Distinguishing cosmologies using the turn-around radius near galaxy clusters

Outside galaxy clusters the competition between the inwards gravitational attraction and the outwards expansion of the Universe leads to a special radius of velocity cancellation, which is called the turn-around radius. Measurements of the turn-around radius hold promises of constraining cosmological parameters, and possibly even properties of gravity. Such a measurement is, however, complicated by the fact that the surroundings of galaxy clusters are not spherical, but instead are a complicated collection of filaments, sheets and voids. In this paper we use the results of numerically simulated universes to quantify realistic error-bars of the measurement of the turn-around radius. We find that for a $Λ$CDM cosmology these error-bars are typically of the order of $20\%$. We numerically simulate three different implementations of dark energy models and of a scalar dark sector interaction to address whether the turn-around radius can be used to constrain non-trivial cosmologies, and we find that only rather extreme models can be distinguished from a $Λ$CDM universe due to the large error-bars arising from the non-trivial cluster environments.