Redshift Drift in the Universe: Theoretical Features and Observational Constraints

We investigate an exact Universe model which is observationally viable and filled with a binary mixture of a perfect fluid and the cosmological constant \(\Lambda\). We consider the redshift drift \(\dot{z}=(1+z)H_{0}-H(z)\) and perform statistical tests to obtain the best fit value of the model parameters of the derived Universe with its observed values. Here, \(H_{0}\) and \(z\) denote the present value of the Hubble constant and the redshift, respectively. We estimate the best fit values of the Hubble constant and the density parameters as \(H_{0}=68.58\pm 0.84\) km/(s Mpc), \((\Omega_{m})_{0}=0.26\pm 0.010\), and \((\Omega_{\Lambda})_{0}=0.71\pm 0.025\) by bounding the derived model with the latest observational Hubble data (OHD), while with joint Pantheon data and OHD, its values are \(H_{0}=71.93\pm 0.58\) km/(s Mpc), \((\Omega_{m})_{0}=0.272\pm 0.06\), and \((\Omega_{\Lambda})_{0}=0.74\pm 0.09\). The analysis of the deceleration and jerk parameters shows that the Universe in the derived model is compatible with the \(\Lambda\)CDM model. We also investigate that the cosmological models owning a redshift drift minimize the \(H_{0}\) tension.