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Probability for Primordial Black Holes Pair in 1/R Gravity

Dilip Paul·Bikash Chandra Paul
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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 ($Λ$) in addition to $ δR^{- 1} $ term, the probability has been evaluated in a semiclassical approximation with Hartle-Hawking boundary condition. We obtain instanton solutions determined by the parameters $δ$ and $Λ$ satisfying the constraint $ δ\leq \frac{4 Λ^{2}}{3}$. However, we note that two different classes of instanton solutions exists in the region $0 < δ< \frac{4 Λ^{2}}{3}$. 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 $0 < δ< Λ^{2}$. It is also found that gravitational instanton solution is permitted even with $Λ= 0$ but one has to consider $δ< 0$. However, in the later case a universe with a pair of black holes is less probable.

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Dilip Paul, Bikash Chandra Paul. 2005-08-18. Probability for Primordial Black Holes Pair in 1/R Gravity. https://doi.org/10.1103/physrevd.72.064012

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