A phenomenological approach to the dark energy models in the Finsler–Randers framework

This study extends two phenomenological models of dark energy within the framework of Finsler–Randers space–time, accommodating anisotropies. The models consider the cosmological constant $\Lambda$ in two scenarios: one where $\Lambda$ is proportional to the second time derivative of the scale factor $\ddot{a}$, and another where it varies with the matter-energy density $\rho$. Earlier, such $\Lambda$-decaying cosmologies were proposed to address long-standing cosmological constant problems. However, following the discovery of late-time cosmic acceleration, the focus shifted to modeling dark energy. Since $\Lambda$ is widely viewed as the most significant and suitable candidate for driving cosmic acceleration, it is worthwhile to revisit the phenomenological approach in this context. This work uses this approach to find solutions for the scale factor $a\left(t\right)$ and other geometrical and physical parameters. Additionally, we analyze the evolution of density parameters ${\Omega }_m$, ${\Omega }_{\Lambda }$, and ${\Omega }_{\kappa }$, representing matter, dark energy, and curvature, from early to late times. The phenomenological approach is employed to solve the field equations, with model parameters constrained using recent observational data, yielding ranges consistent with observations. The solutions converge to the $\Lambda$CDM cosmology at early and late times. The added complexity introduced by Finsler–Randers geometry enhances accuracy compared to analogous solutions in Riemannian space–time.