Abstract
We investigate a Bianchi-type VI cosmological model that integrates magnetized strange quark matter (MSQM) into the context of \(f(R,L_{m})\) gravity, where \(R\) denotes the Ricci scalar, and \(L_{m}\) signifies the matter Lagrangian. The model examines a nonlinear functional expression of \(f(R,L_{m})=R/2+\lambda R^{2}+\alpha L_{m}\) , resolved by a linearly variable deceleration parameter. We derive cosmological parameters from redshift, including the Hubble parameter, and compare the model predictions with the empirical Hubble dataset values. We also examine the energy conditions within the model in detail, particularly, the effects of dark energy. This paper offers an extensive examination of the physical and geometrical characteristics of the universe while illustrating the significance of strange quark matter, magnetic fields, and dark energy in modified gravity theories. Some of the most important things we found were new information on how the deceleration parameter, anisotropy, and shear scalar behave. This helps us to understand how the universe is expanding in modified theories of gravity.
