Primordial black hole from the running curvaton*

In light of our previous study [Chin. Phys. C 44(8), 085103 (2020)], we investigate the possibility of the formation of a primordial black hole in the second inflationary process induced by the oscillation of the curvaton. By adopting the instability of the Mathieu equation, one can utilize the delta function to fully describe the power spectrum. Owing to the running of the curvaton mass, we can simulate the value of the abundance of primordial black holes covering almost all of the mass ranges. Three special cases are given. One case may account for dark matter because the abundance of a primordial black hole is approximately 75% . As late times, the relic of exponential potential may be approximated to a constant of the order of a cosmological constant, which is dubbed as the role of dark energy. Thus, our model could unify dark energy and dark matter from the perspective of phenomenology. Finally, it sheds new light on exploring Higgs physics.