Résumé
Phys. Rev. D 103, 063509 (2021) We consider Horndeski modified gravity models obeying stability, velocity of gravitational wavesc_(T)equalscand quasistatic approximation (QSA) on subhorizon scales. We assume further aΛ CDM background expansion and a monotonic evolution on the cosmic background of theαfunctions asαᵢ= αᵢ₀ aˢwherei=M,B ,ais the scale factor andαᵢ₀( α_(M0), α_(B0) ),sare arbitrary parameters. We show that the growth and lensing reduced (dimensionless) gravitational couplingsμ≡ G_(\rm growth)/G ,Σ≡ G_(\rm lensing)/Gexhibit the following generic properties today:Σ₀ < 1for all viable parameters,μ₀<1(weak gravity today) is favored for smallswhileμ₀>1is favored for larges . We establish also the relationμ≥ Σat all times. Taking into account thefσ₈andE_(G)data constrains the parametersto satisfys≲ 2 . Hence these data select essentially the weak gravity regime today ( μ₀<1 ) whens<2 , whileμ₀>1subsists only marginally fors≈ 2 . At least the interval0.5≲ s ≲ 2would be ruled out in the absence of screening. We consider further the growth indexγ(z)and identify the(α_(M0),α_(B0),s)parameter region that corresponds to specific signs of the differencesγ₀-γ₀^(Λ CDM) , andγ₁-γ₁^(Λ CDM) , whereγ₀≡ γ\bigl{|}{_(z=0)}{}andγ₁≡ ((\rm dγ)/(\rm d z))\bigl{|}{_(z=0)}{} . In this way important information is gained on the past evolution ofμ . We obtain in particular the signatureγ₀>γ₀^(Λ CDM)fors<2in the selected weak gravity region.