Cosmology with the EFTofLSS and BOSS: dark energy constraints and a note on priors

We analyse the BOSS DR12 galaxy power spectrum data jointly with BAO data for three models of dark energy. We use recent measurements using a windowless estimator, and an independent and fast pipeline based on EFTofLSS implemented via the FAST-PT algorithm to compute the redshift-space loop corrections. We accelerate our analysis by using the BACCO linear emulator instead of a Boltzmann solver. We perform two sets of analyses: one with $3\sigma$ Planck priors on $A_s$ and $n_s$, and another that is CMB-free, without such priors. Firstly, we study $\Lambda$CDM, reproducing previous results obtained with the same estimator. We find a low value of $A_s$ in the CMB-free case, in agreement with many previous full-shape analyses of the BOSS data. We then study $w$CDM, finding a lower value of the amplitude in the CMB-free run, coupled with a preference for phantom dark energy with $w=-1.17^{+0.12}_{-0.11}$, again in broad agreement with previous results. Finally, we investigate the dark scattering model, which we label $wA$CDM. In the CMB-free analysis, we find a large degeneracy between the interaction strength $A$ and the amplitude $A_s$, hampering measurements of those parameters. On the contrary, in our run with a CMB prior, we are able to constrain the dark energy parameters to be $w=-0.972^{+0.036}_{-0.029}$ and $A = 3.9^{+3.2}_{-3.7}$, which show a 1$\sigma$ hint of interacting dark energy. This is the first measurement of this parameter and demonstrates the ability of this model to alleviate the $\sigma_8$ tension. Our analysis can be used as a guide for any model with scale-independent growth. Finally, we study the dependence of the results on the priors of the nuisance parameters and find these priors to be informative, with their broadening creating shifts in the contours. We argue for an in depth study of this issue, which can affect current and forthcoming analyses of LSS data.