TITLE:
Quest for Potentials in the Quintessence Scenario
AUTHORS:
Tetsuya Hara
KEYWORDS:
Dark Energy, Quintessence, Thawing Model, Freezing Model
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.2,
February
17,
2016
ABSTRACT:
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 + α/Qα), 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
). Such observations would be the values of ΩQ, w, dw/da, ???,
and dwn/dan. From these specific potentials, we can predict the n + 1 and
higher derivative of w; dwn + 1/dan + 1, ???. Since four of the above mentioned
potentials have two parameters, it is necessary to calculate the third
derivative of w for them to estimate the predict values. If they are tested
observationally, it will be under- stood whether the dark energy could be
described by the scalar field with this potential. At least it will satisfy the
necessary conditions. Numerical analysis for d3w/da3 is made under some specified
parameters in the investigated potentials, except the mixed one. It becomes
possible to distinguish the potentials by the accurate observing dw/da and d2w/da2 in some parameters.