Scale‐Dependent Growth of Large‐Scale Structure From Infrared Modifications of Gravity

ABSTRACT Late–time large–scale structure measurements allow for percent–level, scale–dependent departures from the growth predicted by General Relativity, while remaining tightly constrained by gravitational–wave propagation and weak–lensing observations. Imposing Lorentz invariance, metric coupling, luminal tensor speed, and a GR–like lensing sector, we show that, under these assumptions, viable linear modifications of late–time gravity can be effectively described by a restricted two–parameter infrared deformation of the growth sector. The resulting kernel produces a localized modification of growth in the quasi–linear regime while leaving background expansion, lensing, and tensor propagation unchanged. We derive its general form and discuss how it can arise as an effective low–energy description, in representative ultraviolet realizations involving trace–coupled scalar mediators. Using simplified Fisher forecasts for DESI Year–5, we provide indicative sensitivity estimates for the kernel parameters. Growth data alone can probe the amplitude at the percent level under idealized assumptions, with further improvement when combined with external CMB information, while the characteristic mass scale may be constrained at the tens–of–percent level. These results illustrate how upcoming large–scale structure surveys can test a well–defined class of scale–dependent growth scenarios, and provide a systematic framework and validation roadmap for confronting infrared modifications of gravity with observations.