Equation of state description of the dark energy transition between quintessence and phantom regimes

The dark energy crossing of the cosmological constant boundary (the transition between the quintessence and phantom regimes) is described in terms of the implicitly defined dark energy equation of state. The generalizations of the models explicitly constructed to exhibit the crossing provide the insight into the cancellation mechanism which makes the transition possible. The determination of the physical mechanism behind the observationally established latetime accelerated expansion of the universe [1] is presently a major challenge in theoretical cosmology. Among many different approaches to the solution of this problem, the concept of dark energy plays a central role, either as a fundamental component of the universe or as an effective description of other physical mechanisms. The essential characteristics of the dark energy model are contained in the parameter of its equation of state (EOS), p = wρ, where p and ρ denote the pressure and energy density of dark energy, respectively. Many recent analyses of the cosmological observational data [2] obtain the transition of the dark energy from the quintessence regime (w > −1) to the phantom regime (w < −1) as a best fit description. Apart from being favoured observationally (although presently other possibilities such as the ΛCDM cosmology are consistent with the data), the cosmological constant boundary crossing is of substantial theoretical interest [3] since it unifies important aspects of many previously extensively studied dark energy models. Unlike the standard definition of the dark energy EOS in which the dark energy pressure is given as an analytical function of the energy density, p = p(ρ), we define the dark energy EOS in a more general way [4]. The dark energy EOS is defined parametrically, i.e. as a pair of quantities depending on the cosmic time (p(t), ρ(t)) or the scale factor in the expanding universe (p(a), ρ(a)). This definition is sufficiently general to comprise large classes of dark energy models. We start with an explicit construction of the dark energy model which possesses the property of the CC boundary crossing. Its energy density has the following scaling ρ = C1 ( a a0 ) −3(1+γ) + C2 ( a a0 ) −3(1+η) , (1) 1 On leave of absence from the Theoretical Physics Division, Rudjer Bošković Institute, Zagreb, Croatia where γ > −1 and η < −1. The parameter of its equation of state w = γ + η γ−w0 w0−η (