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Interaction between dark energy and dark matter
Bin WangShanghai JiaotongUniversity
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?
What is the Dark Energy?
Einstein introduced the Cosmological Constant to explain what was then thought to be a static Universe, “my biggest mistake . . . ”
A surprising recent discovery has been the discovery that the expansion of the Universe is accelerating.
Implies the existence of dark energy that makes up 70% of the Universe
Dark Energy maybe related to Einstein’s Cosmological Constant; its nature is a mystery.
Solving this mystery may revolutionize physics . . .
What is the Dark Energy?
We do not know what 95% of the universe is made of!
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.
The Friedmann equation
The competition between the
Decelerating effect of the mass density
and the accelerating effect of
the dark energy
density
Acceleration
Deceleration
Distancebetween galaxies
Time (Age of universe)
Beginning
Now (13.7 billion years)
Inflation (acceleration)
Closed
Acc.(-1 <w<-1/3)
Super Acc. (w<-1)
? Expand, but w>0
The fate of our universe depends on the nature of dark energy, not only the geometry
Radiation + dust)
(dark energy dominated)
Concordance Cosmology• Emerging paradigm: ‘CONCORDANCE COSMOLOGY’:
70% DE + 30% DM. • 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
Coincidence problem
w = -1
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!
Exorcising w<-1
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: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.
Evolution of the equation of state of DE
Crossing -1 behavior
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)357B. Wang, C.Y.Lin and E. Abdalla, Phys.Lett.B637(2006)357
暗物质 理论及实验
暗能量
相互作用
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 problemS.Chen, Bin Wang, J.Liang, arXiv:0808.3482; D.Pavon et al, arXiv:0806.2116 etc.
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 constraintsB. Wang, Y.G.Gong and E. Abdalla, Phys.Lett.B(2005),Phys.Lett.B(2005),
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(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:0710.1198
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 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.
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
Perturbation TheoryThe perturbed equations of motion
Zeroth component
i-th component
(He, Wang, Jing JCAP0907,030(2009)
The perturbed pressure of DE:
Perturbation Theory
QT
DM:
DE:
Perturbation Theory
We assume the phenomenological description of the interaction
between dark sectors in the comoving frame as,
TGG 8
The curvature perturbation relates
to density contrast
Perturbations
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
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
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
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)
ISW imprint of the interaction Interaction proportional to the energy density of DEW>-1
EISW+SWEISW+SW
ISW imprint of the interaction Interaction proportional to the energy density of DEW<-1
EISW+SWEISW+SW
ISW imprint of the interaction Interaction proportional to the energy density of DEW<-1
Limit on too negative coupling
EISW+SWEISW+SW
ISW imprint of the interaction Interaction proportional to the energy density of DMW<-1
EISW+SWEISW+SW
ISW imprint of the interaction Interaction proportional to the energy density of DE+DMW<-1
EISW+SWEISW+SW
Global fitting results
WMAP5+BOOMERanG,CBI,VSA,ACBAR SDSS
1. Interaction proportional to the energy density of DEW>-1
W<-1
Global fitting results
2. Interaction proportional to the energy density of DM
J.H. He, B.Wang, P.J.Zhang, PRD(09)
Global fitting results3. Interaction proportional to the energy density of DE+DM
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:0710.1198 Growth factor of the structure formationJ.He, B.Wang, Y.P.Jing, arXiv:0902.0660
……
……
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 by integrating 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:0710.1198
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 eachother, 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:0710.1198
33 galaxy clusters optical, X-ray and weak lensing data
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!!!
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, 0902.0660
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
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
arXiv:1001.0079
A lot of effort is required to disclose the signature on the interaction between DE and DM
CMBCluster M
Cluster N
WL
。。。
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.
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 -1
2.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 0th law k =const.
The 1st law d M=k dA/8πG + J d Ω+Φd Q
The 2nd law d A >0
The 3rd law k ->0
From the Classical Einstein equation:Four Laws of Black Hole mechanics:
Four Laws of Black Hole Thermodynamics:
The 0th law T=const. on the horizon
The 1st law d M= T d S + J d Ω+Φ d Q
The 2nd law d (SBH +Smatter)>=0
The 3rd law T->0
AnalogyHawking 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
18
2R g R GT
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
Consideringand 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
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!!!
