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We use the BOSS DR12 galaxy power spectrum to constrain compensatedisocurvature perturbations (CIP), which are opposite-sign primordial baryon anddark 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 linearCIP 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 CIPamplitude 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 uncorrelatedCIP, which may explain the large significance of detection. The constraints on$A$ depend on the assumed priors for the $b_\sigma$ parameter, which weestimate using separate universe simulations. Assuming $b_\sigma$ valuesrepresentative of all halos we find $\sigma_A = 145$ for correlated CIP and$\sigma_{|A|} = 475$ for uncorrelated CIP. Our strongest uncorrelated CIPconstraint is for $b_\sigma$ representative of the $33\%$ most concentratedhalos, $\sigma_{|A|} = 197$, which is better than the current CMB bounds $|A|\lesssim 360$. We also discuss the impact of the local primordialnon-Gaussianity parameter $f_{\rm NL}$ in CIP constraints. Our resultsdemonstrate the power of galaxy data to place tight constraints on CIP, andmotivate works to understand better the impact of data systematics, as well asto determine theory priors for $b_\sigma$.

Constraints on compensated isocurvature perturbations from BOSS DR12 galaxy data