Dynamical dark energy in the Bianchi Type-V Universe with DESI DR2 BAO, SNIa compilation and RSD measurements

We investigate the cosmological implications of dynamical dark energy (DDE) models within an anisotropic, spatially homogeneous Bianchi Type-V spacetime framework using a $1+3$ covariant thermodynamics approach. By implementing both constant ($w$) and time-varying ($w_0,w_a$) parameterized equations of state, we evaluate the background expansion history and track linear matter perturbations via the quasi-static approximation. We confront these scenarios with the latest cosmological datasets, including the Dark Energy Spectroscopic Instrument (DESI) DR2 Baryon Acoustic Oscillations (BAO), the Union3 and Dark Energy Survey 5-year (DESY5) Type Ia Supernovae compilations, Cosmic Chronometers (CC), and Redshift-Space Distortion (RSD) measurements. Our joint statistical analyses reveal that the introduction of spatial anisotropy coupled with DDE efficiently accommodates recent late-time measurements and provides a viable mechanism to mitigate the persistent $H_0$ and $S_8$ cosmological tensions. Model selection metrics show that while Akaike criteria strongly support the extended Bianchi Type-V scenarios across most joint data combinations, Bayesian criteria continue to favor the simpler standard $\mathrm{\Lambda }$CDM baseline due to its lower dimensionality. Finally, we establish tight constraints on the current matter density parameter ${\mathrm{\Omega }}_{m,0}$, the shear parameter ${\mathrm{\Omega }}_{\sigma ,0}$, and the dark energy evolution parameters, confirming that anisotropic extensions remain viable and testable frameworks for modern precision cosmology.