Effect of accretion on primordial black holes in Brans-Dicke theory

We consider the effect of accretion of radiation in the early universe on primordial black holes in Brans-Dicke theory. The rate of growth of a primordial black hole due to accretion of radiation in Brans-Dicke theory is considerably smaller than the rate of growth of the cosmological horizon, thus making available sufficient radiation density for the black hole to accrete causally. We show that accretion of radiation by Brans-Dicke black holes overrides the effect of Hawking evaporation during the radiation dominated era. The subsequent evaporation of the black holes in later eras is further modified due to the variable gravitational ``constant'', and they could survive up to longer times compared to the case of standard cosmology. We estimate the impact of accretion on modification of the constraint on their initial mass fraction obtained from the $\gamma$-ray background limit from presently evaporating primordial black holes.