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In this study, we investigate how the baryonic effects vary with scale andlocal density environment mainly by utilizing a novel statistic, theenvironment-dependent wavelet power spectrum (env-WPS). With fourstate-of-the-art cosmological simulation suites, EAGLE, SIMBA, Illustris, andIllustrisTNG, we compare the env-WPS of the total matter density field betweenthe hydrodynamic and dark matter-only (DMO) runs at $z=0$. We find that theclustering is most strongly suppressed in the emptiest environment of$\rho_\mathrm{m}/\bar\rho_\mathrm{m}<0.1$ with maximum amplitudes $\sim67-89$per cent on scales $\sim1.86-10.96\ h\mathrm{Mpc}^{-1}$, and less suppressed inhigher density environments on small scales (except Illustris). In theenvironments of $\rho_\mathrm{m}/\bar\rho_\mathrm{m}\geqslant0.316$($\geqslant10$ in EAGLE), the feedbacks also lead to enhancement features atintermediate and large scales, which is most pronounced in the densestenvironment of $\rho_\mathrm{m}/\bar\rho_\mathrm{m}\geqslant100$ and reaches amaximum $\sim 7-15$ per cent on scales $\sim0.87-2.62\ h\mathrm{Mpc}^{-1}$(except Illustris). The baryon fraction of the local environment decreases withincreasing density, denoting the feedback strength, and potentially explainingsome differences between simulations. We also measure the volume and massfractions of local environments, which are affected by $\gtrsim 1$ per cent dueto baryon physics. In conclusion, our results show that the baryonic processescan strongly modify the overall cosmic structure on the scales of $k>0.1\h\mathrm{Mpc}^{-1}$, which encourages further research in this direction.

How do baryonic effects on the cosmic matter distribution vary with scale and local density environment?