The $$f(R,T^\phi )$$ f ( R , T ϕ ) gravity models with conservation of energy–momentum tensor

Abstract

In this paper, we have derived a spatially flat homogeneous and isotropic cosmological model in f (R, T φ ) gravity with a scalar field. In addition to a minimally coupled scalar field with self interacting potential, we also have a contribution from the coupling of the geometry and the field. We have reconstructed a form of f (R, T φ ) by requiring the conservation of energy-momentum tensor of the scalar field. The behavior of the reconstructed f (R, T φ ) gravity is examined for a flat potential as well as a massless scalar field model. The evolution of the universe is studied via the deceleration and equation of state parameters. The promising feature of the model is the transition behavior of the universe from deceleration to the present acceleration.

FLRW Transit Cosmological Model in f (R, T) Gravity

“…In Ref. [90], two of the present authors studied such a case. For a complete discussion on this, we would like to refer to a recent study [91].…”

“…It is well known that the conservation equation does not necessarily hold in f (R, T) gravity -see appendix A. Moreover, a scalar field with flat potential was studied earlier in the f (R, T) = R + 2 f (T) theory of gravity [90], looking for conditions for energy conservation. Surprisingly, it was found that the expression f (R, T) = R + 2 f (T) had the same form as before, viz., f (R, T) = R + 2λT.…”

Linearized Field Equations and Extra Force in $f(R,{\bf T}^{(n)})$ Extended Gravity

“…Eq. (66) shows that the motion is non-geodesic and the extra force F λ is perpendicular to the four-velocity u λ , i.e.…”

“…For f (R, T φ ), see Ref. [66]. Here the authors constrained the field equations by a specific ansatz on the shape of starting function.…”

Polar gravitational waves in f(R, T ϕ ) framework

“…In the present work, we will use the framework of f (R, T f ) gravity where T f stands for trace of energy momentum tensor of scalar field f. The authors in [4] have discussed the cosmic evolution in f (R, T f ) context. The authors in [5] investigated a flat homogeneous and isotropic cosmos in f (R, T f ) background. To reconstruct the models of f (R, T f ), they considered a massless scalar field with its corresponding potential.…”