A Note on Gravitational Memory in F(R)-theories and their Equivalent Scalar-Tensor Theories

In this paper we consider the implications that the effect gravitational memory would have on primordial black holes, within the theoretical context of $F(R)$ related scalar-tensor theories. As we will demonstrate, under the assumption that the initial mass of the primordial black hole is such so that it evaporates today, this can potentially constrain the $F(R)$ related theories of gravity. We study two scalar-tensor models and discuss the evolution of primordial black holes created at some initial time $t_f$ in the early universe. The results between the two models vary significantly which shows us that, if the effect of gravitational memory is considered valid, some of the scalar-tensor models and their corresponding $F(R)$ theories must be further constrained.

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