Primordial black holes save $R^2$ inflation

Abstract

In light of the latest Planck and 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 $\chi$-extended $R^2$ inflation model--can naturally accommodate a larger spectral index $n_s$ and a small positive running $\alpha_s$ at cosmic microwave background (CMB) scales, both of which are consistent with the latest P-ACT constraints. 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 deviation of the $n_s$ and $\alpha_s$ from the single field $R^2$ inflation is related to the non-minimal coupling constant $\xi$. The consequent enhancement in the primordial power spectrum can be large enough to lead to the formation of primordial black holes (PBHs) of mass $\lesssim 10^{20}\mathrm{g}$ as dark matter candidates. 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. We stress its strong connection to the seesaw mechanism for the generation of the observed small masses.