Dynamics of Quasi-Exponential Expansion: Scalar Field Potential Insights

Our current observations have not definitively determined the exact form of the expansion factor of spacetime. It is possible that we are experiencing a transitional stage of expansion, characterized by a combination of inflation and power-law expansion. We consider spatially homogeneous tachyon scalar fields, quintessence, and phantom fields as potential candidates for dynamical dark energy. The time-dependent potentials and fields of these three classes of scalar fields are calculated for three different mixed forms of the scale factor of expansion: firstly, a logarithmic function of time; secondly, a linear combination of power law functions of time; and thirdly, a product of power law and exponential functions of time, respectively.