Cosmic and thermodynamic study of non-canonical scalar field in parameterized modified gravity

Cosmological and thermodynamic implications of non-canonical scalar field are investigated in the cubic gravity by assuming various parameterizations (linear, Chevallier-Polarski-Linder and Jassal-Bagla-Padmanabhan) and recently proposed entropies (Tsallis and Sharma-Mittal). We develop the expressions for Hubble ( H ) and deceleration ( q ) parameters in each case and find consistent values with the observational data as H 0 ≃ 67.0, q 0 = − 0.55 ± 0.15. We investigate the perturbed squared speed of sound ( C s 2 ) parameter in terms of redshift parameter ( z ) which leads to the stability for all models. It is also found that the generalized second law of thermodynamics holds for Tsallis as well as for Sharma-Mittal entropies in all the cases of parameterizations.