Evolution of a Bianchi Type-V Universe in Modified Gravity: Anisotropy Decay, Energy Conditions and Dark Energy Emergence

We investigate the evolution of a Bianchi type-V universe within the framework of f(R, T) gravity, incorporating a time-varying cosmological constant and a quadratic equation of state. By employing a specific form of the Hubble parameter, exact solutions to the modified field equations are obtained. The model exhibits an initial singularity, followed by anisotropy decay and a transition to a ΛCDM-like behaviour. The matter–geometry coupling inherent to f(R, T) gravity drives late-time acceleration. Energy conditions are examined and shown to be consistent with current observational bounds. The model asymptotically approaches a de Sitter phase, indicating the emergence and dominance of dark energy.