Relic abundance of dark matter in universal extra dimension models with right-handed neutrinos

Relic abundance of dark matter is investigated in the framework of universal extra dimension models with right-handed neutrinos. These models are free from the serious Kaluza-Klein (KK) graviton problem that the original universal extra dimension model has. The first KK particle of the right-handed neutrino is a candidate for dark matter in this framework, and its relic abundance is determined by three processes, (1) the decay of the KK photon into the first KK right-handed neutrino in the late universe, (2) production of the first KK right-handed neutrino from the thermal bath in the early universe, and (3) the decay of higher KK right-handed neutrinos into the first KK right-handed neutrino in the late universe. When ordinary neutrino masses are large enough such as the degenerate mass spectrum case, the last process contributes to the abundance significantly, even if the reheating temperature is low. The scale of the extra dimension consistent with cosmological observations can be 500 GeV in the minimal setup of universal extra dimension models with right-handed neutrinos.

Figure 1

(Left) Top loop diagram contributing to the thermal mass of Higgs bosons, where $l+m$ or $|l-m|$ is equal to $n$. (Right) Higgs loop diagram.

Figure 2

The dependence of the abundance on $m_{\nu }$ with fixed $T_R=10/R$ and $m_h=120\mathrm{GeV}$. The solid lines are the relic abundance for $m_{\nu }=0$, 0.3, 0.5, 0.66 eV from bottom to top. The gray band represents the allowed region from the WMAP observation at the $2\sigma$ level.

Figure 3

The parameter region of the model consistent with the WMAP observation in the $(1/R,m_h)$-plane. The neutrino mass and the reheating temperature are taken as $m_{\nu }=0–0.66\mathrm{eV}$ and $T_R=10/R$. The dark (light) gray region shows the $1\sigma$ ($2\sigma$) allowed region. The dashed line shows the constraint from the electroweak precision measurements [13]. The right side of dashed line is the allowed region (99% confidence level).

Figure 4

The dependence of the abundance from the ${\Phi }^{(n)}$ decay on $T_R$. The compactification scale, the neutrino mass, and the SM Higgs mass are taken to be $1/R=600\mathrm{GeV}$, $m_{\nu }=0.66\mathrm{eV}$, and $m_h=120\mathrm{GeV}$. The dotted line represents the abundance of the first right-handed neutrino produced from the thermal bath (${\Omega }_{\mathrm{thermal}}$). The dashed line represents the abundance of the first KK right-handed neutrino produced from the decays of higher KK right-handed neutrinos (${\Omega }_{N^{(n\ge 2)}\mathrm{decay}}$). The solid line represents the sum of abundances by the ${\Phi }^{(n)}$ decay (${\Omega }_{\mathrm{thermal}}+{\Omega }_{N^{(n\ge 2)}\mathrm{decay}}$).