Primordial power spectrum reconstructions from BOSS + eBOSS

We reconstruct the primordial power spectrum $P_{\mathcal{R}}(k)$ from the BOSS DR 12 LRG and eBOSS DR 16 QSO catalogs with a non-parametric Bayesian method. The $P_{\mathcal{R}}(k)$ is reconstructed by linearly interpolating $N$ knots in the $\{ \log k, \log P_{\mathcal{R}}(k) \}$ plane. We use a parametric model to describe the galaxy power spectra of the BOSS+eBOSS catalogs, assuming any power-law deviations and BAO contributions separately from the matter power spectrum template, composed of seven parameters $\Theta_{\text{model}}$. This parametric model enables us to reconstruct $P_{\mathcal{R}}(k)$ at non-linear scales, reaching $k = 0.3 \text{ h} \text{ Mpc}^{-1}$. The method is validated by applying it to different Primordial Features (PF) templates and by recovering the input power law of \textsc{MD-Patchy} and \textsc{EZmock} mock catalogs, representative of the BOSS and eBOSS data. These mocks provide additional information on $\Theta_{\text{model}}$, enabling us to impose Gaussian correlated priors on $\Theta_{\text{model}}$. This prior set allows us to reconstruct $P_{\mathcal{R}}(k)$ more precisely and to alleviate the degeneracies between the model and knot parameters. The results for both individual and combined $z$-bins and galactic caps of the BOSS and eBOSS catalogs are consistent, showing no evidence of the presence of PF in $P_{\mathcal{R}}(k)$ and pointing to a quasi-scale-invariant power law as the preferred model for $P_{\mathcal{R}}(k)$, as predicted by most slow-roll inflationary models. With a different prior set that relaxes the Gaussian constraints on $\Theta_{\text{model}}$ and imposes Planck-based priors on the extreme knots, the results also favor the power law. From the knot reconstructions, we robustly constrain the spectral index $n_s = 0.976 \pm 0.021$, compatible with the Planck value.