  Density profiles are important tools in galaxy cluster research, offering
insights into clusters dynamical states and their relationship with the broader
Universe. While these profiles provide valuable information about the matter
content of the Universe, their utility in understanding its dark energy
component has remained limited due a lack of tools allowing us to study the
transition from cluster portions that are relaxed and infalling, to those that
are merging with the Hubble flow. In this work we investigate signatures of
this transition in stacked density profiles of simulated cluster-sized halos at
different redshifts. To highlight the Hubble flow around clusters we use their
turnaround radius to normalize stacked simulated density profiles and calculate
their logarithmic slope. Then, we complement our analysis by modeling the outer
portions of these profiles assuming Gaussian early Universe statistics and
spherical collapse without shell-crossing. We find the logarithmic slope of
median cluster density profiles beyond the turnaround radius - where the Hubble
flow dominates - to be Universal and well described by our model. Importantly,
we find the slope of the profiles to diverge from the SCM prediction from
within the turnaround radius where the actual profiles exhibit caustics which
give rise to the splashback feature. We suggest utilizing this divergence from
the spherical collapse model as a method to identify the turnaround radius in
stacked cluster density profiles, offering a new perspective on understanding
cluster dynamics and their cosmological implications.
