Cosmology with cosmic web environments I. Real-space power spectra

We undertake the first comprehensive and quantitative real-space analysis of the cosmological information content in the environments of the cosmic web (voids, filaments, walls, and nodes) up to non-linear scales, $k = 0.5$ $h$/Mpc. Relying on the large set of $N$-body simulations from the Quijote suite, the environments are defined through the eigenvalues of the tidal tensor and the Fisher formalism is used to assess the constraining power of the power spectra derived in each of the four environments and their combination. Our results show that there is more information available in the environment-dependent power spectra, both individually and when combined all together, than in the matter power spectrum. By breaking some key degeneracies between parameters of the cosmological model such as $M_\nu$--$\sigma_\mathrm{8}$ or $\Omega_\mathrm{m}$--$\sigma_8$, the power spectra computed in identified environments improve the constraints on cosmological parameters by factors $\sim 15$ for the summed neutrino mass $M_\nu$ and $\sim 8$ for the matter density $\Omega_\mathrm{m}$ over those derived from the matter power spectrum. We show that these tighter constraints are obtained for a wide range of the maximum scale, from $k_\mathrm{max} = 0.1$ $h$/Mpc to highly non-linear regimes with $k_\mathrm{max} = 0.5$ $h$/Mpc. We also report an eight times higher value of the signal-to-noise ratio for the combination of spectra compared to the matter one. Importantly, we show that all the presented results are robust to variations of the parameters defining the environments hence suggesting a robustness to the definition we chose to define them.