Maximum turnaround radius in f(R) gravity

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, rta. By construction, it provides a bound on maximum structure sizes of the observed universe. Once an upper bound on rta is provided, i.e. RTA,max, one can check whether cosmological models guarantee structure formation. Here, we focus on f(R) gravity, without imposing a priori the form of f(R). We thus provide an analytic expression for the turnaround radius in the framework of f(R) 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 f(R) models, circumscribing the class of f(R) theories as suitable alternative to dark energy. In particular, we get that for constant curvature, the viability condition becomes RdSf‧(R dS) ≤ 5.48Λ ⇒ f‧(R dS) ≤ 1.37, with Λ and RdS, respectively, the observed cosmological constant and the Ricci curvature. This prescription rules out models which do not pass the aforementioned RTA,max limit.