fkPT: constraining scale-dependent modified gravity with the full-shape galaxy power spectrum

Modified gravity models with scale -dependent linear growth typically exhibit an enhancement in the power spectrum beyond a certain scale. The conventional methods for extracting cosmological information usually involve inferring modified gravity effects via Redshift Space Distortions (RSD), particularly through the time evolution of f sigma 8. However, classical galaxy RSD clustering analyses encounter difficulties in accurately capturing the spectrum's enhanced power, which is better obtained from the broad -band power spectrum. In this sense, full -shape analyses aim to consider survey data using comprehensive and precise models of the whole power spectrum. Yet, a major challenge in this approach is the slow computation of non-linear loop integrals for scale -dependent modified gravity, precluding the estimation of cosmological parameters using Markov Chain Monte Carlo methods. Based on recent studies, in this work we develop a perturbation theory tailored for Modified Gravity, or analogous scenarios introducing additional scales, such as in the presence of massive neutrinos. Our approach only needs the calculation of the scale -dependent growth rate f (k, t) and the limit of the perturbative kernels at large scales. We called this approximate technique as fk-Perturbation Theory and implemented it into the code fkpt, capable of computing the redshift space galaxy power spectrum in a fraction of a second. We validate our modeling and code with the f (R) theory MG -GLAM and General Relativity NSERIES sets of simulations. The code is available at https://github.com/alejandroaviles/fkpt.