The maximum sizes of large scale structures in alternative theories of gravity

TL;DR

This paper derives general formulas for the maximum size of cosmic structures in various gravity theories, applying them to Brans-Dicke theory, and finds that these sizes are consistent with current observations.

Contribution

It provides a unified method to estimate the maximum turnaround radius in any gravity theory obeying Einstein equivalence principle, including specific calculations for Brans-Dicke gravity.

Findings

Maximum sizes in Brans-Dicke theory exceed CDM values by a factor depending on omega

Derived formulas agree on spherically symmetric and perturbed FRW spacetimes

Results support the consistency of Brans-Dicke theory with observational data

Abstract

The maximum size of a cosmic structure is given by the maximum turnaround radius -- the scale where the attraction due to its mass is balanced by the repulsion due to dark energy. We derive generic formulae for the estimation of the maximum turnaround radius in any theory of gravity obeying the Einstein equivalence principle, in two situations: on a spherically symmetric spacetime and on a perturbed Friedman-Robertson-Walker spacetime. We show that the two formulae agree. As an application of our formula, we calculate the maximum turnaround radius in the case of the Brans-Dicke theory of gravity. We find that for this theory, such maximum sizes always lie above the \LCDM value, by a factor $1 + \frac{1}{3\omega}$, where $\omega\gg 1$ is the Brans-Dicke parameter, implying consistency of the theory with current data.