Where the world stands still: turnaround as a strong test of Λ CDM cosmology

Our intuitive understanding of cosmic structure formation works best in scales small enough so that bound, relaxed gravitating systems are no longer adjusting their radius; and large enough so that space and matter follow the average expansion of the Universe. Yet one of the most robust predictions of $\Lambda$CDM cosmology concerns the scale that separates these limits: the turnaround radius, which is the non-expanding shell furthest away from the center of a bound structure. The maximum possible value of the turnaround radius within the framework of the $\Lambda$CDM model is, for a given mass $M$, equal to $(3GM/\Lambda c^2)^{1/3}$, with $G$ Newton's constant and $c$ the speed of light, independently of cosmic epoch, exact nature of dark matter, or baryonic effects. We discuss the possible use of this prediction as an observational test for $\Lambda$CDM cosmology.