The scale at which anti-gravity becomes relevant:

The cosmic antigravity can be stronger than gravity not only globally, but also locally on scales of ~ 1–10 Mpc (Chernin et al. 2000, 2006; Chernin 2001; Byrd et al. 2007, 2012), as studied using the HST observations made by Karachentsev’s team (e.g., Chernin et al. 2010, 2012a).

The local weak-field dynamical effects of dark energy can be adequately described in terms of Newtonian mechanics (e.g., Chernin 2008). Such an approach borrows from general relativity the major result: the effective gravitating density of a uniform medium is given by the sum

ρₑ𝒻𝒻 = ρ + 3P,

where ρ and P are the fluid’s density and pressure (c = 1 hereafter). In this model, the dark energy equation of state is Pᴅᴇ = −ρᴅᴇ, and its effective gravitating density.