A new creation-field cosmology in Hoyle–Narlikar gravity: Dark energy dynamics, cosmic acceleration, and the Hubble tension

In this study, we explore a cosmological framework based on Hoyle–Narlikar’s creation-field theory by introducing a novel form of the creation field with respect to time, [Formula: see text], within the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We also investigate the behaviour of dark energy and cosmic acceleration/deceleration based on our proposed model (Hoyle–Narlikar gravity model) with new creation field. To test its observational consistency, we constrain the independent parameters [Formula: see text] and some derived parameters [Formula: see text] using Markov Chain Monte Carlo (MCMC) analysis with the emcee sampler, incorporating the Observational Hubble Data (OHD) and Pantheon Plus (PP) supernova datasets. Our analysis yields a best-fit value of the Hubble constant, [Formula: see text] km s −1 Mpc −1 at 68% C.L. from the OHD+PP data. This result agrees well with the SH0ES calibration and alleviates the [Formula: see text] Hubble tension between the Planck and SH0ES measurements. Our model further predicts a deceleration–acceleration transition at redshift [Formula: see text], with a present deceleration parameter [Formula: see text], and estimates the current age of the universe to be in the range of [Formula: see text][Formula: see text]Gyr, consistent with observational bounds. The creation field coupling constant [Formula: see text] remains positive, ensuring physical stability. Moreover, analysis of the [Formula: see text] diagnostic reveals a distinct dynamical behavior of dark energy:the slope of [Formula: see text] transitions from negative to positive at [Formula: see text], indicating a shift from a quintessence-like phase to a phantom regime, and from positive to negative at [Formula: see text], suggesting a subsequent return from phantom to quintessence. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values of our model are slightly higher than those of the standard and dynamical dark energy models, indicating that our model remains statistically consistent.