Asymmetric dark matter and effective number of neutrinos

We study the effect of the MeV-scale asymmetric dark matter annihilation on the effective number of neutrinos $N_{\mathrm{eff}}$ at the epoch of the big bang nucleosynthesis. If the asymmetric dark matter $\chi$ couples more strongly to the neutrinos $\nu$ than to the photons $\gamma$ and electrons $e^{-}$, ${\mathrm{\Gamma }}_{\chi \gamma ,\chi e}\ll {\mathrm{\Gamma }}_{\chi \nu }$, or ${\mathrm{\Gamma }}_{\chi \gamma ,\chi e}\gg {\mathrm{\Gamma }}_{\chi \nu }$, the lower mass limit on the asymmetric dark matter is about 18 MeV for $N_{\mathrm{eff}}\simeq 3.0$.

Figure 1

The dependence of the extra effective number of neutrinos $\mathrm{\Delta }{N}_{\nu }$ on the maximum ADM number asymmetry ${\epsilon }_{\max }$.

Figure 2

The dependence of the effective number of neutrinos $N_{\mathrm{eff}}$ on the ADM mass $m_{\chi }$ with the various chemical potential $\xi$ at BBN. The figure (a) shows the dependence in the case of ${\mathrm{\Gamma }}_{\chi \gamma ,\chi e}\ll {\mathrm{\Gamma }}_{\chi \nu }$ while the figure (b) shows the dependence in the case of ${\mathrm{\Gamma }}_{\chi \gamma ,\chi e}\gg {\mathrm{\Gamma }}_{\chi \nu }$.

Figure 3

The dependence of the lower mass limit of the ADM $m_{\chi }^{\min }$ on the chemical potential $\xi$ with the various effective number of neutrinos $N_{\mathrm{eff}}$ at BBN ($T=2\mathrm{MeV}$). The figure (a) shows the ${\mathrm{\Gamma }}_{\chi \gamma ,\chi e}\ll {\mathrm{\Gamma }}_{\chi \nu }$ case while the figure (b) shows the ${\mathrm{\Gamma }}_{\chi \gamma ,\chi e}\gg {\mathrm{\Gamma }}_{\chi \nu }$ case.

Figure 4

ADM number asymmetry. Figure (a): the dependence of the ADM number asymmetry $\epsilon$ on the mass $m_{\chi }$ with fixed chemical potential $\xi$. Figure (b) and (c): the dependence of the upper limit of the ADM number asymmetry ${\epsilon }_{\max }$ on the chemical potential $\xi$ with the various bound of the effective number of neutrinos $N_{\mathrm{eff}}^{\max }$ or $N_{\mathrm{eff}}^{\min }$ at BBN. The figure (b) shows the ${\mathrm{\Gamma }}_{\chi \gamma ,\chi e}\ll {\mathrm{\Gamma }}_{\chi \nu }$ case while the figure (c) shows the ${\mathrm{\Gamma }}_{\chi \gamma ,\chi e}\gg {\mathrm{\Gamma }}_{\chi \nu }$ case.

Figure 5

The dependence of the relic abundance of the MeV ADM ${\mathrm{\Omega }}_{\mathrm{ADM}}{h}^2$ on the mass $m_{\chi }$ in the s-wave dominant case. The figure (a) shows the dependence with the various number asymmetry $\epsilon$, while the figure (b) shows the dependence with the various cross section $⟨{\sigma }_{\chi \overline{\chi }}v⟩\simeq a+b{x}^{-1}$. The figure (c) shows the value of parameter “$a$” required to satisfy the observed relic abundance of DM, ${\mathrm{\Omega }}_{\mathrm{ADM}}{h}^2=0.12$ and lower mass limit for the $N_{\mathrm{eff}}=3.0$. The vertical line in figure (c) shows the lower mass limit.

Figure 6

Same as Fig. 5 but p-wave dominant case.