Dynamical Dark Energy from a Massive Vector Field in Generalized Proca Theory

In this paper, we emphasise the recent observational findings from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI DR2), which provide compelling evidence for a possible deviation from the standard $\Lambda$CDM (Cold Dark Matter) cosmology, suggesting the presence of a dynamically evolving effective dark energy component. Motivated by this, we construct a theoretical framework in which a massive cosmological vector field, $B^{\mu}$, couples non-minimally to the background curvature through marginal interactions, offering a controlled mechanism to realise the deviation from the $\Lambda$CDM model. A detailed analysis of the effective Equation of State (EoS) parameter $w(\tilde H)$ reveals a narrow region of parameter space consistent with current cosmological observations presented by DESI. The analysis yields a stringent upper bound for the coupling constant $\lambda$ to be $\lambda<2.98\times10^{-11}$, a very strong bound on mass $3.1356\times10^{-66}~\text{g} \leq m \leq 3.3627\times10^{-66}~\text{g},$ and the admissible range $-0.405 \leq \log_{10}\tilde\gamma \leq -0.38$ for which present-day value $w_0 = w(\tilde H = 1)$ corresponding to a deviation $\delta = w_0 + 1$ that lies within the region $0.107 \leq \delta \leq 0.217$. This interval reproduces the deviation inferred from the combined DESI, Cosmic Microwave Background (CMB), and Pantheon+ data, reflecting a controlled departure from the $\Lambda$CDM behaviour. In summary, the results suggest that the proposed framework of a massive vector field can account for the departure from $\Lambda$CDM behaviour highlighted by DESI in the current cosmic acceleration. Furthermore, the framework approaches the $\Lambda$CDM behaviour in late-time $t\gtrsim28$ Gyr, establishing a direct phenomenological link between the underlying parameters and the observed dynamical nature of dark energy.