2012. 12. 20 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) L14Chen, 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 relationCosmological distances:

Luminosity distance DL：

24/ LDLF

Angular diameter distance (ADD) DA：

dDdA 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:L233,2010Li, 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:

HolandaConstitution

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:1104.2497)

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)

RiessPerlmutterSchmidt

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. 2009 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