Bin Wang Fudan University Shanghai Interaction between dark energy and dark matter

Outline  Why do we need the interaction between DE&DM?  Is the interaction between DE&DM allowed by observations?  Perturbation theory when DE&DM are in interaction  How to understand the interaction between DE&DM?

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) The Friedmann equation The competition between the Decelerating effect of the mass density and the accelerating effect of the dark energy density

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

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 The period when energy densities of DE and DM are comparable is longer The coincidence problem is less acute can be achieved by a suitable interaction between DE & DM

Coincidence problem We pay attention to the ratio of energy densities between DE and DM, and its evolution. The positive coupling 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!!!

Do we need to live with Phantom? Degeneracy in the data. SNe alone however are consistent with w in the range, roughly -1.5 ≤ w eff ≤ -0.7 Hannestad et al, Melchiorri et al, Carroll et al WMAP 3Y(06) w=-1.06{+0.13,-0.08} One can try to model w<-1 with scalar fields like quintessence. But that requires GHOSTS: fields with negative kinetic energy, and so with a Hamiltonian not bounded from below: 3 M 4 2 H 2 = - ( ’ ) 2 /2 + V(  ) `Phantom field ’, Caldwell, 2002 Phantoms and their ills: instabilities, negative energies …, w<-1 from data is strong! Theoretical prejudice against w<-1 is strong!

MAYBE NOT! Conspiracies are more convincing if they DO NOT rely on supernatural elements! Ghostless explanations: 1) Modified gravity affects EVERYTHING, with the effect to make w<-1. S. Yin, B. Wang, E.Abdalla, C.Y.Lin, arXiv: , PRD (2007) A. Sheykhi, B. Wang, N. Riazi, Phys. Rev. D 75 (2007) R.G. Cai, Y.G. Gong, B. Wang, JCAP 0603 (2006) 006 2) Another option: Interaction between DE and DM Super-acceleration (w<-1) as signature of dark sector interaction Phys.Lett.B624(2005)141 B. Wang, Y.G.Gong and E. Abdalla, Phys.Lett.B624(2005)141 B. Wang, C.Y.Lin and E. Abdalla, Phys.Lett.B637(2006)357. S. Das, P. S. Corasaniti and J. Khoury, Phys.Rev. D73 (2006)

Evolution of the equation of state of DE  Crossing -1 behavior Phys.Lett.B624(2005)141 B. Wang, Y.G.Gong and E. Abdalla, Phys.Lett.B624(2005)141 B. Wang, C.Y.Lin and E. Abdalla, Phys.Lett.B637(2006)357

The Interaction Between DE & DM 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 et al) Q>0 accelerated scaling attractor to alleviate the coincidence problem S.Chen, Bin Wang, J.Liang, arXiv: ; D.Pavon et al, arXiv: etc.arXiv: arXiv: For Q > 0 the energy proceeds from DE to DM Phenomenological interaction forms: Phenomenological forms of Q Constrain Q from SNIa+CMB+BAO+LookBack Time Not specify any special DE model, but using

 Is the interaction between DE & DM allowed by observations? Universe expansion history observations: SN constraint CMB BAO Age constraints Phys.Lett.B(2005), B. Wang, Y.G.Gong and E. Abdalla, Phys.Lett.B(2005), B. Wang, C. Lin, E. Abdalla, PLB (06) B.Wang, J.Zang, C.Y.Lin, E.Abdalla, S.Micheletti, Nucl.Phys.B(2007) C.Feng, B.Wang, Y.G.Gong, R.Su, JCAP (2007); C.Feng, B.Wang, E.Abdalla, R.K.Su, PLB(08), J.He, B.Wang, JCAP(08) Galaxy cluster scale test ……. E. Abdalla, L.Abramo, L.Sodre, B.Wang, PLB(09) arXiv:

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

Age constraints Simple models Interacting DE&DM model

Universe expansion history observations: SN Ia data BAO measurement from SDSS CMB shift parameter age estimates of 35 galaxies

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

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), J.He, B.Wang, JCAP(08), The tendency shows that the coupling is a small positive.

To reduce the uncertainty and put tighter constraint on the value of the coupling between DE and DM, new observables should be added. Galaxy cluster scale test E. Abdalla, L.Abramo, L.Sodre, B.Wang, PLB(09) arXiv: Growth factor of the structure formation J.He, B.Wang, Y.P.Jing, arXiv: ……

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

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.

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:

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

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.

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, PLB (09) arXiv: galaxy clusters optical, X-ray and weak lensing data

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

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.

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, GRG(09) ArXiv:

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>0, the coincidence problem is less acute!!!

Perturbation theory when DE&DM are in interaction Choose the perturbed spacetime DE and DM, each with energy-momentum tensor denotes the interaction between different components. Project along the space direction by using, we have is the acceleration. For the homogeneous and isotropic universe For the DM particle, its world line is the geodesic, The spatial part of vanishes. There is no momentum transfer between dark sectors. For the whole system:

Perturbations The perturbed energy-momentum tensor: we shall neglect the intrinsic momentum transfer the intrinsic momentum transfer can produce acoustics in the DM fluid as well as pressure which may resist the attraction of gravity and hinder the growth of gravity fluctuations during tightly coupled photon baryon period, The perturbed pressure of DE:

Perturbations Phenomenological interactions between DE and DM Special cases: Perturbation equations:

Perturbations Assuming: By using the gauge-invariant quantity and letting the adiabatic initial condition, The curvature perturbation relates to density contrast by

Perturbations Choosing interactions Maartens et al, JCAP(08) Curvature perturbation is not stable ！ Is this result general?? How about the interaction proportional to DE energy density case? Stable?? How about the case with w<-1? W>-1

