The dark matter (DM) can consist of the primordial black holes (PBHs) in addition to the conventional weakly interacting massive particles (WIMPs). The Poisson fluctuations of the PBH number density produce the isocurvature perturbations which can dominate the matter power spectrum at small scales and enhance the early structure formation. We study how the WIMP annihilation from those early formed structures can affect the CMB (in particular the E-mode polarization anisotropies and $y$-type spectral distortions) and global 21cm signals. Our studies would be of particular interest for the light (sub-GeV) WIMP scenarios which have been less explored compared with the mixed DM scenarios consisting of PBHs and heavy ($gtrsim 1$ GeV) WIMPs. For instance, for the self-annihilating DM mass $m_{chi}=1$ MeV and the thermally averaged annihilation 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 whole DM to be at most ${cal O}(10^{-3})$ for the sub-solar mass PBHs and an even tighter bound (by a factor $sim 5$) can be obtained from the global 21-cm measurements.
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