In this letter , 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 _ { RH } \sim T _ { GUT } and N \sim 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 .