Transcript Interaction between DE/DM and its relation to the modified

Dark Matter, Dark Energy Interaction:
Cosmological Implications, Observational Signatures and
Theoretical Challenges
Bin Wang
Shanghai Jiao Tong University
May 4, 2015, Beijing
Outline
Cosmological Implications:
 Why do we need the interaction between DE&DM?
 Perturbation theory when DE&DM are in interaction
Observational Signatures:
 Is the interaction between DE&DM allowed by observations?
 CMB
 ISW effect
 Kinetic SZ
 Galaxy Cluster scale tests
 Growth factor and Structure formation
 Number of Galaxy Cluster counting
Theoretical Challenges:
 How to understand the interaction between DE&DM?
 Relation to the modified gravity
95% Unknown: 25% DM+70% DE
DE--  ?
1.
2.

QFT value 123 orders larger than the observed
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?
is not the end story to account for the cosmic acceleration
Reason for proposing Quintessence, tachyon field, Chaplygin gas
models etc.
No clear winner in sight
Suffer fine-tuning
Why do we need the interaction between DE&DM?
 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
WMAP: w=-1.06{+0.13,-0.08}
w<-1 from data is strong!
• 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 = - (f’)2/2 + V(f)
`Phantom field’ , Caldwell, 2002
• Phantoms and their ills: instabilities, negative energies…,
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: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)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) 083509.
Is Einstein’s GR successful on large scale?
Modified gravity: f(R) model ------ Extended GR by introducing
Non-minimal coupling
between DE and DM
Motivations to introduce the interaction between DE and DM:
1. Alleviate the coincidence problem
2. Accommodate the DE with w<-1
3. Relate to the study of the modified gravity
Interaction
70% Dark Energy
25% Dark Matter
The Interaction Between DE & DM
Phenomenological interaction forms:
For Q > 0 the energy proceeds from DE to DM
Phenomenological forms of Q
Signature of the interaction in the CMB
Sachs-Wolfe effects:
non-integrated
integrated
photons’ initial conditions
Early ISW
Late ISW
has the unique ability to probe the
“size” of DE: EOS, the speed of sound
Signature of the interaction
between DE and DM?
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.
The perturbed energy-monentum tenser reads
,
Perturbation Theory
The perturbed Einstein equations

g 

R

G 
The perturbed pressure of DE:

T
Perturbation Theory

   T   Q 
DM:
DE:
He, Wang, Jing, JCAP(09);
He, Wang, Abdalla, PRD(11)
We have not specified the form of
the interaction between dark
sectors.
Perturbation Equations
Phenomenological interaction forms:
Perturbation equations:
Stability in the Perturbations
Choosing interactions


 G   8 G  T 
w>-1
Maartens et al, JCAP(08)
Curvature perturbation is not stable！
Is this result general??
Stability in the Perturbations
Stable perturbation depends on the form of the interaction
and the value of the DE EoS
couplings
ξ~DE
ξ~DM
ξ~DE+DM
For
W>-1
Stable
Unstable
Unstable
constant
W<-1
Stable
Stable
Stable
DE EoS
J.He, B.Wang, E.Abdalla, PLB(09)
For time varying DE EoS, stability can be kept when DM
density appears in the coupling term for w>-1. PLB(10,11)
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
EISW+SW
 Interaction proportional to the energy density of DM & DE+DM
EISW+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
Suppression caused by ξ cannot be
distinguished from that by w
ξ ~DE
He, Wang, Abdalla, PRD(11)
Suppression caused by ξ is more than
that by w
ξ ~DM, DE+DM
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
ξ ~DE
ξ ~DM
ξ ~DE+DM
,w and ξ
Fitting results
 WMAP7-Y
He, Wang, Abdalla, PRD(11)
 WMAP+SN+BAO+H
PLANCK data: A Costa, X Xu, B Wang, E Ferreira, E Abdalla 1311.7380
Alleviate the coincidence problem
Interaction proportional to the energy density of DM
J.H. He, B.Wang, P.J.Zhang, PRD(09); J.H.He, B.Wang, E.Abdalla, PRD(11)
Sunyaev Zel'dovich effect
The thermal SZ effect
CMB photon
1% probability
Inverse
Compton
scattering
free energetic
electron in
thermal motion
distortion in the CMB spectrum
scattered CMB photon
Blue shifted,
boost CMB photon ≤1mK
218GHz
Features of TSZ effect:
1. CMB at frequency <218GHz, CMB at frequency>218GHz
2. TSZ depends on the depth of the cluster gas, distortion strong at the center,
weak at the edge
• Independent of the redshift
• Intensity of TSZ depends on the cluster mass
The kinetic SZ effect
TCMB=2.73K
electron motion
with big peculiar
velocity vp
vp: peculiar velocity
scattering probability
Interesting to
study KSZ
effect
PLANCK result: the upper limit of the
peculiar velocity can be three times of
the LCDM prediction. 1303.5090
TCMB=2.73+T
The KSZ effect
n_e: the electron density,
σ_T: the Thomson cross section
k: the Thomson optical depth
v: the peculiar velocity of the electrons
n: the unit vector along the l.o.s.
Using the comoving distance x and neglecting any interaction of electrons with
other particles,
the mean electron number density at present
the ionization fraction
peculiar momentum
p_E : gradient component
p_B: curl component
p_E: no contribution to KSZ, cancels out when integrating along the l.o.s.
p_B: contributes to KSZ
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the rotational mode of v
the cross-talk between the density and the velocity
In the linear regime, only the irrotational component of the velocity fields couples to gravity
The KSZ effect is due to the cross-talk between the density
gradient and the velocity.
The contribution of the kSZ effect to CMB:
Where,
the correlation between the density
gradient and the velocity in Fourier space
This formula is in the same form as the KSZ
effect of the LCDM model
27
These equations are formally identical to the KSZ contribution in the
concordance ΛCDM model, BUT…
In the small scale approximation k>>aH, neglect the time variation of the
potential
Interaction
Evolution of
DE, DM
perturbation;
background
density
Density
perturbation
of electrons
Velocity
field of
electrons
KSZ effect
X.D.Xu, B.Wang, P.J.Zhang,
F.Atrio-Barandela, JCAP(13)
28
ξ ~DE, w>-1
• The amplitude increases with
decreasing of coupling
• ξ >0, smaller than the LCDM
model
• ξ <0, larger than the LCDM
model
ξ ~DE, w<-1
X: upper limit from ACT
8.6uk^2 at l=3000
+: upper limit from SPT
2.8uk^2 at l=3000
ξ~DM, w<-1
Upper limits depend on:
•reionization history
•the modeling of CIB
•TSZ contribution
We just consider:
homogeneous, linear
patchy reionization,
nonlinear
29
The non-linear evolution of
matter density perturbations
enhances the kSZ effect.
Employ the halofit model
to estimate the non-linear
corrections.
Summary:
KSZ effect:
• potential,
• peculiar velocity,
• Large at big l,
• from the moment of
reionization z ~10.
ISW effect:
• time evolution of the
potential,
• at large angular scales,
• during the period of
acceleration
complementary
X.D.Xu, B.Wang, P.J.Zhang, F.Atrio-Barandela, JCAP(13)
31
To reduce the uncertainty and put tighter constraints
on the value of the coupling between DE and DM, new
observables in addition to CMB should be added.
Galaxy cluster scale test
E. Abdalla, L.Abramo, L.Sodre, B.Wang, PLB(09)
E. Abdalla, L.Abramo, J.Souza, PRD(09)
Growth factor of the structure formation
J.He, B.Wang, Y.P.Jing, JCAP(09)
Number of cluster counting
J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)
……
……
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:
The Influence of the DE perturbation on the structure formation



