Behavior of various scalar field potentials under tracking parameter of quintessence class of scalar field models

Scalar field models are known for their dynamical nature i.e, dynamical equation of state parameter to explain the late time cosmic acceleration of the universe unlike cosmological constant which is known for its constant equation of state. Quintessence cosmological model or canonical scalar field with a potential is one such simplest class of model which is introduced to account for late time acceleration of the universe. Till now, there are numerous scalar field models proposed like canonical, non-canonical, galileon scalar field models etc. which can be broadly classified into two classes, namely, thawing and tracking. In the present work, we mathematically investigate different kinds of scalar field potentials under quintessence cosmological model using tracking parameter to examine whether these potentials are showing thawing or tracking behaviour. Tracking parameter is considered because during cosmic evolution the dynamics of tracking depends susceptibily on the variation of this particular parameter. We analyze each potential using this parameter and accordingly get their behaviour. It is found that among the four potentials used, three are showing tracking properties and only one is showing thawing property as per the tracking parameter . The tracking and thawing properties / behavior are discussed in result and discussion section of the paper.