A perturbative approach on the stability of the Einstein universe in f(R,φ ,χ ) gravity

The aim of this paper is to investigate the stability and existence of the closed Einstein Universe (EU) under linear homogeneous perturbations within the framework of f(R, φ , χ ) f ( R , ϕ , χ ) gravity. For this, we consider a closed Friedmann–Roberson–Walker universe filled with isotropic matter. Perturbations are imposed on the matter parameters and on the scale factor. We systematically derive the static and perturbed field equations for scenarios with and without conservation of the energy–momentum tensor and examine the associated stability regions through selected models in f(R,φ ,χ ) f ( R , ϕ , χ ) gravity. The graphical analysis shows that for suitable choices of model parameters such as α α , b and scalar field φ ₒ ϕ o , the stable regions of the Einstein universe can be obtained in this theory of gravity. Significant differences in stability regions are observed for scalar fields governed by standard kinetic energy and for those characterized by negative kinetic energy. The scalar field and coupling parameters play a key role in the existence of stable regions of the Einstein universe.