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In this paper, we adopt minimal gravitational decoupling scheme to extend anon-static spherically symmetric isotropic composition to anisotropic interiorin$f(\mathcal{R},\mathcal{T},\mathcal{R}_{\mathrm{a}\mathrm{b}}\mathcal{T}^{\mathrm{a}\mathrm{b}})$theory. A geometric deformation is applied only on $g_{rr}$ metric componentthrough which the modified field equations are separated into two sets, each ofthem correspond to their parent (seed and newly added) source. An isotropicmodel suggested by the Friedmann-Lemaitre-Robertson-Walker metric is adopted toreduce the unknowns in the first set. We then obtain an isotropic solution bymaking use of a linear equation of state and a particular form of the scalefactor. A density-like constraint is chosen to solve the other sectorcontaining the deformation function and multiple components of an additionalmatter source. Further, the graphical interpretation of the developed model iscarried out to analyze how a decoupling parameter and modified gravityinfluence the evolutionary phases of the universe. It is concluded that onlythe radiation-dominated era meets stability criteria everywhere in thismatter-geometry coupled theory.

general relativity and gravitation

Cosmological Solutions through Gravitational Decoupling in  $f(\mathcal{R},\mathcal{T},\mathcal{R}_{\mathrm{a}\mathrm{b}}\mathcal{T}^{\mathrm{a}\mathrm{b}})$  Gravity