Search for tracker potentials in quintessence theory

Abstract

We report a significant finding in quintessence theory that scalar fields with tracker potentials have a model-independent scaling behaviour in the expanding universe. So far, widely discussed exponential, power law or hyperbolic potentials can simply mimic the tracking behaviour over a limited range of redshift. A new version of the tracker field theory is proposed and it is shown that in the small redshift range where the variation of the tracking parameter ϵ may be taken to be negligible, the differential equation of generic potentials leads to hyperbolic sine and hyperbolic cosine potentials which may approximate a tracker field in the present-day universe. We have plotted the variation of the tracker potential and the equation of state of the tracker field as a function of the redshift z for the model-independent relation derived from tracker field theory; we have also plotted the variation of V(Φ) in terms of the scalar field Φ for the chosen hyperbolic cosine function and have compared it with the curves obtained by the reconstruction of V(Φ) from real observational data from the supernovae.