TY - JOUR
T1 - Cosmological applications of Padé approximant
AU - Wei, Hao
AU - Yan, Xiao Peng
AU - Zhou, Ya Nan
PY - 2014/1/1
Y1 - 2014/1/1
N2 - As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.
AB - As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.
KW - cosmology of theories beyond the SM
KW - dark energy experiments
KW - dark energy theory
UR - http://www.scopus.com/inward/record.url?scp=84893450117&partnerID=8YFLogxK
U2 - 10.1088/1475-7516/2014/01/045
DO - 10.1088/1475-7516/2014/01/045
M3 - Article
AN - SCOPUS:84893450117
SN - 1475-7516
VL - 2014
JO - Journal of Cosmology and Astroparticle Physics
JF - Journal of Cosmology and Astroparticle Physics
IS - 1
M1 - 045
ER -