Probability for Primordial Black Holes Pair in 1/R Gravity

TL;DR

This paper studies the quantum probability of creating an inflationary universe with black hole pairs in 1/R gravity, revealing suppression effects depending on the cosmological constant and model parameters.

Contribution

It provides a semiclassical analysis of black hole pair creation probabilities in 1/R gravity with a cosmological constant, identifying conditions for instanton solutions and their likelihood.

Findings

Probability is suppressed with positive cosmological constant.

Two classes of instanton solutions exist for certain parameters.

Black hole pair creation is less probable with negative or zero cosmological constant.

Abstract

The probability for quantum creation of an inflationary universe with a pair of black holes in 1/R - gravitational theory has been studied. Considering a gravitational action which includes a cosmological constant ($\Lambda$) in addition to $ \delta R^{- 1} $ term, the probability has been evaluated in a semiclassical approximation with Hartle-Hawking boundary condition. We obtain instanton solutions determined by the parameters $\delta$ and $\Lambda$ satisfying the constraint $ \delta \leq \frac{4 \Lambda^{2}}{3}$. However, we note that two different classes of instanton solutions exists in the region $0 < \delta < \frac{4 \Lambda^{2}}{3}$. The probabilities of creation of such configurations are evaluated. It is found that the probability of creation of a universe with a pair of black holes is strongly suppressed with a positive cosmological constant except in one case when $0 < \delta < \Lambda^{2}$. It is also found that gravitational instanton solution is permitted even with $\Lambda = 0$ but one has to consider $\delta < 0$. However, in the later case a universe with a pair of black holes is less probable.