Scalar Field Dark Energy With Derivative Coupling To Gravity

Various cosmological observations have revealed that our universe is undergoing anaccelerating expansion.Usually,an exotic energy component with negative pressure, nameddark energy, is attributed to the inducement of the observed acceleration. There are manydark energy models. Among them, generic dark energy models based on a scalar feld have been proposed. Quintessence,phantom and quintom are important ones.The quintessence dark energy model with a derivative coupling to gravity within thePalatini formalism is studied in this paper. Two diferent non-minimal derivative couplingforms: ωR μ μμ and ξR μν ν are analyzed, respectively. We fnd that when ω equalsto some special values,the model with the frst coupling can behave like quintessence andphantom, respectively. In addition, It can realize the phantom divide line crossing fromphantom to quintessence at late time for its efective equation-of-state,and in the futureit will return to the phantom-like state by crossing the-1line again but in the oppositedirection. As for the model with the ξR μν μ ν coupling, when ξ equals to some specialvalues, it can realize the phantom divide line crossing for its EoS twice. One occurs athigh redshift from larger than-1to less than-1,the other in the low redshift or in thefuture, which is from less than-1to larger than-1. Furthermore, this model can alsobehave like quintessence.