Cosmological reconstruction and energy constraints in generalized Gauss–Bonnet-scalar–kinetic–matter couplings

Abstract

Abstract Recently introduced $$f(\mathcal {G},T)$$ f ( G , T ) theory is generalized by adding dependence on the arbitrary scalar field $$\phi $$ ϕ and its kinetic term $$(\nabla \phi )^2$$ ( ∇ ϕ ) 2 , to explore non-minimal interactions between geometry, scalar and matter fields in context of the Gauss–Bonnet theories. The field equations for the resulting $$f\left( \mathcal {G},\phi ,(\nabla \phi )^2,T\right) $$ f G , ϕ , ( ∇ ϕ ) 2 , T theory are obtained and show that particles follow non-geodesic trajectories in a perfect fluid surrounding. The energy conditions in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime are discussed for the generic function $$f\left( \mathcal {G},\phi ,(\nabla \phi )^2,T\right) $$ f G , ϕ , ( ∇ ϕ ) 2 , T . As an application of the introduced extensions, using the reconstruction techniques we obtain functions that satisfy common cosmological models, along with the equations describing energy conditions for the reconstructed $$f\left( \mathcal {G},\phi ,(\nabla \phi )^2,T\right) $$ f G , ϕ , ( ∇ ϕ ) 2 , T gravity. The detailed discussion of the energy conditions for the de Sitter and power-law spacetimes is provided in terms of the fixed kinetic term i.e. in the $$f\left( \mathcal {G},\phi ,T\right) $$ f G , ϕ , T case. Moreover, in order to check viability of the reconstructed models, we discuss the energy conditions in the specific cases, namely the $$f(R,\phi ,(\nabla \phi )^2)$$ f ( R , ϕ , ( ∇ ϕ ) 2 ) and $$f=\gamma (\phi ,X)\mathcal {G}+\mu T^{1/2}$$ f = γ ( ϕ , X ) G + μ T 1 / 2 approaches. We show, that for the appropriate choice of parameters and constants, the energy conditions can be satisfied for the discussed scenarios.