Primordial black hole pair creation in R2 theory

The probability for quantum creation of an inflationary universe with a pair of black holes has been studied in semiclassical approximation with Hartle-Hawking boundary conditions, assuming a gravitational action which includes a quadratic term in the scalar curvature alpha R-2, alpha being a constant. The action of the instanton responsible for creating such a universe, with a spatial section with S-1 x S-2 topology, is seen to be less than that of a de Sitter S-3 instanton, unless alpha < -1/(8 Lambda), where Lambda is the cosmological constant. Since negative alpha implies a classical instability, the probability for production of primordial black holes seems to be suppressed in R-2-theory.