Perturbations divergence divergence disappears Stable perturbation J.He, B.Wang, E.Abdalla, PLB(09) the interaction proportional to DE density W>-1 W<-1, always

Growth of structures Observations of cosmic expansion history alone cannot break the degeneracies among different models explaining the cosmic acceleration. The rate of expansion of the universe as a function of cosmic time can in turn affect the process of structure formation Studying the clustering properties of cosmic structure to detect the possible effects of DE The contribution of non-vanishing DE perturbations, are fundamental in determining the DE clustering properties, have effects on the evolution of the growth of DM perturbations He, Wang, Jing,

Growth of structures The perturbation metric:

Growth of structures In the Fourier space, the perturbed energy-momentum equations read: Using gauge invariant quantities, the perturbed Einstein equations read:

Growth of structures Using the gauge invariant quantities, DM perturbation Gauge invariant DE perturbation

Growth of structures In the subhorizon approximation k>>aH, DM perturbation DE perturbation Introducing the interaction In the subhorizon approximation k>>aH

Growth of structures Perturbation equations for dark sectors with constant w

Growth of structures The coupling between dark sectors in proportional to the DM energy density by setting while keeping nonzero,

Growth of structures  When is not so tiny and  w close to -1, in subhorizon approximation,  DE perturbation is suppressed

Growth of structures

The interaction influence on the growth index overwhelm the DE perturbation effect. This opens the possibility to reveal the interaction between DE&DM through measurement of growth factor in the future. He, Wang, Jing,

Understanding the interaction between DE and DM from Field Theory S. Micheletti, E. Abdalla, B. Wang,

Two fields describing each of the dark components: a fermionic field for DM, a bosonic field for the Dark Energy,

similar to the one usually used as a phenomenological model, RHS does not contain the Hubble parameter H explicitly, but it does contain the time derivative of the scalar field, which should behave as the inverse of the cosmological time, replacing thus the Hubble parameter in the phenomenological models.

compare the interacting DE with the observational data SNIa + CMB shift + BAO + age of galaxy clusters diagram is unbounded for negative β, its allowed values are, generally speaking, negative: Most of the allowed values are negative if there is a coupling connecting the dark sectors, it is more probable for the dark energy to decay into dark matter

Results: The sign of β is important, and being negative, in consistent with DE decaying into DM The interaction is consistent with the observations at one standard deviation. Look for more sophisticated theoretical field models: 1. Have w crossing The comparison with the structure formation

Understanding the interaction between DE and DM from thermodynamics B. Wang, C.Lin, D. Pavon, E.Abdalla,PLB(08)

The 0 th lawk =const. The 1 st lawd M=k dA/8πG + J d Ω+Φd Q The 2 nd lawd A >0 The 3 rd lawk ->0 From the Classical Einstein equation: Four Laws of Black Hole mechanics: Four Laws of Black Hole Thermodynamics: The 0 th law T=const. on the horizon The 1 st law d M= T d S + J d Ω+Φ d Q The 2 nd law d (S BH +S matter )>=0 The 3 rd law T->0 Analogy Hawking Radiation Identity

B. Can we derive the Einstein equation from thermodynamics? A. How did the classical GR know that the horizon area =S, surface gravity=T? Einstein Gravity Thermodynamics?? T. Jacobson was the first who asked this question. T.Jacobson, Phys. Rev. Lett. 75 (1995) 1260 Thermodynamics of Spacetime: The Einstein Equation of State

Some related works: (1) A. Frolov and L. Kofman, JCAP (2003) (2) Ulf H. Daniesson, PRD (2005) (3) R. Bousso, PRD (2005) (4) Cai, JHEP(05) In the cosmological context

Einstein equation has a predisposition to thermodynamic behavior Is the obtained relation between thermodynamics and the Einstein equation just an accident? Does the connection between thermodynamics and gravity hold in all spacetimes and even beyond Einstein gravity? Does it imply something in deep? Braneworld models with correction terms, 4D scalar curvature from IG on the brane + 5D GB curvature term --MOST general model Thermodynamics Gravity: Deep understanding on the entropy of the GB braneworld (A. Sheykhi, B. Wang, R.G.Cai, Nucl.Phys.B 2007; PRD 2007)

Gravity Thermodynamics not just an accident, deep physical meaning sheds lights on Holgraphy Whether the thermodynamics can shed some lights on the interaction between DE nd DM? B. Wang, C.Lin, D. Pavon, E.Abdalla,PLB(08)

Understanding the interaction between DE & DM  The entropy of the dark energy enveloped by the cosmological event horizon is related to its energy and the pressure in the horizon by the Gibb's equation Considering and using the equilibrium temperature associated to the event horizon we get the equilibrium DE entropy described by Now we take account of small stable fluctuations around equilibrium and assume that this fluctuation is caused by the interaction between DE and DM. It was shown that due to the fluctuation, there is a leading logarithmic correction to thermodynamic entropy around equilibrium in all thermodynamical systems, C>0 for DE domination. Thus the fluctuation is indeed stable

Understanding the interaction between DE & DM  the entropy correction reads This entropy correction is supposed arise due to the apparence of the coupling between DE and DM. Now the total entropy enveloped by the event horizon is from the Gibb's law we obtain where is the EOS of DE when it has coupling to DM If there is no interaction, the thermodynamical system will go back to equilibrium and the system will persist equilibrium entropy and

Understanding the interaction between DE & DM  With interaction:

Understanding the interaction between DE & DM

 Comparing to simple model Our interacting DE scenario is compatible with the observations.

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  Perturbation theory and growth of structure  Understanding the interaction from field theory and thermodynamics

 Thanks!!!

The Cosmic Triangle  The Friedmann equation The competition between the Decelerating effect of the mass density and the accelerating effect of the dark energy density