Maximum turnaround radius in f(R) gravity

Abstract

The accelerating behavior of cosmic fluid opposes gravitational attraction at present epoch, whereas standard gravity is dominant at small scales. As a consequence, there exists a point where the effects are counterbalanced, dubbed turnaround radius, [Formula: see text]. By construction, it provides a bound on maximum structure sizes of the observed universe. Once an upper bound on [Formula: see text] is provided, i.e. [Formula: see text], one can check whether cosmological models guarantee structure formation. Here, we focus on [Formula: see text] gravity, without imposing a priori the form of [Formula: see text]. We thus provide an analytic expression for the turnaround radius in the framework of [Formula: see text] models. To figure this out, we compute the turnaround radius in two distinct cases: (1) under the hypothesis of static and spherically symmetric spacetime, and (2) by using the cosmological perturbation theory. We thus find a criterion to enable large scale structures to be stable in [Formula: see text] models, circumscribing the class of [Formula: see text] theories as suitable alternative to dark energy. In particular, we get that for constant curvature, the viability condition becomes [Formula: see text], with [Formula: see text] and [Formula: see text], respectively, the observed cosmological constant and the Ricci curvature. This prescription rules out models which do not pass the aforementioned [Formula: see text] limit.