\(f\left( R,\phi \right) \) cosmology with the parametrization of H(z) parameter

Abstract

Building FRW cosmological models within the context of the \(f(R,\phi )\) theory of gravity is our goal in this effort. We investigate the universe’s accelerating behavior for a specific form of the \(f(R,\phi )\) gravity model by employing a new, straightforward parametrization of the Hubble parameter in the form \(H(z)=\frac{H_0}{\sqrt{2}}\left[ 1+(1+z)^{(2(1+\alpha )) } \right] ^{\frac{1}{2}}\). Using the \(\chi ^2\)-minimization approach, we impose constraints on the related free parameters that are present in H(z) within the \(1\sigma \), \(2\sigma \), and \(3\sigma \) confidence bounds. It has been observed that the values obtained are all within the range that is indicated by cosmological observations. Through the utilization of the free parameter best-fit values, we have ascertained the current geometrical parameter values and illustrated the Universe’s accelerating behavior. Through the use of physical characteristics such as energy density, pressure, and equation of state parameter, we have talked about the physical behavior of the cosmos in our model. Additionally, we have looked at the kinematic parameters such as the jerk, deceleration, and Hubble parameters of the cosmos in our model. The deceleration parameter q(z) in our model represents the phase transition of the cosmos from deceleration to acceleration. Additionally, the deceleration parameter’s current value is \(q_0=-0.361\), and the transition redshift value is \(z_t=0.62\). This kind of situation is closely linked to the conventional \(\Lambda \)CDM model.