Neutralino versus axion/axino cold dark matter in the 19 parameter SUGRA model

We calculate the relic abundance of thermally produced neutralino cold dark matter in the general 19 parameter supergravity (SUGRA-19) model. A scan over GUT scale parameters reveals that models with a bino-like neutralino typically give rise to a dark matter density \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega_{\tilde{\chi }_1^0}}{h^2} \sim 1 - 1000 $$\end{document}, i.e. between 1 and 4 orders of magnitude higher than the measured value. Models with higgsino or wino cold dark matter can yield the correct relic density, but mainly for neutralino masses around 700-1300 GeV. Models with mixed bino-wino or bino-higgsino CDM, or models with dominant co-annihilation or A-resonance annihilation can yield the correct abundance, but such cases are extremely hard to generate using a general scan over GUT scale parameters; this is indicative of high fine-tuning of the relic abundance in these cases. Requiring that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {m_{\tilde{\chi }_1^0}}\mathop { < }\limits_\sim 500\,{\text{GeV}} $$\end{document} (as a rough naturalness requirement) gives rise to a minimal probably dip in paramet er space at the measured CDM abundance. For comparison, we also scan over mSUGRA space with four free parameters. Finally, we investigate the Peccei-Quinn augmented MSSM with mixed axion/axino cold dark matter. In this case, the relic abundance agrees more naturally with the measured value. In light of our cumulative results, we conclude that future axion searches should probe much more broadly in axion mass, and deeper into the axion coupling.