Dynamics in Hybrid Cosmology within $f\left(R,\mathcal{G}\right)$ Assisted by the Scalar Field $？$

In this paper, we investigate a cosmic model in transition explaining the late expansion of the universe in $f\left(R,\mathcal{G}\right)$ gravity where $R$ and $\mathcal{G}$ are the Ricci scalar and the Gauss Bonnet invariant, respectively. The form of the scale factor used for this goal is $a\left(t\right)=t^{\lambda }{\text{e}}^{\sigma t}$ where $\lambda$ and $\sigma$ are free parameters but already constrained in order to meet the present value of Hubble constant. We deal with dynamical evolution of the universe through our model by describing the energy density, cosmic energy pressure and equation of state parameter of the scalar field $？$ considered as the only universe content. As results, our considered theoretical $f\left(R\right)$ model assisted by the scalar field $？$ indicates an phantom-like early evolution followed by accelerated expansion of universe leading to a conclusion that the investigated $f\left(R\right)$ model mimics the ΛCDM model in cosmological hybrid scale. Pacs numbers: 04.50.Kd, 95.36.+x, 98.80.-k.