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[en] In this article, we argue that the past of the Universe, extrapolated from standard physics and measured cosmological parameters, might be a non-singular bounce. We also show that, in this framework, quite stringent constraints can be put on the reheating temperature and number of inflationary e-folds, basically fixing T∼T and N∼70. We draw some conclusions about the shape of the inflaton potential and raise the "naturalness" issue in this context. Finally, we argue that this could open a very specific window on the "pre big bounce" universe.