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
References
[1]
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[2]
Hara, T., Sakata, R., Muromachi, Y. and Itoh, Y. (2014) Time Variation of Equation of State for Dark Energy. Progress of Theoretical & Experimental Physics, 2014, 113E01. [arXiv:1409.2726[astro-ph]]
[3]
Planck Collaborations: Ade, P.A.R., et al. (2015) Planck 2015 Results. XIV. Dark energy and Modified Gravity. [ar-Xiv:1502.01590[astro-ph]]
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http://dx.doi.org/10.1103/PhysRevD.59.123504
[6]
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http://dx.doi.org/10.1103/PhysRevLett.95.141301
[8]
Peebles, P.J.E. and Ratra, B. (1988) The Cosmology with a Time-Variable Cosmological “Constant”. Astrophysical Journal, 325, L17-L20. http://dx.doi.org/10.1086/185100
[9]
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http://dx.doi.org/10.1016/S0370-2693(99)01209-5
[10]
Amendola, L. and Tsujikawa, S. (2010) Dark Energy. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511750823
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