Probabitlity 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 (Λ) in addition to δ 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 δ and Λ satisfying the constraint δ ≤ 4Λ23 . However, we note that two different classes of instanton solutions exists in the region 0 < δ < 4Λ23 . 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 < Λ2. 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.