Towards testing interacting cosmology by distant type Ia supernovae

We investigate the possibility of testing cosmological models with interaction between matter and energy sector. We assume the standard FRW model while the so called energy conservation condition is interpreted locally in terms of energy transfer. We analyze two forms of dark energy sectors: the cosmological constant and phantom field. We find a simple exact solution of the models in which energy transfer is described by a Cardassian like term in the relation of $H^{2}(z)$, where $H$ is Hubble's function and $z$ is redshift. The considered models have two additional parameters $(\Omega_{\text{int}},n)$ (apart the parameters of the $\Lambda$CDM model) which can be tested using SNIa data. In the estimation of the model parameters Riess et al.'s sample is used. We also confront the quality of statistical fits for both the $\Lambda$CDM model and the interacting models with the help of the Akaike and Bayesian informative criteria. Our conclusion from standard best fit method is that the interacting models explains the acceleration of the Universe better but they give rise to a universe with high matter density. However, using the tools of information criteria we find that the two new parameters play an insufficient role in improving the fit to SNIa data and the standard $\Lambda$CDM model is still preferred. We conclude that high precision detection of high redshift supernovae could supply data capable of justifying adoption of new parameters.