Cosmological model with energy transfer

The observations of SNIa suggest that we live in the acceleration epoch when the densities of the cosmological constant term and matter are almost equal. This leads to the cosmic coincidence conundrum. As the explanation for this problem we propose the FRW model with dark matter and dark energy which interact each other exchanging energy. We show that the cubic correction to the Hubble law, measured by distant supernovae type Ia, probes this interaction. We demonstrate that influences between nonrelativistic matter and vacuum sectors are controlled by third and higher derivatives of the scale factor. As an example we consider flat decaying $\Lambda(t)$ FRW cosmologies. We point out the possibility of measure of the energy transfer by the cubic and higher corrections to Hubble's law. The statistical analysis of SNIa data is used as an evidence of energy transfer. We find that there were the transfer from the dark energy sector to the dark matter one without any assumption about physics governing this process. We confront this hypothesis about the transfer with SNIa observations and find that the transfer the phantom and matter sector is admissible for $\Omega_{\text{m},0}=0.27$. We also demonstrate that it is possible to differentiate between the energy transfer model and the variable coefficient equation of state model.