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. ΛCDM, 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 3 × 2 pt and Planck PR4 CMB lensing data, assuming a ΛCDM linear growth and first order expansion, the reconstructed matter power spectrum P m ( k ) is compatible with that computed from ΛCDM and halo model. In particular, we show that the method reconstructs the non-linear part of P m ( k ) for k ≳ 1 Mpc -1 without the need of assuming a non-linear model.