Constraints on dark energy and modified gravity from the BOSS Full-Shape and DESI BAO data

We constrain dark energy and modified gravity within the effective field theory of dark energy framework using the full-shape BOSS galaxy power spectrum, combined with PLANCK cosmic microwave background (CMB) data and recent baryon acoustic oscillations (BAO) measurements from DESI. Specifically, we focus on a varying braiding parameter alpha B, a running of the "effective" Planck mass alpha M, and a constant dark energy equation of state w. The analysis is performed with two of these parameters at a time, including all the other standard cosmological parameters and marginalizing over bias and nuisance parameters. The full-shape galaxy power spectrum is modeled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory. We find that the CMB data is most sensitive to alpha B, and that adding large-scale structure information only slightly changes the parameter constraints. However, the large-scale structure data significantly improve the bounds on alpha M and w by a factor of two. This improvement is driven by background information contained in the BAO, which breaks the degeneracy with H0 in the CMB. We confirm this by comparing the BOSS full-shape information with BOSS BAO, finding no significant differences. This is likely to change with future high-precision full-shape data from EUCLID and DESI however, to which the pipeline developed here is immediately applicable.