Observational constraint in f(R, ∇R) gravity model in power-law cosmology

In this paper, we have considered the flat Friedmann-Lemaître-Robertson-Walker (FRW) model in the framework of f( R, ∇ R) gravity. We have analyzed the significance of bulk viscosity in the f( R, ∇ R) gravity model to study the expansion of the universe. We have considered two bulk viscosity parameterizations and the use of power-law cosmology to constrain the model parameters H0 and q. Using the Bayesian analysis and likelihood function in conjunction with the Markov Chain Monte Carlo method, we obtained the model parameters [Formula: see text] and [Formula: see text]. The behaviors of energy density, bulk viscous pressure, and the effective equation of the state parameter with redshift are investigated in detail. These features demonstrate that the bulk viscosity is a valid candidate for acquiring the negative pressure needed to effectively drive the expansion of the universe. To check the validity of the f( R, ∇ R) model, we also analyze the behavior of energy conditions. The adiabatic squared speed of the sound is used to test the model’s stability. The Om( z) diagnostic is used in the model to identify the quintessence and phantom regions.