Combined Effects of f(R) Gravity and Massive Neutrinos on the Turnaround Radii of Dark Matter Halos

We present a new statistics based on the turnaround radii of cluster halos to break the dark sector degeneracy between the ?CDM model and the alternative ones with f(R) gravity and massive neutrinos (nu) characterized by the strength of the fifth force, divide f ( R0) divide , and the total neutrino mass, M ( nu ). Analyzing the Rockstar halo catalogs at the present epoch from the DUSTGRAIN-pathfinder N-body simulations performed for four different cosmologies, namely, ?CDM ( divide f ( R0) divide = 0, n-ary sumation m ( nu ) = 0.0 eV), fR6 ( divide f ( R0) divide = 10(-6), n-ary sumation m ( nu ) = 0.0 eV), fR6+0.06 eV( divide f ( R0) divide = 10(-6), n-ary sumation m ( nu ) = 0.06 eV), and fR5+0.15 eV( divide f ( R0) divide = 10(-5), n-ary sumation m ( nu ) = 0.15 eV), which are known to yield very similar conventional statistics to one another. For each model, we select those cluster halos that do not neighbor any other larger halos in their bound zones and construct their bound-zone peculiar velocity profiles at z = 0. Then, we determine the radial distance of each selected halo at which the bound-zone velocity becomes equal to the recession speed of the Hubble flow as its turnaround radius, and evaluate the cumulative probability distribution of the ratios of the turnaround radii to the virial counterparts, P(r ( t )/r ( v ) >= alpha). The degeneracy between the fR6 and fR5+0.15 eV models is found to be readily broken by the 10 sigma (Delta P ) difference in the value of P(alpha = 4), while the 3.2 sigma (Delta P ) difference between the ?CDM and fR6+0.06 eV models is detected in the value of P(alpha = 8.5). It is also found that the four models yield smaller differences in P(alpha) at higher redshifts.