Cosmological implications and constraints in Hoyle–Narlikar gravity theory

We discuss some cosmological implications and constraints in Hoyle–Narlikar’s creation field theory to explain the cosmic evolution of the expanding universe. To obtain an analytical solution of the modified field equations, we use the specific choices of the creation field $C\left(t\right)=t+\int \frac{1}{a^2}+c_1,t+\int \frac{1}{a}+c_2,t+\int \frac{1}{\sqrt{a}}+c_3$ and get three alternatives as Model I, II, and III. For the background source of dust fluid, we find the Hubble function for each model and subsequently obtain values for the model parameters $H_0$ and ${\Omega }_{m0}$ by combining the examination of the CC and Pantheon datasets with $1\sigma$ and $2\sigma$ confidence levels. Using these values of model parameters, we measure the values of derived parameters and discuss the results by presenting the geometrical behavior of cosmological parameters. We talk about three models side by side and compare them using the effective equation of state parameter ${\omega }_{eff}$, the deceleration parameter $q\left(z\right)$, and Om diagnostic analysis to group the models into stages of evolution. We also discuss the present age of the universe.