1. Bin Wang Fudan University Shanghai Signature on the interaction between dark energy and dark matter

2. COSMIC TRIANGLE Tightest Constraints: Low z: clusters(mass-to-light method, Baryon fraction, cluster abundance evolution) — low-density Intermediate z: supernova — acceleration High z: CMB — flat universe Bahcall, Ostriker, Perlmutter & Steinhardt, Science 284 (1999) 1481.

3. Concordance Cosmology Emerging paradigm: ‘ CONCORDANCE COSMOLOGY ’ : 70% DE + 30% DM. DE-- ? 1. QFT value 123 orders larger than the observed 2. Coincidence problem: Why the universe is accelerating just now? In Einstein GR: Why are the densities of DM and DE of precisely the same order today? Reason for proposing Quintessence, tachyon field, Chaplygin gas models etc. No clear winner in sight Suffer fine-tuning

4. Scaling behavior of energy densities  A phenomenological generalization of the LCDM model is LCDM model, Stationary ratio of energy densities Coincidence problem less severe than LCDM can be achieved by a suitable interaction In the framework of field theory, the interaction between 70%DE and 30%DM is nature, could be even more general than uncoupled case. (Pavon, Almendola, Zimdahl et al) Q accelerated scaling attractor to alleviate the coincidence problem S.Chen, Bin Wang, J.Liang, arXiv:0808.3482; D.Pavon et al, arXiv:0806.2116 etc.arXiv:0808.3482arXiv:0806.2116 For Q > 0 the energy proceeds from DE to DM

5. Argument from the universe expansion history for Q>0 Phenomenological forms of Q Constrain Q from SNIa+CMB+BAO+AGE Not specify any special DE model, but using

6. Age constraints  The age of the universe is effective to provide a complementary test of different models.  Present age of our universe different models may give the same age of the universe  degeneration  Expanding age of the Universe at high z> age of oldest objects at that z. May help to distinguish models Constraints can be placed on cosmological models. B.Wang et al, Nucl.Phys.B778:69,2007, C. Feng, B.Wang, Y.Gong, R.Su, JCAP 0709:005,2007

7. Age constraints Simple models Interacting DE&DM model

8. Argument from the universe expansion history for Q>0 The parameter space from the Monte-Carlo Markov Chain exploration.

9. Argument from the universe expansion history for Q>0 The compatibility among CMB, SNIa+BAO, AGE C.Feng, B.Wang, E.Abdalla, R.K.Su, PLB(08),0804.0110 J.He, B.Wang, JCAP(08), 0801.4233 The tendency shows that the coupling is a small positive.

10. Argument from the dynamics of glaxay clusters for Q>0  Phenomenology of coupled DE and DM Collapsed structure: the local inhomogeneous density is far from the average homogeneous density The continuity equation for DM reads the peculiar velocity of DM particles. Considering: the continuity equation with DM coupled to DE reads

11. Argument from the dynamics of glaxay clusters for Q>0  Equilibrium condition for collapsed structure in the expanding universe ---Newtonian mechanics The acceleration due to gravitational force is given by is the (Newtonian) gravitational potential. Multiplying both sides of this equation byintegrating over the volume and using continuity equation, LHS: kinetic energy of DM RHS: where Potential energy of a distribution of DM particles LHS=RHS the generalization of the Layzer-Irvine equation: how a collapsing system reaches dynamical equilibrium in an expanding universe.

12. Argument from the dynamics of glaxay clusters for Q>0  Virial condition: For a system in equilibrium Taking Layzer-Irvine equation describing how a collapsing system reaches a state of dynamical equilibrium in an expanding universe. presence of the coupling between DE and DM changes the time required by the system to reach equilibrium, Condition for a system in equilibrium presence of the coupling between DE and DM changes the equilibrium configuration of the system E. Abdalla, L.Abramo, L.Sodre, B.Wang, arXiv:0710.1198

13. Argument from the dynamics of glaxay clusters for Q>0  Galaxy clusters are the largest virialized structures in the universe  Ways in determining cluster masses:  Weak lensing: use the distortion in the pattern of images behind the cluster to compute the projected gravitational potential due to the cluster. D-cluster+D-background images mass cause the potential  X-ray: determine electrons number density and temperature. If the ionized gas is in hydrostatic equilibrium, M can be determined by the condition that the gas is supported by its pressure and gravitational attraction  Optical measurement: assuming cluster is virialized, M~U/K The M got by assuming will be biased by a factor

14. Argument from the dynamics of glaxay clusters for Q>0  Comparing the mass estimated through naïve virial hypothesis with that from WL and X-ray, we get There are three tests one can make: f1 and f2, should agree with each other, and put limits on the coupling parameter f3, is a check on the previous two, and should be equal to one unless there are unknown systematics in the X-ray and weak lensing methods.

15. Argument from the dynamics of glaxay clusters for Q>0 Best-fit value Indicating a weak preference for a small but positive coupling DE  DM Consistent with other tests E. Abdalla, L.Abramo, L.Sodre, B.Wang, arXiv:0710.1198 33 galaxy clusters optical, X-ray and weak lensing data

16. Thermodynamical argument for Q>0 If DE and DM conserve separately the equation of state of dark matter can be approximately written in parametric form as As a consequence, The temperatures dependence on the scale factor from Gibbs’ equation, and the integrability condition

17. Thermodynamical argument for Q>0 When both components interact, Assuming For: Second Law For: The temperature difference would augment, Tx will increase more slowly as the Universe expands than in the absence of interaction Tm will also decrease more slowly. the answer of the system to the equilibrium loss is a continuous transfer of energy from DE to DM. Whereas this does not bring the system to any equilibrium it certainly slows down the rate it moves away from equilibrium.

18. Thermodynamical argument for Q>0 The entropy production associated to our two interacting fluids Zimdahl, Mon. Not. R. Astron. Soc., 288, 665 (1997) From the second law, The fact that nowadays Q>0 D. Pavon, B. Wang, ArXiv: 0712.0565

19. Coincidence problem We pay attention to the ratio of energy densities between DE and DM, and its evolution. The positive coupling obtained from the best-fit leads to a slower change of r as compared to the noninteracting case. This means that the period when energy densities of DE and DM are comparable is longer compared to the noninteracting case. With Q, the coincidence problem is less acute!!!

20. Summary  Is there any interaction between DE & DM? SN constraint CMB BAO Age constraints Galaxy cluster scale test  Q > 0 the energy proceeds from DE to DM consistent with second law allowed by observations  Alleviate the coincidence problem

21.  Thanks!!!