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 $\alpha_{\rm B}$, a running of the ``effective'' Planck mass $\alpha_{\rm M}$, 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 $\alpha_{\rm B}$, and that adding large-scale structure information only slightly changes the parameter constraints. However, the large-scale structure data significantly improve the bounds on $\alpha_{\rm M}$ and $w$ by a factor of two. This improvement is driven by background information contained in the BAO, which breaks the degeneracy with $H_0$ 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.