In this paper, we study modified homogeneous and isotropic cosmological models based on the Gauss–Bonnet invariant term as models of an accelerating universe. We discuss and criticize the late-time dynamics of six independent cosmological models: in the first model, we discuss the case of the modified gravity f(R) ∝ R1+δ for δ = −1/2 and 1 augmented by the Gauss–Bonnet invariant term; in the second model, we discuss the general case of f(R) ∝ R1+δ accompanied by a nonminimal coupling between the scalar field and the Ricci curvature as well as the Gauss–Bonnet invariant; in the third model, we discuss a generalized modified gravity model that includes the Einstein–Hilbert action, a dynamical cosmological constant, and an effective gravitational coupling constant; in the fourth model, we discuss a more generalized modified scalar–tensor cosmology that includes in addition to the Gauss–Bonnet invariant term, stringy corrections motivated from string and heterotic superstring arguments; in the fifth model, we discuss the cosmological dynamics of a nonminimal scalar Gauss–Bonnet gravity theory motivated from string theory; and finally in the sixth model, we discuss the possibility of having an extension of the generalized modified gravity theory, free from nonminimal coupling with δ = 0, with a Hubble expansion rate and an equation of state parameter that depend on the Gauss–Bonnet invariant term. In the first five models, we conjecture that the Hubble parameter is related to the scalar field by the relation [Formula: see text], which is applied merely to the late time epoch. This ansatz is in fact motivated by some recent advances in scalar–tensor theory and string theory. All of the six models reveal interesting consequences, which are discussed in some detail. Our main objective in this work is to analyze, criticize, and differentiate between viable realistic models and those that are not. Many critical points are discussed in some detail.
A Thermodynamic Approach to Holographic Dark Energy