Prospects of the cosmic scenery in a quintom dark energy model with generalized nonminimal Gauss-Bonnet couplings

In this work we propose a novel dark energy model in the formalism of quintom scenarios in scalar-tensor theories based on general relativity, taking into account generalized couplings between the scalar fields and Gauss-Bonnet terms. By employing linear stability theory, we reveal the structure of the phase space and analyze the dynamical effects of the Gauss-Bonnet couplings. We show that the present model exhibits various classes of critical points, corresponding to distinct cosmological scenarios that affect the dynamical evolution of the Universe. At the critical points, the cosmological scenarios correspond to either an accelerated expansion or a stiff-fluid case in which the expansion is decelerated, while for some solutions the expansion is neither accelerated nor decelerated. Finally, the present model also exhibits scaling behavior at some of the critical points, in which the dark energy mimics the behavior of matter.

Figure 1

We have represented here one of the multitude of cases where the critical line ${\mathcal{Z}}_2$ exhibits saddle behavior.

Figure 2

Various existence conditions for the ${\mathcal{Z}}_5$ critical point.

Figure 3

Different explicit existence conditions for the ${\mathcal{Z}}_6$ solution.

Figure 4

Nonexclusive conditions where the ${\mathcal{Z}}_6$ critical point is a saddle point (see the discussion).

Figure 5

Various existence conditions associated with the ${\mathcal{Z}}_7$ critical point.

Figure 6

Nonexclusive conditions associated with the critical point ${\mathcal{Z}}_7$ where the stable scaling behavior is present: $w_m=0,{\lambda }_2=2,{\lambda }_1=1$.

Figure 7

Numerical evolution of the dynamical system of differential equations toward the ${\mathcal{Z}}_7$ critical point ($w_m=0,{\lambda }_1=1,{\lambda }_2=2,\alpha =0,\beta =1.95$).

Figure 8

Nonexclusive regions that correspond to a stable scaling solution at the ${\mathcal{Z}}_8$ critical point ($w_m=0,{\lambda }_2={\lambda }_1$).

Figure 9

Crossing of the phantom divide line for the effective equation of state in the evolution of the dynamical system of equations toward the ${\mathcal{Z}}_9$ critical point ($w_m=0,{\lambda }_1=0.1,{\lambda }_2=3,\alpha =-1,\beta =-3$).

Figure 10

A possible stable region for the ${\mathcal{Z}}_9$ solution ($w_m=0,{\lambda }_1=0.1,{\lambda }_2=3$).