A Smolin-like branching multiverse from multiscalar-tensor theory

Abstract

We implement a Smolin-like branching multiverse through a directed, acyclic graph of $N$ metrics. Our gravitational and matter actions are indistinguishable from $N$ decoupled statements of General Relativity, if one varies with respect to metric degrees of freedom. We replace $N-1$ metrics with scalar fields by conformally relating each metric to its unique graph predecessor. Varying with respect to the $N-1$ scalar fields gives a multiscalar-tensor model which naturally features dark matter candidates. Building atop an argument of Chapline and Laughlin, branching is accomplished with the emergence of order parameters during gravitational collapse: we bootstrap a suitably defined $N$ scalar field model with initial data from an $N-1$ field model. We focus on the nearest-neighbour approximation, determine conditions for dynamical stability, and compute the equations of motion. The model features a novel screening property where the scalar fields actively adjust to decouple themselves from the stress, oscillating about the requisite values. In the Newtonian limit, these background values for the scalar fields exactly reproduce Newton's law of gravitation.