Equation of state for the Universe from similarity symmetries

Abstract

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 = − + w 1 ρ(a) + w 2 a β + 0 and energy density ρ = + ρ 01 a −3(1+w) + ρ 02 a β + ρ 03 a −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 m,0 0.4 and n −1 (β = −3n), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that m,0 = 0.3 then the favoured model is close to concordance CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in the CDM model, while intermediate distant SNIa should be fainter than in the CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over CDM model. As a result we find from the Akaike model selection criterion: it prefers the model with noninteracting scaling fluid.

About Bianchi I with VSL

“…We think that the followed tactic is too restrictive, for this reason we are only able to obtain this class of solutions. Nevertheless there are other Lie approaches as the followed by Szydlowski et al (2006) which we think that may be more useful than the followed one here. Trying to improve the obtained solutions, in Appendix A, we will study through the LM the third order ODE, but as we will show, we arrive to the same solutions and therefore to the same conclusions.…”

A Symmetry of the Einstein–Friedmann Equations for Spatially Flat, Perfect Fluid, Universes

“…leaves the Einstein-Friedmann equations (2.5)-(2.7) unchanged. In particular, the matter source, the barotropic perfect fluid, maintains the equation of state P = wρ with the same equation of state parameter w. This is in contrast with other symmetries of the same equations which change an "ordinary" fluid satisfying the weak energy condition into a phantom fluid with different equation of state parameter and are ultimately inspired by string theory dualities [21,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], and with other solutions of the EinsteinFriedmann equations obtained using methods of supersymmetric quantum mechanics [24,25,26].…”

“…In the recent literature, there have been many studies of the symmetries of the Einstein-Friedmann equations of spatially homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology. These studies are ultimately inspired by (although not always directy related to) string dualities [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] or by methods introduced in supersymmetric quantum mechanics [24,25,26]. Here we discuss a simpler symmetry arising in the context of pure Einstein gravity.…”

Scalar field cosmology — geometry of dynamics

“…The role of symmetries in the context of the generation of new cosmological solution for the inflation was investigated in [25][26][27]. Liddle and Scherrer classified all forms of the potentials of the scalar field V (φ) for which the energy density of the scalar field ρ φ = 1 2φ 2 + V (φ) scales in a similar way to the barotropic matter as a power law of the scale factor.…”