BBN in Constrained f(T,φ) Gravity Through Various Observational Schemes

In this article, we investigate the observational constraints for early universe as well as the late-time accelerated expansion of the universe in the realm of f(T,φ) gravity, where T is the torsion scalar and φ is a scalar field that modifying gravitational interactions. To analyze the early universe, we utilize the big bang nucleosynthesis (BBN) constraints while with cosmic chronometers (CC), baryon acoustic oscillation (BAO) and Markov Chain Monte Carlo (MCMC) analysis we dealt with the-late time accelerated expansion constraints. Focusing on three specific models within the framework of f(T,φ) gravity, we assess whether the freeze-out temperature Tf predicted by each model meets the latest BBN observational bounds |Δ Tf/Tf|. To further evaluate the viability of these models in the late time universe, we analyze the Hubble parameter $H(z)$ across redshift z, utilizing CC and BAO datasets incorporating a 2-σ confidence region to ensure alignment with empirical data. Additionally, MCMC analysis using CC data provides detailed constraints on parameters and quantifies uncertainties through contour plots. Results indicate that each f(T,φ) model satisfactorily aligns with observational data from BBN, CC, and BAO measurements, positioning this framework as a promising alternative to the standard ΛCDM cosmology. We wrap up by conducting a thorough analysis of how each model, dataset, and prior combination interacts, offering insights into their collective impact on the cosmological parameter estimations and the overall model evaluation.