Coupled vacuum energy model producing endless alternated phases of accelerated and decelerated expansion

We consider a flat Universe filled with a vacuum energy coupled to matter and radiation by respectively positive coupling functions Qₘ and Qᵣ. We require that these functions be such as Universe exits from inflation to go to a radiation dominated epoch and allow us to reproduce the observed ΛCDM 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 Qₘ and Qᵣ 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 ΛCDM Universe) unifying inflation and present time expansion acceleration.