Constraints on primordial black holes and curvature perturbations from the global 21-cm signal

The recent observations of the global 21cm signal by EDGES and gravitational waves by LIGO/VIGO have revived interest in PBHs. Different from previous works, we investigate the influence of PBHs on the evolution of the IGM for the mass range $6\times 10^{13} {\rm g} \lesssim M_{\rm PBH}\lesssim 3\times 10^{14} \rm g$. Since the lifetime of these PBHs is smaller than the present age of the Universe, they have evaporated by the present day. Due to Hawking radiation, the heating effects of PBHs on the IGM can suppress the absorption amplitude of the global 21cm signal. In this work, by requiring that the differential brightness temperature of the global 21cm signals in the redshift range of $10\lesssim z \lesssim 30$, e.g., $\delta T_{b} \lesssim -100~\rm mK$, we obtain upper limits on the initial mass fraction of PBHs. We find that the strongest upper limit is $\beta_{\rm PBH} \sim 2\times 10^{-30}$. Since the formation of PBHs is related to primordial curvature perturbations, by using the constraints on the initial mass fraction of PBHs we obtain the upper limits on the power spectrum of primordial curvature perturbations for the scale range $8.0\times 10^{15}\lesssim k \lesssim 1.8\times 10^{16}~\rm Mpc^{-1}$, corresponding to the mass range considered here. We find that the strongest upper limit is $\mathcal P_{\mathcal R}(k) \sim 0.0046$. By comparing with previous works, we find that for the mass range (or the scale range) investigated in this work the global 21cm signals or the 21cm power spectrum should give the strongest upper limits on the initial mass fraction of PBHs and on the power spectrum of primordial curvature perturbations.