Probing modified gravity with compensated spherical regions: Broken Birkhoff locality and a scale-dependent growth rate
Year: 2026
Type: article
Abstract: In general relativity, Birkhoff's theorem makes the dynamics of a spherical region depend only on the mass it encloses. However, a scalar-mediated force of finite range breaks this locality and couples shells across the whole profile. Compensated spherical regions (CoSpheres), built around local extrema of the density field, describe cosmic voids and the large-scale environments of galaxy clusters on the same footing and single out the compensation radius R_1 at which the enclosed mass contrast vanishes. We investigated how this loss of locality modifies the collapse of compensated regions and what survives of the observables built on R_1 once gravity departs from general relativity. We formulated the Lagrangian shell dynamics in the quasi-static Horndeski scalar sector and applied it to Hu--Sawicki f(R) gravity. The non-local response is a radial convolution of the mass-contrast profile with a kernel set by the scalar Compton wavelength. For realistic compensated profiles, it compresses into a Yukawa-like coupling governed by a single parameter, α łesssim10^ insensitive to profile shape, to profile size, and to whether the central extremum is a void or a cluster environment; a compensated region of any size responds as a point source of range ̌armg/α would. The compensation shell itself stays at a fixed co-moving radius whatever the effective coupling so that the observables built on it remain well defined beyond general relativity. Profiles at z=0 become nearly indistinguishable from those of the Λ cold dark matter model for abs f_R^0 -5 , a limit set by the Compton wavelength rather than by measurement precision, which δ_1 and f_1(a,R_1) approach from directly measurable quantities. Combining several compensation radii breaks the degeneracy between Ω_m,0 and f_R^0; the illustrative Euclid-like benchmark adopted here gives a 3σ reach around logten f_R^0 ≃-4.1. The distinctive information carried by CoSpheres lies in the joint scale and environmental dependence of the response, as measurements at several compensation radii provide an internal consistency test of gravity rather than one more constraint on a combination of parameters. Cosmic voids are the most robust target because screening is weakest in underdense regions. Non-linear chameleon screening inside dense halo cores is not modelled by the effective kernel used here.
Source: Astronomy and Astrophysics
Authors: P. de Fromont, J.-M. Alimi
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,865
OpenAlex ID: W7223131308