What is our Universe now ? For the century of the formula 15 written by de Sitter

Starting with the Friedmann-Lemaître (FL) metric g F L of an isotropic universe, we give the radially inertial form of this metric which is a generalized Gullstrand-Painlevé form of metric g GP. Then, for g GP , the equivariant stress-energy tensor is convenient because it has a straightforward interpretation in terms of velocity and potential. The energy and the entropy are well-dened. For each model of the Universe , the osculating manifold is a de Sitter model. Moreover, if the Universe is the open cone of the future of a point (a big bang event), then this de Sitter model is an open, accelerated one. So, we could easily confront this model with local observations through the osculating de Sitter model, taking into account the observed SNIa and the Hubble parameter H(z) for redshifts z ≤ 2. The recent data about H(z) provide a tool to estimate cosmological parameters for the de Sitter models and their Milne limits ; we nd : H 0 = 65 ± 2 km/s/M pc, Ω 0 = 0.05 ± 0.02, and an age = 15.2 ± 0.3 Gyr. In other words, our Universe contains only baryonic matter