Zusammenfassung
We present a new statistics based on the turn-around radii of cluster halos
to break the dark sector degeneracy between the $Łambda$CDM model and the
alternative ones with $f(R)$ gravity and massive neutrinos ($\nu$)
characterized by the strength of the fifth force, $f_R0\vert$, 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, $Łambda$CDM ($\vert
f_R0\vert=0$, $M_\nu=0.0$eV), fR6 ($f_R0\vert=10^-6$,
$M_\nu=0.0$eV), fR6+$0.06$eV ($f_R0\vert=10^-6$, $M_\nu=0.06$eV)
and fR5+$0.15$eV ($f_R0\vert=10^-5$, $M_\nu=0.15$eV), which are
known to yield very similar conventional statistics to one another. For each
model, we select those cluster halos which 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 turn around radius, and evaluate the cumulative probability
distribution of the ratios of the turn-around 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 $Łambda$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.
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