Constraining Deceleration, Jerk and Transition Redshift Using Cosmic Chronometers, Type Ia Supernovae and the ISW Effect

We present constraints on the deceleration (\(q\)) and jerk (\(j\)) parameters using the late-time integrated Sachs-Wolfe effect, type Ia supernovae, and \(H(z)\) data . We first directly measure the deceleration and jerk parameters using the cosmic chronometers data with the Taylor series expression of \(H(z)\).However, due to the unusual variations in the deceleration parameter with slight changes in other parameters like snap (\(s\)) and lerk (\(l\)), we found that direct measurements using the series expansion of \(H(z)\) is not a suitable method for non-\(\Lambda\)CDM models, and so we will need to derive the deceleration parameter after constraining the density parameters and dark energy equation of state. Then we present the derived values of the deceleration parameter from the \(\Lambda\)CDM, WCDM and CPL models. We also discuss the transition redshift \(z_{t}\) in relation with the deceleration parameter. Our best fit values for the deceleration parameter, after combining results from \(H(z)\), Union 2.1 and NVSS-ISW, are obtained as \(-0.5808\pm 0.025\) for \(\Lambda\)CDM, \(-0.61\pm 0.15\) for both WCDM and CPL models. Our best fit for the combined jerk parameter for the \(\Lambda\)CDM model is \(1\pm 3.971e-07\), for WCDM it is \(1.054\pm 0.141\), and for the CPL model it is \(1.0654\pm 0.1345\). Also, the combined transition redshift is obtained as \(0.724\pm 0.047\) for the \(\Lambda\)CDM model.