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

Abstract

Recently introduced f(G, T) theory is generalized by adding dependence on the arbitrary scalar field ϕ and its kinetic term (∇ 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(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(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(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(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, ϕ, (∇ ϕ) 2) and f= γ(ϕ, X) G+ μT1 / 2 approaches. We show, that for the appropriate choice of parameters and constants, the energy conditions can be satisfied for the discussed scenarios.