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In this research paper, we investigate a Finsler-Randers spacetime in the context of a Bianchi type-V model of universe within the framework of Lyra geometry, employing a modified f( R , T ) gravity theory that incorporates a cosmological constant Λ . We have derived the corresponding anisotropic Friedmann equations for the Finsler–Randers Bianchi type-V model of universe with modified f( R , T ) gravity in Lyra geometry, including the contributions of the cosmological constant and Randers anisotropic terms b0(t) and obtained analytical solutions. Further, we have examined the behavior of various dynamical parameters, commonly used in cosmological analysis, both geometrical and graphical interpretations have been provided. Furthermore, we have derived the Raychaudhuri equation in terms of the cosmological constant as a function of the cosmic time t. Our analysis reveals that the shear scalar σ2 and the scalar expansion θ decrease with cosmic time and tend to zero at late times, indicating the isotropization of the universe in the presence of the cosmological constant; however, the Hubble parameter approaches a constant value rather than vanishing, while the energy density ρ , pressure P , and the Lyra gauge function β remain finite and non-zero even at large cosmic times. Ultimately, we conclude that the universe described by this framework exhibits continuous acceleration, as indicated by the negative value of the deceleration parameter q.

In this research paper, we investigate a Finsler-Randers spacetime in the context of a Bianchi type-V model of universe within the framework of Lyra geometry, employing a modified f(R,T) gravity theory that incorporates a cosmological constant Λ. We have derived the corresponding anisotropic Friedmann equations for the Finsler–Randers Bianchi type-V model of universe with modified f(R,T) gravity in Lyra geometry, including the contributions of the cosmological constant and Randers anisotropic terms b0(t) and obtained analytical solutions. Further, we have examined the behavior of various dynamical parameters, commonly used in cosmological analysis, both geometrical and graphical interpretations have been provided. Furthermore, we have derived the Raychaudhuri equation in terms of the cosmological constant as a function of the cosmic time t. Our analysis reveals that the shear scalar σ2 and the scalar expansion θ decrease with cosmic time and tend to zero at late times, indicating the isotropization of the universe in the presence of the cosmological constant; however, the Hubble parameter approaches a constant value rather than vanishing, while the energy density ρ, pressure P, and the Lyra gauge function β remain finite and non-zero even at large cosmic times. Ultimately, we conclude that the universe described by this framework exhibits continuous acceleration, as indicated by the negative value of the deceleration parameter q.