Quantum Loop Corrections in the Modified Gravity Model of Starobinsky Inflation with Primordial Black Hole Production

Abstract

A modified gravity model of Starobinsky inflation and primordial black hole production is proposed in good (within 1σ) agreement with current measurements of the cosmic microwave background radiation. The model is an extension of the singularity-free Appleby–Battye–Starobinsky model by the R4 term with different values of the parameters whose fine-tuning leads to the efficient production of primordial black holes on smaller scales with the asteroid-size masses between 1016 g and 1020 g. Those primordial black holes may be part (or the whole) of the current dark matter, while the proposed model can be confirmed or falsified by the detection or absence of the induced gravitational waves with the frequencies in the 10−2 Hz range. The relative size of quantum (loop) corrections to the power spectrum of scalar perturbations in the model is found to be of the order of 10−3 or less, so that the model is not ruled out by the quantum corrections.