Primordial black holes from Volkov-Akulov-Starobinsky supergravity

We study the formation of primordial black holes (PBH) in the Starobinsky supergravity coupled to the nilpotent superfield describing Volkov-Akulov goldstino. By using the no-scale K\"ahler potential and a polynomial superpotential, we find that under certain conditions our model can describe effectively single-field inflation with the ultra-slow-roll phase that appears near a critical (nearly-inflection) point of the scalar potential. This can lead to the formation of PBH as part of (or whole) dark matter, while keeping the inflationary spectral tilt and the tensor-to-scalar ratio in good agreement with the current cosmic microwave background (CMB) bounds. After inflation, supersymmetry is spontaneously broken at the inflationary scale with the vanishing cosmological constant.