Energy conditions for the four dimensional cosmological model with nonminimal derivative coupling of scalar field

The energy conditions is a set of linear equations of energy density ρ and pressure p which ensure the the field(s) that we used in our model is physically “reasonable”. We study the energy conditions for four dimensional nonminimal derivative coupling of scalar field and curvature tensor. Considering the scalar field as a perfect fluid, we find some constraint for the coupling constant ξ in order the energy conditions is satisfied or violated. We find that strong energy conditions (SEC) is violated if −1/9H² ≤ ξ < 1/18H². For de Sitter solution a ∝ e^H₀t for some constant H₀, we find that while null, weak, and dominant energy conditions violated when $ξ<−[ 12H02(2+9H02) ]−1$⁠. The accelerating universe is exist for the power law solution (a ∝ t^p for constant p) if ξ < 0.