{ "id": "1805.08230", "version": "v1", "published": "2018-05-21T18:02:52.000Z", "updated": "2018-05-21T18:02:52.000Z", "title": "On the consistency of the expansion with the perturbations", "authors": [ "Radouane Gannouji", "David Polarski" ], "comment": "8 pages, 10 figures", "categories": [ "astro-ph.CO", "gr-qc" ], "abstract": "Assuming a simple form for the growth index gamma(z) depending on two parameters gamma_0 = gamma(z=0) and gamma_1 = gamma'(z=0), we show that these parameters can be constrained using background expansion data. We explore systematically the preferred region in this parameter space. Inside General Relativity we obtain that models with a quasi-static growth index and gamma_1 = -0.02 are favoured. We find further the lower bounds gamma_0 > 0.53 and gamma_1 > -0.15 for models inside GR. Models outside GR having the same background expansion as LCDM and arbitrary gamma(z) with gamma_0 = gamma_0^{LCDM}, satisfy G_{eff,0}>G for gamma_1 > gamma_1^{LCDM}, and G_{eff,0}