LAUSR

We consider a flat Universe filled with a vacuum energy coupled to matter and radiation by respectively positive coupling functions $Q_m$ and $Q_r$. We require that these functions be such as Universe exits from inflation to go to a radiation dominated epoch and allow to reproduce the observed $\Lambda CDM$ expansion after this last epoch. These requirements lead to some necessary constraints on the coupling functions. We then look at one of the simplest forms of $Q_m$ and $Q_r$ able to satisfy them. The cosmological model thus defined describes a Universe with an initial singularity and endless alternated periods of accelerated and decelerated expansion (one of them being our $\Lambda CDM$ Universe) unifying inflation and present time expansion acceleration.