Statefinder Parameters for Quintom Dark Energy Model

Abstract

We perform in this paper a statefinder diagnostic to a dark energy model with two scalar fields, called "quintom", where one of the scalar fields has a canonical kinetic energy term and the other has a negative one. Several kinds of potentials are discussed. Our results show that the statefinder diagnostic can differentiate quintom model with other dark energy models. PACS numbers: 98.80.Es,98.80.Cq, 98.80.Jk * Corresponding author It is widely believed nowadays that the present universe is undergoing an accelerating expansion. The converging evidences come from the analysis of data from supernova [1,2], CMB [3,4,5,6,7,8] and WMAP [9,10]. In order to explain the cosmic accelerating expansion, a modified theory of gravity or the existence of dark energy is required. Perhaps the simplest candidate of dark energy is the cosmological constant with equation of state w = p/ρ = −1. However, there exist two problems with it, i.e., why the cosmological constant is so tiny compared to the theoretical expectations and why the remnant cosmological constant is becoming visible precisely at the present time in the cosmic history and why it does not exactly vanish. The inspiration coming from inflation has suggested that dark energy models are likely to be described by the dynamics of a (multi) scalar field(s), such as quintessence []. The quintessence scalar field has a positive kinetic term in its Lagrangian, which violates the strong energy condition but not the dominant energy condition, and the evolution of its equation of state parameter w is in the range of −1 ≤ w ≤ 1. The phantom scalar field on the other hand possesses a negative kinetic term in its Lagrangian, which leads to some strange properties, such as the violation of the dominant energy condition and the occurrence of Big rip [66,67,68,69,70,71,72,73,74,75]( Let us note here that the possible avoidance of the Big Rip by various kinds of physical effects has been discussed by many authors [76,77,78,79,80,81,82,83].). The evolution of the equation of state parameter w for phantom is in the range of w < −1. Other models including the Chaplygin gas [84,85], braneworld models [86,87,88,89,90], holographic models [91] et al are also proposed to account for the present accelerating cosmic expansion.The recent analysis of various cosmological data seems to indicate that it is mildly favored that the evolution of the equation of state parameter of the dark energy changes from w > −1 to w < −1 at small redshift [92,93,94,95]. Although this result may be considered as tentative only since the standard Λ CDM model remains inside ≈ 2σ error bars for all data, it is worthwhile to explore theoretical models which can bring w crossing -1. In this regard, most models mentioned above can not do the job. "Quintom" [96,97,98], which assumes that the dark energy is composed of quintessence and phantom, on the other hand, can implement w crossing -1 and in some cases fits the cosmological data better than models with w ≥ −1. In addition "quintom" model can reconcile the coincidence ...

Quintom cosmology: Theoretical implications and observations

“…In this paragraph we are going to present a way to discriminate between the various quintom scenarios, in a model independent manner, following [145] and based in the seminal works [146,147]. In those works, the authors proposed a cosmological diagnostic pair {r, s} called statefinder, which are defined as 35) to differentiate between different forms of DE.…”

Statefinder diagnosis in a non-flat universe and the holographic model of dark energy

“…As demonstrated in Refs. [36,37,38,39,40,41,42,43,44,45,46,47,48] the statefinder can successfully differentiate between a wide variety of dark energy models including the cosmological constant, quintessence, phantom, quintom, the Chaplygin gas, braneworld models and interacting dark energy models. We can clearly identify the "distance" from a given dark energy model to the flat-ΛCDM scenatio by using the r(s) evolution diagram.…”

The three-loop Yang–Mills condensate dark energy model and its cosmological constraints

“…Moreover, a new geometrical diagnosis pair (r, s), called statefinder, has been introduced to distinguish DE models [29]. Since the pair (r, s) contains the third order derivative of a(t) and their values is expected to be available from the future SNAP observation [30], the statefinder diagnosis has attracted a lot of attention [31,32,33,34,35,36,37,38,39,40,41]. Finally, another dynamical diagnosis w − w ′ , consisting of the EOS and its time derivative, are also extensively used in the literatures [42,43,44,45,46,47,48,49,50,51].…”