Cosmological abundance of primordial black holes in mixed dark matter scenarios incorporating Kaluza-Klein dark matter

The lightest Kaluza-Klein (KK) dark matter particles and primordial black holes (PBHs) emerge as plausible candidates for dark matter. In scenarios where dark matter is a mix of KK particles and PBHs, PBHs can attract surrounding KK dark matter particles post-formation, leading to the creation of ultracompact dark matter halos (UCMHs). The distribution of KK dark matter particles within UCMHs tends to be steeper than in classical dark matter halo structures, such as the Navarro-Frenk-White model. Consequently, the annihilation rate of KK dark matter particles in UCMHs is significant. The high-energy photons resulting from the annihilation of KK particles in UCMHs contribute to the extragalactic gamma-ray background (EGB). Leveraging data from the $\mathtt{Fermi\text{-}LAT}$ experiment, we have derived, for the first time, upper limits on the cosmological abundance of PBHs in the context of KK dark matter annihilation. For a KK dark matter mass range of $500\le m_{\rm B^{(1)}}\le 1500$ GeV, which aligns with the observed present abundance of dark matter, the conservative limits on the fraction of dark matter in PBHs, for massive PBHs with $M_{\rm PBH}\gtrsim 10^{-11}M_{\odot}$, are $f_{\rm PBH} \lesssim 2\times 10^{-5}$.