Gravitational memory?

We discuss the formation of primordial black holes during the early stages of the Universe if the effective gravitational "constant" evolves with time. We describe two possible courses of cosmological evolution: first, one in which the black-hole horizon evolves on the Hubble time scale, and a second, in which the long-range scalar field from which the gravitational coupling is derived remains constant over the horizon scale while evolving in the cosmological background. The second scenario leads to significant changes to the standard picture of black-hole explosions because black holes retain "memory" of the value of the gravitational constant at the time of their formation. There are significant implications for observational searches for black-hole explosions if the gravitation "constant" has changed with time since the Universe was about ${10}^{-25\mathrm{}}$ s old.