A New Extended Quintessene Dark Energy Model

The observations of cosmic microwave background), type Ia supernova and large-scalestructure have shown that our universe is undergoing an accelerating expansion. To explainthis observed phenomenon, usually, an exotic energy component with negative pressure, nameddark energy, is assumed to exist in our universe. The simplest candidate of dark energy is thecosmological constant. Although it can explain the observation fairly well, it sufers from boththe fine-tuning problem and the coincidence problem. Moreover, recent observation seems tofavor a dynamical dark energy. Thus, some minimally coupled scalar field dark energy models,such as quintessence, k-essence phantom, and quintom, are proposed to explain the observedaccelerating expansion. Since non-minimal couplings are generated by quantum corrections andthey are essential for the renormalizability of scalar field theory in curved space, it is natural toconsider a coupling between the scalar field and gravity. This coupling has been widely studiedfor dark energy, and it has some novel properties, such as the efective equation of state of thenon-minimal coupling quintessence can cross the phantom divide line.The model with a couplingof the normal scalar field and gravity is known as extended quintessence (EQ).It is well known that the general relativity field equation can be obtained not only in themetric formalism but also in the Palatini formalism. In the former case, only the metric isvariable, while in the latter case, both the metric and the connection are independent variables.When the Einstein Hilbert action is generalized to be an arbitrary function f of R, the Palatiniformalism leads to second order diferential equations instead of the fourth order ones thatone gets with the metric variation. Thus, when a non-minimal coupling is introduced betweenquintessence and the Ricci scalar in the Palatini formalism, some new characters should beobtained. In this paper, we study this case and call this coupled scalar field/new extendedquintessence0. We find that the equation of state of the new extended quintessence can crossthe phantom divide line, and moreover, it oscillates around the1line. We also show that theuniverse driven by the new extended quintessence will enter a dark energy dominated de Sitterphase in the future.