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A locally rotationally symmetric Bianchi-I model filled with strange quark matter (SQM) is explored in f(R, Lm) gravity as a non-linear functional of the form f(R, Lm)=R/2 +Lαm, where α is the free model parameter. We considered the special law of variation of Hubble’s parameter proposed by Berman (1983) and also used the power law relation between the scale factors to obtain the exact solution of the field equation, which matches the model of the universe. We also analyze the physical and geometrical aspects of the universe’s kinematic and dynamic behavior. Additionally, we employ equation-of-state (EoS) parameters and statefinder parameters as analytical tools to gain insights into the evolution of the universe. We use the ΛCDM model as a benchmark to validate the results. By placing the deviations of the universe from ΛCDM model and yet making important contributions to the study of the anisotropic nature of f(R, Lm) gravity within the framework of cosmological dynamics, the paper increases our comprehension of our cosmic evolution.

In this article, we examine the LRS Bianchi type-I cosmological model in the framework of f(R, T) gravity, where R is the Ricci scalar and T is the stress energy momentum tensor in the presence of Domain wall. we used the special law of variation of Hubble’s parameter proposed by Berman (1983) to obtained the exact solution of field equation, corresponds to the model of the universe. The Energy conditions and physical behaviour of the universe has been obtained and their evolution has been discussed using some physical parameter and by means of their graphs. Also, we can use the Statefinder parameter for testing the validity of the model.

In this paper, we aim to describe the cosmic late-time acceleration of the Universe in f(R,Lm) gravity framework proposed by Harko (2010) with the help of an equation of state for strange quark matter. To achieve this, we adopt a specific form of f(R,Lm) gravity as f(R,Lm) =R/2}+ Lnm, where n is arbitrary constants. Here we utilize a hybrid scale factor to resolve the modified field equations in the context of f(R,Lm) gravity for an isotropic and homogeneous Friedmann–Lemaître–Robertson–Walker (FLRW) metric in presence of strange quark matter (SQM). Also, we analyze the dynamics of energy density, pressure and the state finder parameters and explained the distinctions between our model and the current dark energy models in the presence of SQM. We observed a transition from an accelerating to a decelerating phase in the Universe, followed by a return to an accelerating phase at late times. Also, we analyzed the state finder diagnostic as well equation of state parameter and found that the model exhibited quintessence-like behavior. The conclusion drawn from our investigation was that the proposed f(R, Lm) cosmological model aligns well with recent observational studies and effectively describes the cosmic acceleration observed during late times.