中国科技大学交叉中心 吴普训 宁波大学理学院 Distance duality relation and cosmic opacity Collaborators: Zhengxiang Li, Jun Chen, Hongwei Yu Li, Wu and Yu, APJL 729 (2011) L14 Chen, Wu, Yu and Li, JCAP 10 (2012) 029

Distance duality (DD) relation Model-independent tests for the DD relation Cosmic opacity Conclusions Outline

The distance duality relation Cosmological distances:  Luminosity distance D L ：  Angular diameter distance (ADD) D A ： A : the object’s size \theta: the angular size of the object

 the number of photons is conserved  photons travel along null geodesics Distance-duality relation: Two necessary conditions: Valid for all cosmological models based on Riemannian geometry, dependent neither on Einstein field equations nor the nature of matter-energy content (Etherington 1933)

The role of DD relation: Taken for granted in virtually all analyses of cosmological observations Gravitational lensing Galaxy distribution and galaxy clusters observations CMBR observations

The possibilities for the violation of DD relation Absorption of photon by dust and plasma Photon-axion oscillation in an external magnetic field Gravity being not described by a metric theory A signal of new physics? Testable by means of astronomical observations.

Testing the DD relation:  X-ray and Sunyaev-Zel’dovich observations of clusters (Uzan et al. PRD 2004) :18 X-ray and Sunyaev-Zel’dovich data of clusters of galaxies : LCDM model at 1\sigma confidence level The DD relation is consistent with observations at 2 \sigma confidence level

Testing the DD relation Union Type Ia supernovae and the Hubble data (Avgoustidis et al. JCAP 2010) Galaxy clusters provided by elliptical model and the spherical model (Holanda et al. AAL 2010) LCDM model is used.

Model-independent: The ADD is given from galaxy clusters The luminosity distance is from SNe Ia De Bernardis et al. IJMPD 2006 To obtain the values of the ADD and the luminosity distances at the same redshift from SNe Ia, they bin the SN Ia data the DD relation is not violated at 1\sigma confidence level Caution

The galaxy clusters data The X-ray emission takes the form:

The method: Parametrize: the DD relation: MODEL-INDEPENDENT TESTS FROM GALAXY CLUSTERS AND TYPE Ia SUPERNOVA Holanda,Lima and Ribeiro,ApJL,722:L233,2010 Li, Wu and Yu, APJL, 729:L14,2011

Data: The luminosity distance: 397 Constitution SNe Ia 557 Union2 SNe Ia The ADD: galaxy clusters: 25 data from the elliptical model 38 data from the spherical model Parameterizations:

The selection criteria Constitution: 12 ADD data points are discarded in spherical model Union2: All ADD data points included Holanda ( Constitution )

Constitution: 6 ADD data points are discarded in elliptical model Union2: All ADD data points included

The results: Holanda Constitution Without the errors of SNe Ia

without and with the errors of SNe Ia Constitution

Union2

The DD relation can be accommodated at 1σ CL for the elliptical model and at 3σ CL for the spherical model With two more general parameterization forms, the consistencies between the observations and the DD relation are improved markedly for both samples of galaxy clusters. With the inclusion of the errors of SNe Ia, the results become more consistent with the DD relation.

Other works: A Consistent Test of the Distance-Duality Relation with Galaxy Clusters and Type Ia Supernave, (Liang, et al., arXiv: ) Morphology of Galaxy Clusters: A Cosmological Model- Independent Test of the Cosmic Distance-Duality Relation (Meng, Zhang, Zhan, APJ, 2011) Observational cosmology and the cosmic distance duality relation, (Nair, Jhingan and Deepak, JCAP,2011) A test for cosmic distance duality. (Holanda, et al. JCAP 2012) Testing the distance duality relation with present and future data. (Cardona, et al. PRD, 2012)

Riess Perlmutter Schmidt Accelerated cosmic expansion: Type Ia Supernova data: 2010: Nobel prize Cosmic opacity

Sources for photon attenuation Absorption or scattering of gas and plasma Axion-photon mixing The observed luminosity distance derived from SNIa will be modified and it will be larger than the true one

： the opacity between an observer at redshift z = 0 and a source at z The relation between the observe luminosity distance and the true one (Chen and Kantowski, 2009) The luminosity distance

For a spatially homogeneous and nondispersive absorption (Chen and Kantowski 2009 PRD) Two Models: is the dimensionless cosmic absorption parameter

Union2 SNIa data (Lima, et al., 2011 ApJL):

With systematic error for SNIa To break the degeneracy: Union2 SNIa+Six BAO data

With systematic error for SNIa

Testing cosmic opacity Data: SNIa BAO Hubble The distance modulus The distance modulus difference

: SNIa data : BAO data Hubble data+SNIa: BAO data: z=0.2 and 0.35 from SDSS and 2DFGRS 95% CL (More, et al APJ) (Avgoustidis, et al, 2010 JCAP)

7 BAO data points Chen, Wu, Yu and Li, JCAP (2012) Is the Cosmic Transparency Spatially Homogeneous?

Union2 SNIa

Chen, Wu, Yu and Li, JCAP (2012)

Conclusions The DD relation can be accommodated at 1σ CL for the elliptical model and at 3σ CL for the spherical model. The best-fit cosmic opacity oscillates between zero and some nonzero values as the redshift varies. A transparent universe is consistent with observations at the 1σ confidence level. An opaque universe is favored by SNe Ia+BAO. The cosmic opacity is not enough to account for the present observations and dark energy or modified gravity remains to be required.

Thanks