Testing gravity with the full-shape galaxy power spectrum: first constraints on scale-dependent modified gravity

Since the discovery of the accelerated expansion of the Universe in 1998, modified gravity (MG) theories have attracted considerable attention as alternatives to dark energy (DE). While distinguishing the effects of MG from those of DE using cosmic background expansion alone is difficult, the large-scale structure is expected to differ significantly. Among the plethora of MG models, we are particularly interested in those that introduce a scale dependence in the growth of perturbations; specifically, theories that introduce fifth forces mediated by scalar fields with a finite range accessible to cosmological probes. This is the case with $f(R)$ gravity, which is widely regarded as the most studied model in cosmology. In this work, we utilize, for the first time, the full-shape power spectrum of galaxies to constrain scale-dependent modified gravity theories. By using BOSS DR12 dataset, along with a big bang nucleosynthesis prior on $ \omega_b $ and a Planck 2018 prior on $ n_s $, we obtain an upper bound of $ |f_{R0}| < 5.89 \times 10^{-6} $ at 68% confidence level (c.l.) and $ < 1.53 \times 10^{-5} $ at 95% c.l. for the Hu-Sawicki ($ n=1 $) model. We discuss that it is highly unlikely these constraints will be significantly improved by future galaxy spectroscopic catalogs, such as DESI and Euclid.