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$ΛCDM$ periodic cosmology

We examine the possibility that Universe expansion be made of some $ΛCDM$ expansions repeating periodically, separated by some inflation and radiation dominated phases. This so-called $ΛCDM$ periodic cosmology is motivated by the possibility that inflation and the present phase of accelerated expansion be due to the same dark energy. Then, in a phase space showing the variation of matter density parameter $Ω_m$ with respect to this of the radiation $Ω_r$, the curve $Ω_m(Ω_r)$ looks like a closed trajectory that Universe could run through forever. In this case, the end of the expansion acceleration of the $ΛCDM$ phase is the beginning of a new inflation phase. We show that such a scenario implies the coupling of matter and/or radiation to dark energy. We consider the simplest of these $ΛCDM$ periodic models i.e. a vacuum energy coupled to radiation. From matter domination phase to today, it behaves like a $ΛCDM$ model, then followed by an inflation phase. But a sudden and fast decay of the dark energy into radiation periodically ends the expansion acceleration. This leads to a radiation dominated Universe preceding a new $ΛCDM$ type expansion. The model is constrained with Markov Ch