The Quantum Primordial Black Holes, Dimensionless Small Parameter, Inflationary Cosmology and Non-Gaussianity

TL;DR

The paper investigates quantum-gravitational corrections (qgcs) for ultralight primordial black holes (PBHs) formed in the preinflationary era within Schwarzschild–de Sitter spacetimes. By adopting a generalized uncertainty principle (GUP*) framework, it derives a dimensionless deformation parameter $oldsymbol{rac{A_0}{A}}$ and a small parameter $oldsymbol{rac{M_0}{M}}$, enabling a systematic series expansion of qgcs that modify PBH thermodynamics, the preinflationary dynamics, and inflationary perturbations. The main findings show that qgcs shift inflationary parameters via $H o H_q$ and $V o V_q$, raise PBH appearance probabilities, deform Friedmann equations, and enhance non-Gaussianity in scalar and tensor perturbations with a characteristic exponential scaling in $oldsymbol{W(-oldsymbol{rac{M_0}{M}}^2/e)}$. These results suggest observable imprints on the primordial power spectrum and bispectrum, linking Planck-scale physics to inflationary cosmology, and motivate comparisons with observational data and extensions to other PBH metrics.

Abstract

In the present work consideration is given to the primordial black holes ({\bf pbhs}) in the Schwarzschild-de Sitter Metric with small mass (ultralight) in the preinflationary epoch. Within the scope of natural assumptions, it has been shown that the quantum-gravitational corrections ({\bf qgcs}) to the characteristics of such black holes can contribute to all the cosmological parameters, shifting them compared with the semiclassical consideration. These contributions are determined by a series expansion in terms of a small parameter dependent on the hole mass (radius). For this pattern different cases have been considered (stationary, black hole evaporation...). It has been demonstrated that involvement of ({\bf qgcs}) leads to a higher probability for the occurrence of such {\bf pbhs}. Besides, high-energy deformations of Friedmann Equations created on the basis of these corrections have been derived for different patterns. In the last section of this work it is introduced a study into the contributions generated by the above-mentioned {\bf qgcs} in inflationary cosmological perturbations. Besides, it has been shown that non-Gaussianity of these perturbations is higher as compared to the semi-classical pattern.