Gen Relativ Gravit (2017) 49:120
Ricci curvature non-minimal derivative coupling
cosmology with ﬁeld re-scaling
· Yuttana Jawralee
Received: 19 April 2017 / Accepted: 12 August 2017
© Springer Science+Business Media, LLC 2017
Abstract In this letter, cosmology of a simple NMDC gravity with ξ Rφ
and a free kinetic term is considered in ﬂat geometry and in presence of dust matter. A
logarithm ﬁeld transformation φ
= μ ln φ is proposed phenomenologically. Assum-
ing slow-roll approximation, equation of motion, scalar ﬁeld solution and potential are
derived as function of kinematic variables. The ﬁeld solution and potential are found
straightforwardly for power-law, de-Sitter and super-acceleration expansions. Slow-
roll parameters and slow-roll condition are found to depend on more than one variable.
At large ﬁeld the re-scaling effect can enhance the acceleration. For slow-rolling ﬁeld,
the negative coupling ξ could enhance the effect of acceleration.
Keywords Non-minimal derivative coupling · Field re-scaling · Dark energy
Various observations such as supernova type Ia (SNIa) [1–10], large-scale structure
surveys [11,12], cosmic microwave background (CMB) anisotropies [13–16] and X-
ray luminosity from galaxy clusters [15,17,18] agree on recent cosmic acceleration.
Yet to be known form of dark energy is believed to drive the acceleration [19–22]. As
The Institute for Fundamental Study “The Tah Poe Academia Institute”, Naresuan University,
Phitsanulok 65000, Thailand