Formation and evaporation of primordial black holes in scalar-tensor gravity theories

We discuss how the constraints on models of the early Universe derived from considering the formation and evaporation of primordial black holes (PBH's) are modified if the gravitational "constant" varies with time. The modifications depend crucially on whether $G$ has the same value everywhere (so that it maintains the evolving background value) or whether the local value within the black hole is preserved (corresponding to what is termed "gravitational memory"). The simplest varying-$G$ scenario is Brans-Dicke theory, in which one has a scalar field $\phi$ (with $G\sim {\phi }^{-1\mathrm{}}$) and a coupling constant ${\omega }_0$. In this case, solar system observations imply that ${\omega }_0$ is very large and the modifications to the PBH constraints are negligible whether or not there is gravitational memory. However, in more general scalar-tensor theories, the coupling "constant" $\omega \left(\phi \right)$ varies, so $\omega$ may be large today but small at early times. In this case, the value of $G$ and the dynamics of the early Universe could be strongly modified during the period when PBH's form. We present a class of scalar-tensor models which exhibit this feature and discuss how the PBH constraints are modified according to whether or not one has gravitational memory.