Equation of state for the Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This method is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise to the equation of state in the form p =- Lambda + w sub(1) rho (a) + w sub(2)a super( beta ) + 0 and energy density rho = Lambda + rho sub(01)a super(-3(1+w)) + rho sub(02)a super( alpha ) + rho sub(03)a super(-3), which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data.We showed that the model with scaling fluid fits well to supernovae data. We found that Omega sub(m,0) [sime] 0.4 and n [sime] -1 ( beta = -3n), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that Omega sub(m,0) = 0.3 then the favoured model is close to concordance Lambda CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in the Lambda CDM model, while intermediate distant SNIa should be fainter than in the Lambda CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over Lambda CDM model. As a result we find from the Akaike model selection criterion: it prefers the model with noninteracting scaling fluid.