Accelerated Brans-Dicke universe in higher-derivative induced gravity-like conformally coupling and dominated by Gauss-Bonnet dark energy

Abstract

We investigate the late-time dynamics of a fourdimensional universe based on the effective action of a Brans-Dicke scalar field in the presence of the matter source term, conformal coupling of the scalar curvature to the scalar field, a dynamical cosmological constant and Gauss-Bonnet higher-order terms in the scalar curvature. Many new interesting features are revealed and discussed in some details.Keywords Brans-Dicke cosmology · Conformal coupling · Gauss-Bonnet invariant term · Dark energy · Accelerated expansionOver the past few years, there have been considerable efforts in understanding the physics behind the accelerated expansion of the universe. In fact, several cosmological observations coming from the CMBR dataset of the Three-Year WMAP and data from Supernova Legacy Survey of type SNeIa and large galaxy clustering indicate that our universe is undergoing an amazing stage of accelerated expansion (fact shows that the accelerated expansion is due to some mysterious form of energy usually dubbed dark energy (DE) with equation of state parameterSo far, several phenomenological cosmological models have been introduced in literature to explain the nature of DE. Two natural suspects are a tiny cosmological constant A.R. El-Nabulsi ( ) characterized by w = −1 or a time-dependent quintessence field which dominates the dynamics of the universe with w > −1 at a low-redshift. However, these possibilities in principle are ruled out as a consequence of the enormous inconsistency between the theoretical and experimental values of the cosmological constant. Furthermore, both models require fine tunings of the parameters to fit correctly with observational data. Phantom energy models with concurrently w < −1 and a positive energy density have been also proposed in literature. In fact, analysis of recent observational data also support w < −1 strongly, violating strong or weak energy condition. Some other alternative dark energy models are discussed largely in literature range from scalar tensor theories (Bento et al. 2002 and references therein) to quintessence models (Peebles and Ratra 2003). One remarkable ingredient of these theories is that the nature of the DE could in fact be related with the cosmological constant problem. However, most of them are based on a particular choice of the scalar field potential and furthermore, fine tuning is also required.Truly speaking, a successful dark energy theory may be derived from either a modified gravity approach (MGA) or from string and M-theory (superstring). In reality, MGA (usually refereed as f (R), R being the scalar curvature) is extremely attractive in the applications for late accelerating universe and dark energy as it presents very natural unification of the early-time inflation and late-time acceleration. The success of such unification is due to different role of gravitational terms relevant at small and at large curvature. Moreover, various models of modified gravity are predicted by string/M-theory considerations. It may as well provide as the source for uni...