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 ΛCDM value, by a factor
1 + 1
3ω
, where ω ≫ 1 is the Brans-Dicke parameter, implying consistency of the theory with
current data.
