Probability for Primordial Black Holes Pair in 1/R Gravity

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 $\delta \le \frac{4{\Lambda }^2}{3}$. 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.

15 pages, no figure. submitted to Phys. Rev. D

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• Reconciling dark energy models with f(R) theories
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• Curvature driven acceleration : a utopia or a reality ?
• Generalized Chaplygin Gas in a modified gravity approach
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Cited by in corpus (4)

• f(R) Theories Of Gravity
• Primordial Black Holes
• Fundamental Particle Structure in the Cosmological Dark Matter
• Primordial Black Hole Pair Creation Probability in Modified Gravitational Theory