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The dark matter (DM) can consist of the primordial black holes (PBHs) inaddition to the conventional weakly interacting massive particles (WIMPs). ThePoisson fluctuations of the PBH number density produce the isocurvatureperturbations which can dominate the matter power spectrum at small scales andenhance the early structure formation. We study how the WIMP annihilation fromthose early formed structures can affect the CMB (in particular the E-modepolarization anisotropies and $y$-type spectral distortions) and global 21cmsignals. Our studies would be of particular interest for the light (sub-GeV)WIMP scenarios which have been less explored compared with the mixed DMscenarios consisting of PBHs and heavy ($\gtrsim 1$ GeV) WIMPs. For instance,for the self-annihilating DM mass $m_{\chi}=1$ MeV and the thermally averagedannihilation cross section $\langle \sigma v \rangle \sim 10^{-30} \rm cm^3/s$,the latest Planck CMB data requires the PBH fraction with respect to the wholeDM to be at most ${\cal O}(10^{-3})$ for the sub-solar mass PBHs and an eventighter bound (by a factor $\sim 5$) can be obtained from the global 21-cmmeasurements.

CMB and 21cm bounds on early structure formation boosted by primordial black hole entropy fluctuations