Primordial Black Holes Save $R^2$ Inflation

Abstract: In light of the latest Planck-Atacama Cosmology Telescope (P-ACT) joint results on the primordial scalar power spectrum, we show that the $R^2$ inflation model extended with a non-minimally coupled scalar field $\chi$--namely the $R^2$-Higgs model--can yield a larger spectral index $n_s$ and a small positive running $\alpha_s$ at cosmic microwave background (CMB) scales, which are consistent with the data. This is because the $\chi$ field contributes a blue-tilted component to the primordial power spectrum which both modifies the large-scale power and, as a result, significantly enhances power on small scales. The consequent enhancement be large enough to lead to the formation of primordial black holes (PBHs) of mass $\lesssim 10^{20}\mathrm{g}$, accounting for all of the dark matter. Furthermore, future observations of the small-scale power spectrum, CMB spectral distortions, and stochastic gravitational waves will provide decisive tests of this model and its predictions for PBHs.