Duel of cosmological screening lengths

Abstract

Two distinct perturbative approaches have been recently formulated within General Relativity, arguing for the screening of gravity in the ΛCDM Universe. In this paper we compare them and show that the offered screening concepts, each characterized by its own interaction range, can peacefully coexist. Accordingly, we advance a united scheme, determining the gravitational potential at all scales, including regions of nonlinear density contrasts, by means of a simple Helmholtz equation with the effective cosmological screening length. In addition, we claim that cosmic structures may not grow at distances above this Yukawa range and confront its current value with dimensions of the largest known objects in the Universe.As the science rapidly progresses, higher and higher accuracy of observations is achieved. For instance, such a future space mission as Euclid [3,4,5] is designed to probe the Universe expansion with unprecedented precision and impose new restrictions on dark energy, dark matter, and various cosmological parameters. In this connection, the legitimate demand for an advanced theory soars up too. In particular, it is quite natural to expect that Newtonian gravity is modified at large distances and ultimately reconciled with the standard relativistic perturbation theory. By dint of our narration, we aim at sparking interest in two distinct approaches [6,7] relying on General Relativity, which argue that gravity is actually screened, ceasing to be longrange far enough from its every single source. Hereinafter this Yukawa-type screening is sometimes called "cosmological" or "cosmic", since it originates from the presence of the cosmological background.Both cosmic screening approaches have been formulated in the framework of the standard ΛCDM (Λ cold dark matter) model, which is consistent with the observational data [8], though it is noteworthy that currently there is tension between the direct local measurement of the Hubble constant and the value of this very constant following from the Planck data on cosmic microwave background temperature and polarization (see, e.g., [9,10,11]). Furthermore, both original papers [6,7] focus on the matter-and Λ-dominated stages of the Universe evolution, so radiation and relativistic neutrinos are disregarded (though the results of [6] have been subsequently generalized to the case of additional perfect fluids with linear and nonlinear equations of state [12,13,14], as well as to the cases of nonzero spatial curvature [15], f (R) gravity [16] and the phantom braneworld model [17]).From the mathematical point of view, the cosmological Yukawa screening inevitably comes into play when the Einstein equation for the gravitational potential (scalar perturbation) is reduced to the Helmholtz equation, which replaces its popular rival of Poisson type. Meanwhile, the underlying physical reasons and resulting screening ranges are different in [6] and [7]. The scheme of [6] (see additionally [18,19]) is rooted in the so-called discrete cosmology studying how discrete gravitating mass...

Gravitation in the Space with Chimney Topology

“…It is worth noting that the selected values of eff serve well in depicting the observable Universe as they both satisfy eff < 1: for the chimney topology studied here, the lower bound on physical periods of the tori is of the order of 20 Gpc [1]. Additionally, according to [18], the current value of the effective screening length is approximately 2.6 Gpc, so the ratio eff /( ) , in terms of these values, limits the physically interesting range for eff today.…”

“…As we have indicated earlier, Equations (1) and, therefore, (2) do not incorporate the effects of peculiar motion. In [18], however, it has been shown that the role of such contribution is essential in the cosmological setting and that peculiar velocities may be effectively reintroduced by using the effective cosmological screening length λ eff (see formula (41) of [18]) in replacement of the screening length λ in Equations (1) and (2). At this point, this amounts to substituting with eff in the right-hand side of (4) and (5), which yields…”

Gravitational Interaction in the Chimney Lattice Universe

“…As we have noted previously, the peculiar motion of gravitating bodies is disregarded in Equation ( 1) and, consequently, in (4). Nevertheless, the significance of such a contribution has recently been pointed out in [29], where the authors have also shown that peculiar velocities may be effectively restored by employing the effective screening length λ eff (given by the Formula (41) of [29]) instead of the screening length λ in Equations ( 1) and ( 4). Specifically, in the matter-dominated epoch, the two quantities λ eff and λ are related to one another as λ eff = √ 3/5λ.…”

Gravitational potentials and forces in the Lattice Universe: a slab

“…(2.4) with the corresponding solutions (2.16) and (2.23) does not take into account the peculiar velocities of gravitating masses. However, in [23], the authors argued the importance of such account. It was demonstrated that the peculiar velocities can be included back into consideration effectively in eq.…”