General aspects of Gauss-Bonnet models without potential in dimension four

Understand

In the present work, the isotropic and homogenous solutions with spatial curvature $k=0$ of four dimensional Gauss-Bonnet models are characterized.

• The main assumption is that the scalar field $\phi$ which is coupled to the Gauss-Bonnet term has no potential [50]-[51].
• Some singular and some eternal solutions are described.
• The evolution of the universe is given in terms of a curve $\gamma=(H(\phi), \phi)$ which is the solution of a polynomial equation $P(H^2, \phi)=0$ with $\phi$ dependent coefficients.