Defying the laws of Gravity I: model-independent reconstruction of the Universe expansion from growth data

Using redshift space distortion data, we perform model-independent reconstructions of the growth history of matter inhomogeneity in the expanding Universe using two methods: crossing statistics and Gaussian processes. We then reconstruct the corresponding history of the Universe background expansion and fit it to type Ia supernovae data, putting constraints on $(\Omega_\mathrm{m,0},\sigma_{8,0})$. The results obtained are consistent with the concordance flat-$\Lambda$CDM model and General Relativity as the gravity theory given the current quality of the inhomogeneity growth data.