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

Abstract

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.

Cosmic structure sizes in generic dark energy models

“…It has been explicitly demonstrated that these approaches yield the same result for the CDM model [5], as well as for the BransDicke theory with a positive [36]. Let us now emphasize the new results we derive in the rest of this paper.…”

“…For the explicit form of the above equation in the case of Brans-Dicke cosmology we refer the reader to [36]. Using Eq.…”

“…Since its proposal, the maximum turn around radius as a useful cosmological observable has received considerable attention in the context of modified or alternative gravity/dark energy models [31][32][33][34][35][36][37]. The goal is of course to constrain the additional parameters of such theories.…”

“…The lower bound is new, while the upper bound is improved by about 50% from what was known on the basis of the solar system [44] data. The derivation of R TA,max in the Brans-Dicke theory [45] in the presence of a positive cosmological constant was carried out in [35,36]. In this theory the R TA,max is greater than that of CDM.…”

Stability of cosmic structures in scalar–tensor theories of gravity

“…This is very similar to what happens in neutron stars where the mass-to-radius relation depends crucially on the poorly known equation of state [20], and observed pulsars with a mass at two solar masses rule out equations-of-state that predict a lower higher value for the star mass [21]. Then in [22] the authors considered dark energy models with a constant equation-of-state w, and soon after that the idea was further pursued in subsequent work applied to generic dark anergy models [23], Brans-Dicke theory [24] and DGP brane model [25]. Unfortunately, in novel cosmologies characterized by non-standard Friedmann-like equations it is highly non-trivial to see the implications of the prediction of the models regarding the maximum turnaround point, although a formula for R T may exist.…”