Towards testing interacting cosmology by distant supernovae

We investigate the possibility of testing cosmological models with interaction between dark matter and the dark energy sector. We assume the standard Friedmann-Robertson-Walker (FRW) model while the so called the energy conservation condition is interpreted locally in terms of energy transfer. We analyze two forms of the dark energy sector: the cosmological constant and the 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 (₈₍ₓ, n) (apart from the parameters of the model) which can be tested using SNIa data. In the estimation of the model parameters both Riess et al. 's and Astier et al. 's samples are used. We also confront the quality of statistical fits for both the model and the interacting models with the help of the Akaike and Bayesian information criteria. Our conclusion from the standard best fit method is that the interacting models explain 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 model is still preferred. We conclude that high precision detection of high redshift supernovae could supply data capable of justifying the adoption of new parameters.