Probability for primordial black holes in a multidimensional universe with nonlinear scalar curvature terms

Abstract

We investigate multidimensional universe with nonlinear scalar curvature terms to evaluate the probability of creation of primordial black holes. For this we obtain Euclidean instanton solution in two different topologies: (a) ${S}^{D\ensuremath{-}1}$---topology which does not accommodate primordial black holes and (b) ${S}^{1}\ifmmode\times\else\texttimes\fi{}{S}^{D\ensuremath{-}2}$---topology which accommodates a pair of black holes. The probability for quantum creation of an inflationary universe with a pair of black holes has been evaluated assuming a gravitational action which is described by a polynomial function of scalar curvature with or without a cosmological constant ($\ensuremath{\Lambda}$) using the framework of semiclassical approximation of Hartle-Hawking boundary conditions. We discuss here a class of new gravitational instantons solution in the ${R}^{4}$ theory which are relevant for cosmological model building.