The primordial black hole from running curvaton

In light of our previous work \cite{Liu:2019xhn}, we investigate the possibility of the formation of a primordial black hole in the second inflationary process induced by the oscillation of curvaton. By adopting the instability of the Mathieu equation, one could utilize the $\delta$ function to fully describe the power spectrum. Due to the running of curvaton mass, we can simulate the value of abundance of primordial black holes nearly covering all of the mass ranges, in which we have given three special cases. One case could account for the dark matter in some sense since the abundance of a primordial black hole is about $75\%$. At late times, the relic of exponential potential could be approximated to a constant of the order of cosmological constant dubbed as a 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.