%0 Journal Article
%T Quest for Potentials in the Quintessence Scenario
%A Tetsuya Hara
%J Journal of Applied Mathematics and Physics
%P 211-214
%@ 2327-4379
%D 2016
%I Scientific Research Publishing
%R 10.4236/jamp.2016.42027
%X
The time evolution of the equation of state
w for quintessence scenario with a scalar field as dark energy is studied up to
the third derivative (d3w/da3) with respect to the scale factor a, in order to
predict the future observations and specify the scalar potential parameters
with the observables. The third derivative of w for general potential V is
derived and applied to several types of potentials. They are the inverse
power-law (V = M4 + ¦Á/Q¦Á), the exponential , the mixed
, the cosine
and the Gaussian types
, which are prototypical potentials for the freezing and
thawing models. If the parameter number for a potential form is n, it is
necessary to find at least for n + 2 independent observations to identify the
potential for0m and the evolution of the scalar field (Q and