Constraining extended Proca-Nuevo theory through big bang nucleosynthesis

This study explores a covariant extension of the Proca framework, incorporating nonlinear terms for a massive spin-1 field while ensuring consistency and ghost-free behavior. Coupled with gravity, this effective extended Proca-Nuevo model provides viable cosmological solutions, constrained by Big Bang Nucleosynthesis observations. By enforcing \( |\Delta T_f / T_f| < 4.7 \times 10^{-4} \), the model parameter \(\Lambda \) is restricted to the range \( \Lambda \in \left( -2.80025 \times 10^{-4}, \, 2.80025 \times 10^{-4}\right) \). This correction supports a consistent description of the Big Bang Nucleosynthesis era, effectively aligning the freeze-out temperature predictions with observational bounds and the constrained Hubble function predicting accelerated expansion across all redshifts. These findings highlight the potential of extended Proca-Nuevo theories in bridging modified gravity and Effective Field Theory, providing the aspects of early-time cosmology.