Interaction between dark energy and dark matter

Bin WangShanghai Jiao TongUniversity

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?

25% Dark Matter

70% Dark Energy

Interaction

Why do we want to introduce the interaction between dark sectors?

• DE-- ? 1. QFT value 123 orders larger than the observed2. 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

Do we need to live with Phantom?• Degeneracy in the data. SNe alone however are consistent with w in the range, roughly -1.5 ≤ weff ≤ -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 M42 H2 = - (’)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!

Do we need to live with Phantom?

Theoretical cosmology

w<-1 from data is strong!

Theoretical prejudice against w<-1 is strong!

Exorcising w<-1

Ghostless explanations:

1) Modified gravity affects EVERYTHING, with the effect to make w<-1.

S. Yin, B. Wang, E.Abdalla, C.Y.Lin, arXiv:0708.0992, PRD (2007)

A. Sheykhi, B. Wang, N. Riazi, Phys. Rev. D 75 (2007) 123513

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

B. Wang, Y.G.Gong and E. Abdalla, Phys.Lett.B624(2005)141Phys.Lett.B624(2005)141

B. Wang, C.Y.Lin and E. Abdalla, Phys.Lett.B637(2006)357.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) 083509.

MAYBE NOT!!•Conspiracies are more convincing if they DO NOT rely on supernatural elements!

The Interaction Between DE & DM

Phenomenological interaction forms:

For Q > 0 the energy proceeds from DE to DM

Phenomenological forms of Q

Stephen Hawking

S=A/4

小魔镜

让天文观测来告诉我们答案吧

魔镜啊，魔镜，

暗物质和暗能量有相互作用吗？

Is the interaction between DE & DM allowed by observations?

Universe expansion history observations:SNIa+CMB+BAO+Age constraints

B. Wang, Y.G.Gong and E. Abdalla, Phys.Lett.B(05),Phys.Lett.B(05),

B. Wang, C. Lin, E. Abdalla, PLB (06) B. Wang, C. Lin, E. Abdalla, PLB (06) B.Wang, J.Zang, C.Y.Lin, E.Abdalla, S.Micheletti, Nucl.Phys.B(07)

C.Feng, B.Wang, Y.G.Gong, R.K.Su, JCAP (07);

C.Feng, B.Wang, E.Abdalla, R.K.Su, PLB(08),

J.He, B.Wang, JCAP(08),

J.H. He, B.Wang, P.J.Zhang, PRD(09)

J.H.He, B.Wang,E.Abdalla, PRD(11), X.D.Xu, J.H.He, B.Wang (11)

Galaxy cluster scale testE. Abdalla, L.Abramo, L.Sodre, B.Wang, PLB(09)

J.H.He, B.Wang, Y.P.Jing, JCAP(09)

J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)

Signature of the interaction in the CMB

Sachs-Wolfe effects:non-integrated photons’ initial conditions

integrated Early ISW

Late ISWhas the unique ability to probe the

“size” of DE: EOS, the speed of sound

Signature of the interaction between DE and DM?

The Sachs-Wolfe EffectThe Sachs-Wolfe effect is an imprint on the cosmic

microwave background(CMB) that results from gravitational potentials shifting the frequency of CMB photons as they leave the surface of last scattering and are eventually observed on Earth.

Two categories of Sachs-Wolfe effects alters the CMB:

non-integrated

integrated

The Non-Integrated Sachs-Wolfe Effect The non-integrated Sachs-Wolfe effect takes place at the

surface of last scattering and is a primary anisotropy. The photon frequency shifts result from the photons

climbing out of the potential wells at the surface of last scattering created by the energy density in the universe at that point in time.

The effect is not constant across the sky due to the perturbations in the energy density of the universe at the time the CMB was formed.

