capable of predicting the final relic abundance correctly. Choosing the $\chi$ annihilation cross section such that the observed cold dark matter abundance is reproduced in standard cosmology, we constrain possible modifications of the expansion rate at $T \sim m_\chi/20$, well before Big Bang Nucleosynthesis.