Asymmetric dark matter with a possible Bose-Einstein condensate

We investigate the properties of a Bose gas with a conserved charge as a dark matter candidate, taking into account the restrictions imposed by relic abundance, direct and indirect detection limits, big-bang nucleosynthesis and large scale structure formation constraints. We consider both the WIMP-like scenario of dark matter masses $\gtrsim 1\mathrm{GeV}$, and the small mass scenario, with masses $\lesssim {10}^{-11}\mathrm{eV}$. We determine the conditions for the presence of a Bose-Einstein condensate at early times, and at the present epoch.

Figure 1

Plot of the Bose charge in the excited states per entropy when ${\lambda }_{\text{be}}=0.5$ (solid curves) and ${\lambda }_{\text{be}}=0$ (dashed curves) and for two mass values and $m_{\text{be}}=10\mathrm{GeV}$ (black curves) $m_{\text{be}}={10}^{-12}\mathrm{eV}$ (gray curves); the dotted line corresponds to the bound in Eq. (12). For illustration purposes we assumed the Bose gas and the SM have the same temperature. The discontinuities are caused by the step functions in Eq. (9) and $x=m_{\text{be}}/T$ [cf. Eq. (3)].

Figure 2

Values of $T_d$ satisfying the decoupling condition Eq. (26)as a function of $m_{\text{be}}$ for $\epsilon =0.001$, 0.01, 0.1, 1, 10 (bottom to top curves) and for low and high values of $m_{\text{be}}$ (top left and top right graphs, respectively), and in the resonance region (bottom graph). The trough at $m_{\text{be}}\simeq 62.5\mathrm{GeV}$ corresponds to the effects of the Higgs resonance. The shaded region is excluded by the relic abundance constraint.

Figure 3

Left: the curves give the direct-detection cross section Eq. (53) for (lower to upper curves, respectively) $\log \epsilon =-6,-4.5,-3,-0.5$, 1 with the shaded area denoting the region excluded by the XENON and CDMSLite experiments. Right: the shaded area denotes the region of the $m_{\text{be}}-\epsilon$ plane excluded by direct-detection.

Figure 4

Regions of the $m_{\text{be}}-T$ and $r-\mathrm{x}$ planes where a non-relativistic Bose condensate occurs consistent with the LSS constraint of Eq. (55). On the left-hand graph the $\mathrm{low}\text{−}T$ limit results form Eq. (56), while the upper limit is due to Eq. (55).

Figure 5

Region in the ${\mathrm{x}}_{\mathrm{BBN}}-{\mathrm{x}}_{\text{now}}$ plane consistent with the conservation laws, and with the assumption that a BEc is currently present. We used the expressions in Appendix pp1 and $s_{\text{sm}}{|}_{\text{now}}=2889.2/{\mathrm{cm}}^3$, $s_{\text{sm}}{|}_{\mathrm{BBN}}=4.82\times {10}^{28}/{\mathrm{cm}}^3$ and took ${\lambda }_{\text{be}}=0.5$. When ${\lambda }_{\text{be}}=0$ the allowed region collapses to the bold dark line in the figure.

Figure 6

Plot of the critical density as a function of $T$ for ${\lambda }_{\text{be}}=0$ (light gray), 0.1 (dark gray), and 0.5 (black).

Figure 7

Plot of the condensate density $q_{\text{be}}^{(c)}$ as a function of $T$ for constant volume and ${\lambda }_{\text{be}}=0$ (light gray), 0.1 (dark gray) and 0.5 (black), when the critical temperature (see text) $T_C=10m_{\text{be}}$. When $T_C\ll m_{\text{be}}$ the $O({\lambda }_{\text{be}})$ effects are negligible.