Constraints on compensated isocurvature perturbations from BOSS DR12 galaxy data

We use the BOSS DR12 galaxy power spectrum to constrain compensated isocurvature perturbations (CIP), which are opposite-sign primordial baryon and dark matter perturbations that leave the total matter density unchanged. Long-wavelength CIP $\sigma(\vec{x})$ enter the galaxy density contrast as $\delta_g(\vec{x}) \supset b_\sigma\sigma(\vec{x})$, with $b_\sigma$ the linear CIP galaxy bias parameter. We parameterize the CIP spectra as $P_{\sigma\sigma} = A^2P_{\mathcal{R}\mathcal{R}}$ and $P_{\sigma\mathcal{R}} = \xi\sqrt{P_{\sigma\sigma}P_{\mathcal{R}\mathcal{R}}}$, where $A$ is the CIP amplitude and $\xi$ is the correlation with the curvature perturbations $\mathcal{R}$. We find a significance of detection of $Ab_\sigma \neq 0$ of $1.8\sigma$ for correlated ($\xi = 1$) and $3.7\sigma$ for uncorrelated ($\xi = 0$) CIP. Large-scale data systematics have a bigger impact for uncorrelated CIP, which may explain the large significance of detection. The constraints on $A$ depend on the assumed priors for the $b_\sigma$ parameter, which we estimate using separate universe simulations. Assuming $b_\sigma$ values representative of all halos we find $\sigma_A = 145$ for correlated CIP and $\sigma_{|A|} = 475$ for uncorrelated CIP. Our strongest uncorrelated CIP constraint is for $b_\sigma$ representative of the $33\%$ most concentrated halos, $\sigma_{|A|} = 197$, which is better than the current CMB bounds $|A| \lesssim 360$. We also discuss the impact of the local primordial non-Gaussianity parameter $f_{\rm NL}$ in CIP constraints. Our results demonstrate the power of galaxy data to place tight constraints on CIP, and motivate works to understand better the impact of data systematics, as well as to determine theory priors for $b_\sigma$.