Cosmological Implications of a New Creation Field in Hoyle-Narlikar Gravity with Bulk Viscous Fluid

In this study, we present a comprehensive investigation of the Narlikar gravity model with bulk viscous fluid by the new foam of creation field $C(t) = t + \int α(1 - a)dt + c_1$, based on the Hoyle-Narlikar's creation-field theory, using a joint analysis of Observational Hubble Data (OHD) and the Pantheon supernova (PP) compilation. Our analysis reveals that the creation field coupling constant $(f)$ is always positive within the Narlikar gravity model from OHD+PP data sets. The best-fit estimates yield $ H_0 = 71.2 \pm 2.1 \text{km s}^{-1}\text{Mpc}^{-1}$ and $ξ_0 = 0.23$, quoted at the $1 σ$ level. The Narlikar gravity model predicts a transition redshift of $z_t \approx 0.63$ marking the onset of late-time cosmic acceleration, with the corresponding age of the Universe estimated as $13.50\pm1.80 Gyr$. Interestingly, the inferred higher value of $H_0$, relative to SH0ES determinations, suggests a possible alleviation of the $\sim 4.1σ$ Hubble tension. Furthermore, we assess the stability of the model and demonstrate that the late-time acceleration can be consistently explained through the energy conditions. This model retains dynamical flexibility while ensuring analytical tractability and provides a promising framework to investigate the cosmological implications of Hoyle-Narlikar gravity, particularly regarding late-time acceleration and the evolution of dark energy.