Primordial Black Hole Pair Creation Probability in Modified Gravitational Theory

TL;DR

This paper calculates the probability of quantum creation of an inflationary universe with black hole pairs in a modified gravity theory, revealing conditions that influence the likelihood of such universe formations.

Contribution

It introduces new instanton solutions in a modified gravitational action including $R^2$ and $R^{-1}$ terms, analyzing their impact on universe and black hole pair creation probabilities.

Findings

Probability suppressed with positive cosmological constant when $ ext{delta} = rac{4 ext{Lambda}^2}{3}$ for $ ext{alpha} > 0$

More probable for $ ext{alpha} < - rac{1}{6 ext{Lambda}}$

Instanton solutions exist without cosmological constant if $ ext{delta} < 0$

Abstract

The probability for quantum creation of an inflationary universe with a pair of black holes is computed in a modified gravitational theory. Considering a gravitational action which includes a cosmological constant ($\Lambda$) in addition to $ \alpha R^{2} $ and $ \delta R^{-1}$ terms, the probabilities have been evaluated for two different kinds of spatial sections, one accommodating a pair of black holes and the other without black hole. We adopt a technique prescribed by Bousso and Hawking to calculate the above creation probability in a semiclassical approximation with Hartle-Hawking boundary condition. Depending on the parameters in the action some new and physically interesting instanton solutions are presented here which may play an important role in the creation of the early universe. We note that the probability of creation of a universe with a pair of black holes is strongly suppressed with a positive cosmological constant when $\delta = \frac{4 \Lambda^{2}}{3}$ for $\alpha > 0$ but it is more probable for $\alpha < - \frac{1}{6 \Lambda}$. It is also found that instanton solutions are allowed without a cosmological constant in the theory provided $\delta < 0$.