We present the first $\mathrm{\Lambda }\mathrm{CDM}$ cosmological analysis performed on a galaxy survey using marked power spectra. The marked power spectrum is the two-point function of a marked field, where galaxies are weighted by a function that depends on their local density. The presence of the mark leads these statistics to contain higher-order information of the original galaxy field, making them a good candidate to exploit the non-Gaussian information of a galaxy catalog. In this work we make use of SimBIG, a forward modeling framework for galaxy clustering analyses, and perform simulation-based inference using normalizing flows to infer the posterior distribution of the $\mathrm{\Lambda }\mathrm{CDM}$ cosmological parameters. We consider different mark configurations (ways to weight the galaxy field) and deploy them in the SimBIG pipeline to analyze the corresponding marked power spectra measured from a subset of the BOSS galaxy sample. We analyze the redshift-space mark power spectra decomposed in $\ell =0$, 2, 4 multipoles and include scales up to the nonlinear regime. Among the various mark configurations considered, the ones that give the most stringent cosmological constraints produce posterior median and 68% confidence limits on the growth of structure parameters equal to ${\mathrm{\Omega }}_m=0.273_{-0.030}^{+0.040}$ and ${\sigma }_8=0.777_{-0.071}^{+0.077}$. Compared to a perturbation theory analysis using the power spectrum of the same dataset, the SimBIG marked power spectra constraints on ${\sigma }_8$ are up to $1.2\times$ tighter, while no improvement is seen for the other cosmological parameters.

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• Cosmological parameters
• Large scale structure of the Universe