Matter power spectrum reconstruction with KiDS-Legacy: Improved internal $Λ$CDM consistency and preference for strong baryonic feedback

TL;DR

Directly reconstructs the matter power spectrum $P_{ m m}(k,z)$ from KiDS-Legacy cosmic shear using two approaches: SPBK25 regularised deprojection and BK24 double-power-law. The large-scale behavior ($k \lesssim 0.1\,h\mathrm{Mpc}^{-1}$) is consistent with the ΛCDM expectation for a DMO baseline with $\sigma_8=0.81$, while nonlinear scales ($k=3$–$20\,h\mathrm{Mpc}^{-1}$) show a suppression relative to DMO with $\bar{f}_\delta=0.70\pm0.10\,({\rm stat})\pm0.04\,({\rm sys})$, a $3\sigma$ signal consistent with strong baryonic feedback. The suppression aligns with FLAMINGO predictions and indicates a preference for stronger feedback variants; improvements over KiDS-1000 (area, redshift calibration, IA modelling) yield improved internal ΛCDM consistency. The work demonstrates the feasibility of deprojection-based $P_{ m m}(k,z)$ measurements from cosmic shear as a probe of baryonic physics and structure growth, complementing Planck-era constraints and guiding future lensing analyses.

Abstract

Direct measurements of the matter power spectrum, $P_\mathrm{m}(k,z)$, provide a powerful tool to investigate observed tensions between models of structure growth while also testing the internal consistency of cosmological probes. We analyse cosmic shear data from the final data release of the Kilo-Degree Survey (KiDS), presenting a deprojected $P_\mathrm{m}(k,z)$, measured in up to three redshift bins. Compared to analyses using previous KiDS releases, we find improved internal consistency in the $z\lesssim0.7$ regime. At large scales, $k\lesssim0.1\,h\,\rm Mpc^{-1}$, our power spectrum reconstruction aligns with $Λ$CDM predictions with a density fluctuation amplitude $σ_8=0.81$. Furthermore, at small scales, $k=3$-$20\,h\,\rm Mpc^{-1}$, the average matter power spectrum is suppressed by $30\%\pm10\%\,{\rm (stat.)}\pm4\%\,{\rm (sys.)}$ with $2.8σ$ significance relative to a dark-matter-only model, consistent with expectations of strong baryonic feedback.

Figures (5)

• Figure 1: Power spectrum constraints in three variants. The solid coloured lines are regularised deprojections with $68\%$ CIs for three redshift bins $Z_1=[0,0.3]$, $Z_2=[0.3,0.6]$, and $Z_3=[0.6,2]$, and the dashed lines are best-fits of a double power-law, Eq. (\ref{['eq:dpl_constraints']}), all interpolated to the centres of $Z_1$--$Z_3$. The best-fitting $\Lambda$CDM constraints by Wright20251_cosmoresults are shown as black curves. For clarity, the curves corresponding to different redshift bins are scaled by factors of 0.1, 1, or 10. Lensing constraints for $Z_3$ are mostly from structure near $z\sim0.7$ (see text).
• Figure 2: Average ratio of the matter power spectrum to the DMO reference within the three redshift bins $Z_1$--$Z_3$, derived using the method of regularised deprojection. The shaded regions represent the $68\%$ CIs of the posterior constraints for $Z_1$ (purple), $Z_2$ (blue), and $Z_3$ (green). At large scales, $k\lesssim0.1\,h\,\rm Mpc^{-1}$, all three redshift bins align with the expected DMO redshift evolution.
• Figure 3: Violin plot of the matter power spectrum relative to the DMO spectrum in 20 bands, similar to Fig. \ref{['fig:internal_consistency']}, but for a single broad redshift bin, $Z$, which combines the smaller bins $Z_1$--$Z_3$. The width of the shaded regions represents the posterior probability density, with the 68th and 95th percentile CIs about the median also shown inside the regions as open boxes and sticks, respectively. The green, light blue, and dark blue bands illustrate the suppression predicted by the FLAMINGO cosmological hydrodynamical simulation between $z=0$ and 1.5 for the fiducial, weak, and strong feedback models, respectively. The yellow band indicates the mean suppression at small angular scales ($68\%$ CI), including correlations between the different points (Fig. \ref{['fig:corr_mat']}), preferring the strong feedback model.
• Figure 4: Matrix of Pearson correlation coefficients for the deprojection with a single $z$-bin, $Z$, for in 20 logarithmic $k$-bins between $k=0.01-20~h~\rm Mpc^{-1}$. The scale $k$ increases from the bottom left to the top right.
• Figure 5: Posterior predictive distribution ($68\%$ and $95\%$ CIs as blue regions) of the deprojected $P_{\rm m}(k,z)$ in Fig. \ref{['fig:matter_power_spectra']} relative to the black data points -- $\theta\,\xi_-^{(ij)}(\theta)$ in lower left panels and $\theta\,\xi_+^{(ij)}(\theta)$ in the upper right panels -- for a combination $(ij)$ of tomographic source bins, denoted as "$z-ij$" inside the panels. The red lines represent the reference model, $P^{\rm DMO}_{\rm m}(k,z)$, employed in the regularised deprojection.