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A Model-Independent Test for the Cosmic Distance-Duality Relation Using Type Ia Supernovae and Galaxy Clusters Data | | Xiao-Lei Meng
; Tong-Jie Zhang
; Hu Zhan
; | | Date: |
14 Apr 2011 | | Abstract: | We use two new methods to make a cosmological model-independent test for
distance-duality (DD) relation, $dl=da(1+z)^2$, with luminosity distance
($dl$) from Union2 SNe Ia compilation and angular diameter distance ($da$)
from two galaxy cluster models reported by De Filippis et al. and Bonamente et
al. Unlike previous methods, we employ two different ways to derive $dl$ from
SNe Ia data: Method I, fitting Union2 data to get $dl$ at the same redshifts
with clusters. Method II: binning Union2 data within the redshift range
$|z_{cluster} - z_{SN}|<0.005$ as $dl$ at corresponding redshift. The
advantage of these methods is that it can reduce the statistical error.
Especially, by considering asymmetric uncertainties in Bonamente et al.’s $da$
data, we obtain two different values of $da$. According to different
morphological hypotheses, for cluster models, elliptical and spherical $eta$
model are considered. The latter model is divided into two groups in terms of
different reduction methods of the $da$ data: conservative and corrected
spherical $eta$ model. For a thorough test for DD relation, we use four
1-dimensional parameterizations for $eta$, $eta=1+eta_0z,
eta=1+eta_0z/(1+z), eta=1+eta_0z/(1+z)^2 and eta=1-eta_0
m{ln}(1+z)$.
Four more general 2-dimensional parameterizations, $eta=eta_1+eta_2z,
eta=eta_1+eta_2z/(1+z), eta=eta_1+eta_2z/(1+z)^2 and
eta=eta_1-eta_2
m{ln}(1+z)$, are also used. Our results show that DD
relation is consistent with elliptical model at $1sigma$ CL for both methods,
while for almost all spherical model parameterizations, DD relation can only be
accommodated at $3sigma$ CL, particularly for conservative model. We also show
that the marked triaxial ellipsoidal model is a better hypothesis describing
the structure of galaxy cluster comparing with spherical model if DD relation
is valid in cosmological observations. | | Source: | arXiv, 1104.2833 | | Services: | Forum | Review | PDF | Favorites | |
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