Kinematical models of latetime cosmology and the statefinder diagnostic.

The present work deals with kinematical models of latetime cosmology. It is based on purely phenomenological assumption about the deceleration parameter. The models are confronted to observational data sets of type Ia supernovae distance modulus measurements and measurements of Hubble parameter at different redshift. Constraints on the cosmological parameters are obtained by Markov Chanin Monte Charlo (MCMC) analysis using the observation data sets. The values of present Hubble parameter, deceleration parameter and the redshift of transition from decelerated to accelerated phase of expansion are estimated for the present kinematical models. Further the properties of dark energy for the present models are explored with general relativistic assumptions. The dark energy diagnostics, namely the Om diagnostic and the statefinder are adopted for a comparison of the present models. A phase space constructed of two different statefinder parameters breaks the degeneracy of the models. It is observed that the kinematical models attain the corresponding {\Lambda}CDM value on the phase space in the course of evolution. The evolution of matter density contrast at linear level has also been studied for the present kinematical models.