Quantisation of Parameters and the String Landscape Problem

Abstract

We broaden the domain of application of Brustein and de Alwis recent paper [1], where they introduce a (dynamical) selection principle on the landscape of string solutions using FRW quantum cosmology. More precisely, we (i) explain how their analysis is based in choosing a restrictive range of parameters, thereby affecting the validity of the predictions extracted and (ii) subsequently provide a wider and cohesive description, regarding the probability distribution induced by quantum cosmological transition amplitudes. In addition, employing DeWitt's argument [2] for an initial condition on the wave function of the Universe, we found that the string and gravitational parameters become related through interesting expressions involving an integer, suggesting a quantisation relation for some of the involved parameters.