PROBABILITY FOR PRIMORDIAL BLACK HOLES IN HIGHER DERIVATIVE THEORIES

Abstract

The probability for quantum creation of an inflationary universe with a pair of black holes in higher derivative theories has been studied. Considering a gravitational action which includes quadratic (αR2) and/or cubic term (βR3) in scalar curvature in addition to a cosmological constant (Λ) in semiclassical approximation with Hartle–Hawking boundary condition, the probability has been evaluated. The action of the instanton responsible for creating such a universe, with spatial section with S1XS2 topology, is found to be less than that with a spatial S3 topology, unless α < - 1/8Λ in R2-theory. In the R3 theory, however, there exists a set of solutions without a cosmological constant when βR2 = 1 and [Formula: see text] which admit primordial black holes (PBH) pair in an inflationary universe scenario. We note further that when βR2 ≠ 1, one gets PBH pairs in the two cases: (i) with α and Λ both positive and (ii) with Λ positive and α negative satisfying a constraint 6|α|Λ < 1. However, the relative probability for creation of an inflationary universe with a pair of black holes in the R3-theory suppresses when [Formula: see text] or [Formula: see text]. However, if the above constraints are relaxed one derives interesting results leading to a universe with PBH in R3-theory without cosmological constant.