Method of determining cosmological parameter ranges with samples of candles with an intrinsic distribution
Qin Yi-Ping (覃一平)ab, Zhang Bin-Bin (张彬彬)ac, Dong Yun-Ming (董云明)ac, Zhang Fu-Wen (张富文)abc, Li Huai-Zhen (李怀珍)ac, Jia Lan-Wei (贾兰伟)ac, Mao Li-Sheng (毛李胜)ac, Lu Rui-Jing (陆睿静)abc, Yi Ting-Feng (易庭丰)b, Cui Xiao-Hong (崔晓红)ac, Zhang Zhi-Bin (张志彬)ac
a National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, Kunming 650011, Chinab Physics Department, Guangxi University, Nanning, Guangxi 530004, Chinac The Graduate School of the Chinese Academy of Sciences, Beijing 100049, China
Abstract In this paper, the effect of the intrinsic distribution of cosmological candles is investigated. We find that in the case of a narrow distribution the deviation of the observed modulus of sources from the expected central value can be estimated within a ceratin range. We thus introduce lower and upper limits of $\chi^2$, $\chi_{\min}^2$ and $\chi_{\max}^2$ to estimate cosmological parameters by applying the conventional minimizing $\chi^2$ method. We apply this method to a gamma-ray burst (GRB) sample as well as to a combined sample including this GRB sample and an SN Ia sample. Our analysis shows that: a) in the case of assuming an intrinsic distribution of candles of the GRB sample, the effect of the distribution is obvious and should not be neglected; b) taking into account this effect would lead to a poorer constraint of the cosmological parameter ranges. The analysis suggests that in the attempt of constraining the cosmological model with current GRB samples, the results tend to be worse than was previously anticipated if the mentioned intrinsic distribution does exist.
Received: 09 December 2005
Revised: 10 April 2006
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10273019 and
10463001) and State Key Development Program for Basic Research of China (Grant No G2000077602).
Cite this article:
Qin Yi-Ping (覃一平), Zhang Bin-Bin (张彬彬), Dong Yun-Ming (董云明), Zhang Fu-Wen (张富文), Li Huai-Zhen (李怀珍), Jia Lan-Wei (贾兰伟), Mao Li-Sheng (毛李胜), Lu Rui-Jing (陆睿静), Yi Ting-Feng (易庭丰), Cui Xiao-Hong (崔晓红), Zhang Zhi-Bin (张志彬) Method of determining cosmological parameter ranges with samples of candles with an intrinsic distribution 2006 Chinese Physics 15 1645
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