A model-independent reconstruction of the matter power spectrum

We propose a new model-independent reconstruction method for the matter power spectrum based on its time dependence and a combination of observations from different redshifts. The method builds on a perturbative expansion in terms of the linear growth function, with each coefficient in the expansion being a free function of scale, to be reconstructed from the data. When using the linear growth function of a specific cosmological model, e.g. $\Lambda$CDM, the reconstruction can serve as a consistency check for non-linear modeling in that given model, as well as a new method for detecting departures from the assumed model in the data. As an application, we show how using DES Y3 3x2pt and Planck PR4 CMB lensing data, assuming a $\Lambda$CDM linear growth and first order expansion, the reconstructed matter power spectrum $P_{\rm m}(k)$ is compatible with that computed from $\Lambda$CDM and halo model. In particular, we show that the method reconstructs the non-linear part of $P_{\rm m}(k)$ for $k\gtrsim 1\ \rm{Mpc}^{-1}$ without the need of assuming a non-linear model.