The non-integrated Sachs-Wolfe effect reveals information about the photons’ initial conditions

The Integrated Sachs-Wolfe Effect It appears as the photons pass through the universe on their way

to Earth.

the photons encounter

additional gravitational

potentials and gain & lose energy.one would expect these changes to cancel out over time, but the wells themselves

can evolve, leading to a net change in energy for the photons as they travel.

Why this is the integrated Sachs-Wolfe effect: the effect is integrated over the photon’s total passage through the universe.

The integrated Sachs-Wolfe effect leaves evidence of the change of space as the photon traveled through it

The Integrated Sachs-Wolfe Effect The early ISW effect: takes place from the time following

recombination to the time when radiation is no longer dominant

The early ISW gives clues about what is happening in the universe at the time when radiation ceases to dominate the energy in the universe.

The late ISW effect: gives clues about the end of the matter dominated era.

When matter gives way to DE, the gravitational potentials decay away. Photons travel much farther.

During the potential decay, the photons pass over many intervening regions of low and high density, effectively cancelling the late integrated Sachs-Wolfe effect out except at the very largest scales.

The late ISW effect has the unique ability to probe the “size” of DE: EOS, the speed of sound …… Bean, Dore, PRD(03)

Perturbation theory when DE&DM are in interaction

Choose the perturbed spacetime

DE and DM, each with energy-momentum tensordenotes the interaction between different components.

,

The perturbed energy-monentum tenser reads

Perturbation TheoryThe perturbed Einstein equations

G

TR

g

The perturbed pressure of DE:

Perturbation Theory

QT

DM:

DE:

He, Wang, Jing, JCAP(09);

He, Wang, Abdalla, PRD(11)

We have not specified the form of the interaction between dark sectors.

Perturbations

Phenomenological interaction forms:

Perturbation equations:

PerturbationsChoosing interactions

Maartens et al, JCAP(08)

Curvature perturbation is not stable！

Is this result general??How about the other forms of the

interaction? Stable??

How about the case with w<-1?

w>-1

TGG 8

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

couplings DE DM Total

W>-1 Stable Unstable Unstable

W<-1 Stable Stable Stable

the interaction proportional to DM density

ISW imprint of the interaction

The analytical descriptions for such effect

ISW effect is not simply due to the change of the CDM perturbation. The interaction enters each part of gravitational potential.

J.H. He, B.Wang, P.J.Zhang, PRD(09)

J.H.He, B.Wang, E.Abdalla, PRD(11)

Imprint of the interaction in CMB Interaction proportional to the energy density of DE

Interaction proportional to the energy density of DM & DE+DM

EISW+SWEISW+SW

EISW+SWEISW+SW

J.H.He, B.Wang, P.J.Zhang, PRD(09)

Degeneracy between the ξ and w in CMB The small l suppression caused by changing ξ can also be

produced by changing w ξ can cause the change of acoustic peaks but w cannot

ξ ~DE ξ ~DM, DE+DM

Suppression caused by ξ is more than that by w

Suppression caused by ξ cannot be distinguished from that by w

He, Wang, Abdalla, PRD(11)

Degeneracy between the ξ and The change of the acoustics peaks caused by ξ can also

be produced by the abundance of the cold DM

To break the degeneracy between ξ and , we can look at small l spectrum. ξ can bring clear suppression when ξ~DM or DM+DE, but not for ξ~DE

Likelihoods of ,w and ξ ξ ~DE

ξ ~DM

ξ ~DE+DM

Fitting results WMAP7-Y

WMAP+SN+BAO+H

He, Wang, Abdalla, PRD(11)

Alleviate the coincidence problem

Interaction proportional to the energy density of DM

J.H. He, B.Wang, P.J.Zhang, PRD(09)

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

J.H.He,B.Wang, Y.P.Jing, JCAP(09)

Growth of structuresThe 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 structuresIn 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 structuresThe 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

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, JCAP09

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)   Growth factor of the structure formationJ.He, B.Wang, Y.P.Jing, JCAP(09)

Number of galaxy counting J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)

……

……

Layzer-Irvine equation for DM

Layzer-Irvine equation describes how a collapsing system reaches dynamical equilibrium in an expanding universe

For DM:For DM: the rate of change of the peculiar velocity is

Neglecting the influence of DE and the couplings, ---Newtonian mechanics

Multiplying both sides of this equation by integrating over the volume

and using continuity equation,

describes how DM reaches dynamical equilibrium in the collapsing system in the expanding universe.

