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Quantum fluctuations of scalar fields during inflation could determine the very-large-scale structure of the universe In the case of general scalar-tensor gravity theories these fluctuations lead to the diffusion of fundamental constants such as the Planck mass and the effective Brans-Dicke parameter. In the particular case of Brans-Dicke gravity, where is constant, this leads to runaway solutions with infinitely large values of the Planck mass. However, in a variable theory, if the Planck mass has a maximum, we find stationary probability distributions peaked at exponentially large values of after inflation. We conclude that general relativity is an attractor during the quantum diffusion of the fields.
García-Bellido et al. (Wed,) studied this question.