Relation between the turnaround radius and virial mass in f(R) model

Abstract

We investigate the relationship between the turnaround radius R t and the virial mass M v of cosmic structures in the context of ΛCDM model and in an f (R) model of modified gravity -namely, the Hu-Sawicki model. The turnaround radius is the distance from the center of the cosmic structure to the shell that is detaching from the Hubble flow at a given time, while the virial mass is defined, for this work, as the mass enclosed within the volume where the density is 200 times the background density. We employ a new approach by considering that, on average, gravitationally bound astrophysical systems (e.g., galaxies, groups and clusters of galaxies) follow, in their innermost region, a Navarro-Frenk-White density profile, while beyond the virial radius (R v ) the profile is well approximated by the 2-halo term of the matter correlation function. By combining these two properties together with the information drawn from solving the spherical collapse for the structures, we are able to connect two observables that can be readily measured in cosmic structures: the turnaround radius and the virial mass. In particular, we show that, in ΛCDM, the turnaround mass at z = 0 is related to the virial mass of that same structure by M t 3.07 M v , while in terms of the radii we have that R t 3.7 R v (for virial masses of 10 13 h −1 M ). In the f (R) model, on the other hand, we have M t 3.43 M v and R t 4.1 R v , for |f R0 | = 10 −6 and the same mass scale. Therefore, the difference between ΛCDM and f (R) in terms of these observable relations is of order ∼ 10−20% even for a relatively mild strength of the modification of gravity (|f R0 | = 10 −6 ). For the turnaround radius itself we find a difference of ∼ 9% between the weakly modification in gravity considered in this work (|f R0 | = 10 −6 ) and ΛCDM for a mass of 10 13 h −1 M . Once observations allow precisions of this order or better in measurements of the turnaround R t , as well as the virial mass M v (and/or the virial radius R v ), these quantities will become powerful tests of modified gravity.

Improved Lemaitre–Tolman model and the mass and turn-around radius in group of galaxies

“…Recently, the turn-around radius, R 0 has been proposed as a promising way to test cosmological models [88], DE, and disentangle between ΛCDM model, DE, and MG models [88][89][90][91][92][93].…”

“…[89] calculated R 0 for ΛCDM, and [90] did the same for smooth DE. According to [93] R 0 is affected by modified gravity (MG) theories. In MG theories [94] found a general relation for R 0 , and [91] found a method to get the same quantities in generic gravitational theories.…”

Turnaround size of non-spherical structures

“…(26), the correction −φ N R (HR) 2 is neglected for structures of size R much smaller than the Hubble radius (this term is of second order in R/H −1 ). The current literature on the turnaround radius is restricted to this spherical situation [12][13][14][15][24][25][26][27][28][29][30][31]. In this context, the turnaround radius is obtained when the "local" and the "cosmological" contributions to the right hand side of Eq.…”

“…The turnaround radius has been discussed also in alternative theories of gravity (see e.g. [24][25][26][27][28][29][30][31]), but in this work we focus solely on the standard GR picture. Thus far, the literature on the turnaround radius has studied only spherical structures.…”

Turnaround radius in ΛCDM and dark matter cosmologies with shear and vorticity

“…Recently, the turnaround radius (TAR) 5 has been proposed as a promising way to test cosmological models [67], DE, and disentangle between ΛCDM model, DE, and MG models [66,67,[70][71][72][73]. The attention on TAR increased when was shown that MG can affect the maximum TAR (see [73]). According to some authors (e.g., [70]), the TAR is a well-defined, and unambiguous boundary of a structure, in the spherical collapse model (SCM), simulations, analytic calculations, and is clean from baryons physics.…”