Improved model of primordial black hole formation after Starobinsky inflation

Abstract

A new (improved) model of inflation and primordial black hole (PBH) formation is proposed by combining Starobinsky model of inflation, Appleby-Battye-Starobinsky (ABS) model of dark energy and a quantum correction in the modified $F(R)$ gravity. The energy scale parameter in the ABS model is taken to be close to the inflationary scale, in order to describe double inflation instead of dark energy. The quantum correction is given by the term quartic in the spacetime scalar curvature $R$ with a negative coefficient $(-\delta )$ in the $F(R)$ function. It is demonstrated that very good agreement (within $1\sigma$) with current measurements of the cosmic microwave background (CMB) radiation can be achieved by choosing the proper value of $\delta$, thus solving the problem of low values of the tilt of CMB scalar perturbations in the earlier proposed model in arXiv:2205.00603. A large (by the factor of $10^7$ against CMB) enhancement in the power spectrum of scalar perturbations is achieved by fine-tuning the parameters of the model. It is found by numerical analysis that it can lead to formation of asteroid-size PBH with the masses up to $10^{20}$ g, which may form dark matter in the current universe.

12 pages, 6 figures, LaTeX; minor corrections

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• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Inflation in $F(R)$ gravity models revisited after ACT
• Quantum loop corrections in the modified gravity model of Starobinsky inflation with primordial black hole production
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• Resonant amplification of curvature perturbations in inflation model with periodical derivative coupling
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Superpotential method and the amplification of inflationary perturbations
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Primordial Black Holes in Induced Gravity Inflationary Models with Two Scalar Fields
• Primordial black holes formation in inflationary $F(R)$ models with scalar fields