Accelerating cosmological models in Hoyle–Narlikar gravity with observational constraints

In this paper, we explore the cosmic acceleration and the physical aspects of the dark energy nature in Hoyle–Narlikar’s creation-field theory, taking into account observational constraints. We find analytical solutions to the modified field equations for a specific choice of creation field [Formula: see text] with certain background fluid sources as a barotropic fluid and a radiation fluid in a flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime universe. From there, we use observational constraints with data from the cosmic chronometer (CC) Hubble data and the apparent magnitude from the Pantheon SNe sample to get the model parameters’ constrained values with [Formula: see text] and [Formula: see text] confidence levels. We look at the physical properties of the models we’ve made using these estimated values of model parameters. To do this, we look at the deceleration parameter [Formula: see text], the effective equation of state parameter [Formula: see text], the jerk parameter [Formula: see text], the snap parameter [Formula: see text], and the energy conditions. We also examine the cosmic behavior of square sound speed [Formula: see text] for the test of causality and viability of the models. We measure the present age of the universe and transition redshift [Formula: see text] for the signature-flipping point. We obtain two transit-phase accelerating universe models with [Formula: see text] Km/s/Mpc, [Formula: see text], [Formula: see text], and [Formula: see text], respectively, with barotropic and radiation fluid sources.