In this paper, generalized Friedmann–Robertson–Walker universe for Strange Quark Matter (SQM) and Normal Matter (NM) coupled with Domain Wall (DW) in form perfect fluid have been investigated in [Formula: see text] modified theory. [Formula: see text] function has been assumed as [Formula: see text] and Modified Field Equations (MEFEs) have been attained. The MEFEs of the constructed model do not allow solutions of open and closed FRW universe. Obtained modified field equations of higher dimensional flat FRW universe have been solved by using Linearly Varying Deceleration Parameter (LVDP) suggested by Akarsu and Dereli [Int. J. Theor. Phys. 51, 612 (2012)]. Pressure and energy density of the matter distributions for the Linearly Expansion Model (LEM) and Constant Expansion Model (CEM) have been attained as decreasing values by the cosmic time t and constant [Formula: see text] in [Formula: see text] gravity. But for the Exponential Expansion Model (XEM), these quantities have been obtained as time-independent. It is found out that the domain wall behaves like invisible matter when [Formula: see text] due to negative domain wall tension ([Formula: see text]) for SQM with DW of LEM. Strange quark matters for LDW and CDW models behave like cold dark matter when [Formula: see text] and [Formula: see text], respectively. One can say that SQM with DW for LEM and CEM may cause the expansion of the universe in these special situations. Also, solutions of XEM have shown that domain wall matter behaves like stiff matter when [Formula: see text]. All solutions of the constructed model in [Formula: see text] theory have been reduced to General Relativity (GR) theory solutions by assuming [Formula: see text]. Finally, all solutions obtained have been discussed in detail.
