%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 <p class=\"MsoNormal\">
	<span lang=\"EN-US\">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 &nbsp;<img src=\"Edit_d936fade-ff15-4362-8cd9-3813511368f6.bmp\" alt=\"\" />, the mixed <img src=\"Edit_d7329c2f-0573-41da-a4d2-690125603200.bmp\" alt=\"\" /><v:shape id=\"_x0000_i1026\" type=\"#_x0000_t75\" style=\"width:123.75pt;height:16.5pt;\" o:ole=\"\">
 <v:imagedata src=\"file:///C:\Users\fliu\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz\" o:title=\"\">
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 <o:oleobject type=\"Embed\" progid=\"Equation.DSMT4\" shapeid=\"_x0000_i1026\" drawaspect=\"Content\" objectid=\"_1517233582\">
 </o:oleobject>
</xml><![endif]-->, the cosine <img src=\"Edit_e975299d-36bf-4076-97f2-e5021e7bfa59.bmp\" alt=\"\" /><v:shape id=\"_x0000_i1027\" type=\"#_x0000_t75\" style=\"width:99pt;height:16.5pt;\" o:ole=\"\">
 <v:imagedata src=\"file:///C:\Users\fliu\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz\" o:title=\"\">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
 <o:oleobject type=\"Embed\" progid=\"Equation.DSMT4\" shapeid=\"_x0000_i1027\" drawaspect=\"Content\" objectid=\"_1517233583\">
 </o:oleobject>
</xml><![endif]-->&nbsp;and the Gaussian types <img src=\"Edit_f3c7eaa9-7a68-46db-8b07-0f9919e3ff3c.bmp\" alt=\"\" /><v:shape id=\"_x0000_i1028\" type=\"#_x0000_t75\" style=\"width:101.25pt;height:16.5pt;\" o:ole=\"\">
 <v:imagedata src=\"file:///C:\Users\fliu\AppData\Local\Temp\msohtmlclip1\01\clip_image004.wmz\" o:title=\"\">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
 <o:oleobject type=\"Embed\" progid=\"Equation.DSMT4\" shapeid=\"_x0000_i1028\" drawaspect=\"Content\" objectid=\"_1517233584\">
 </o:oleobject>
</xml><![endif]-->, 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 <img src=\"Edit_d7ce7053-34ac-40ac-a7ef-e069f8e11949.bmp\" alt=\"\" /><v:shape id=\"_x0000_i1029\" type=\"#_x0000_t75\" style=\"width:12pt;height:16.5pt;\" o:ole=\"\">
 <v:imagedata
%K Dark Energy
%K Quintessence
%K Thawing Model
%K Freezing Model
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=63510