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 was proposed in good (within $1\sigma$) 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 $R^4$-term with different values of the parameters whose fine-tuning leads to efficient production of primordial black holes on smaller scales with the asteroid-size masses between $10^{16}$ g and $10^{20}$ 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 detection or absence of the induced gravitational waves with the frequencies about $10^{-2}$ Hz. The main purpose of this paper was to estimate the size of quantum (loop) corrections in the model. It was found their relative contribution to the power spectrum of scalar perturbations is about $10^{-3}$ or less, so that the model is not ruled out by the quantum corrections.

14 pages, 8 figures; LaTeX; Section 3 extended, new figures and references added, one reference replaced

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Cited by in corpus (11)

• Comparing sharp and smooth transitions of the second slow-roll parameter in single-field inflation
• Inflation in $F(R)$ gravity models revisited after ACT
• Conservation of superhorizon curvature perturbations at one loop: Backreaction in the in-in formalism and Renormalization
• Role of the counterterms in the conservation of superhorizon curvature perturbations at one loop
• One-loop corrections to the E-type $\alpha$-attractor models of inflation and primordial black hole production
• Superpotential method and the amplification of inflationary perturbations
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• Stochastic Inflation with Interacting Noises
• Starobinsky inflation and Swampland conjectures
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