J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)

Virial conditionIf the DE is distributed homogeneously,

For DM:For DM:

For a system in equilibrium

Virial Condition:

presence of the coupling between DE and DM changes the equilibrium configuration of the system Galaxy clusters are the largest virialized structures in the universe

Comparing the mass estimated through naïve virial hypothesis with that from WL and X-ray

33 galaxy clusters optical, X-ray and weak lensing data

E. Abdalla, L.Abramo, L.Sodre, B.Wang, PLB(09)

Layzer-Irvine equation for DEFor DE: For DE: starting from

Multiplying both sides of this equation by integrating over the volume

and using continuity equation, we have:

For For DE: DE:

For For DM: DM:

The time and dynamics required by DE and DM to reach equilibrium are different in the collapsing system.

DE does not fully cluster along with DM.DE does not fully cluster along with DM.The energy conservation breaks down inside the collapsing system. J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)

Spherical collapse model

Homogenous DE :Homogenous DE :In the background:

The energy balance equation

Friedmann equation

In the spherical region:

Raychaudhuri’s equation – dynamical motion of the spherical region

Local expansion

The energy balance equation in the spherical region:

DM perturbation equation

Spherical collapse model

Inhomogenous DE : Inhomogenous DE : DE does not trace DMDE and DM have different four velocities

Rest on DM frame, we obtain the energy momentum tensor for DE,

The non-comoving perfect fluids

energy flux of DE observed in DM frame

The timelike part of the conservation law,

DMDM

DEDE

Additional expansion due to peculiar velocity of DE relative to DM

The spacelike part of the conservation law

Spherical collapse model

Only DE has non-zero component

is the DE flux observed in DM rest frame

Only keep linear, we obtain:

Raychaudhuri’s equation We can describe the spherical collapse model when DE We can describe the spherical collapse model when DE does not trace DMdoes not trace DM

J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)

Press-Schechter Formalism

J.H

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g, E

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D.P

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DE interacting DM will influence:• the dynamics of structure formation• the number of galaxy clusters formed

The imprint of the interaction between dark sectors in galaxy clusters

Authors: Jian-Hua He, Bin Wang, Elcio Abdalla, Diego Pavon

JCAP(2010)

Referee reportThe authors study the dynamics of a collapsing system within the framework

of interacting dark matter and dark energy. They find that the interaction

between dark sectors does not ensure the dark energy to fully cluster along

with dark matter. The authors present a new treatment of studying the

structure formation in the spherical collapsing system in the case where dark

energy does not cluster together with dark matter. The paper is concluded

by examining the cluster number counts dependence on the interaction between

dark sectors and analyze how dark energy inhomogeneities affect cluster

abundances. Quite interestingly, it is shown that cluster number counts

can provide specific signature of dark sectors interaction and dark energy

Inhomogeneities.

I believe this article presents some quite interesting and original result of

interest for both theoretical cosmologists as well as observational ones. So I

recommend it for publication in JCAP

A lot of effort is required to disclose the signature on the interaction between DE and DM

CMBCluster M

Cluster N

WL

Redshift Distortion

……

Understanding the interaction between DE and DM from

Field Theory

S. Micheletti, E. Abdalla, B. Wang, PRD(09)

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.

Summary Motivation to introduce the interaction between DE & DM

Is the interaction allowed by observations? CMB+SNIa+BAO+Age

Galaxy cluster scale tests

Alleviate the coincidence problem

Understanding the interaction from field theory

Thanks!!!