When
is not so tiny and
w close to -1, in subhorizon approximation,
DE perturbation is suppressed
He, Wang, Jing, JCAP(09)
Growth of structures:
The influence of the interaction between dark sectors
He, Wang, Jing, JCAP(09)
Growth Index:
The influence of the interaction between dark sectors
He, Wang, Jing, JCAP09
The interaction influence on the growth index overwhelms the
DE perturbation effect.
This opens the possibility to reveal the interaction between
DE&DM through measurement of growth factor in the future.
How does the interaction influence the structure formation?
1. The dynamics in the process of the structure formation.
Layzer-Irvine equation
Virial condition of the galaxy cluster
E. Abdalla, L.Abramo, L.Sodre, B.Wang, PLB(09)
E. Abdalla, L.Abramo, J.Souza, PRD(09)
2. Spherical collapse model.
Critical density to collapse
Number of galaxy clusters at different redshift
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: 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.
E. Abdalla, L.Abramo, L.Sodre, B.Wang, PLB(09)
J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)
Virial condition
If the DE is distributed homogeneously,
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
galaxy clusters optical, X-ray
and weak lensing data
E. Abdalla, L.Abramo, L.Sodre, B.Wang, PLB(09)
E. Abdalla, L.Abramo, J.Souza, PRD(09)
Layzer-Irvine equation for DE
For DE: starting from
Multiplying both sides of this equation by
integrating over the volume
and using continuity equation, we have:
For DE:
For 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.
J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)
Spherical collapse model
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 : DE does not trace DM
DE and DM have different four velocities
The non-comoving perfect fluids
Rest on DM frame, we obtain the energy momentum tensor for DE,
energy flux of DE
observed in DM frame
The timelike part of the conservation law,
DM
DE
Additional expansion due to peculiar velocity of DE
relative to DM
Spherical collapse model
The spacelike part of the conservation law
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
does not trace DM
J.H.He, B.Wang, E.Abdalla, D.Pavon, JCAP(10)
Press-Schechter Formalism
 J.H.He, B.Wang, E.Abdalla, D.Pavon,
JCAP(10)
A lot of effort is required to disclose the signature on the interaction
between DE and DM
CMB
Cluster M
Cluster N
kSZ
Redshift
Distortion
……
More tests are needed
Understanding the interaction between DE and DM
from Field Theory
S. Micheletti, E. Abdalla, B. Wang, PRD(09)
E. Abdalla, L. Graef, B. Wang, PLB(13)
Two fields describing each of the dark components:
a fermionic field for DM, a bosonic field for the Dark Energy,
Relating the interaction between DE and DM to the
J.H.He, B. Wang, E.Abdalla PRD(11,12)
modified gravity
Acceleration of our universe may originate from some geometric
modification from Einstein gravity.
The simplest model: f(R) gravity
R: Ricci scalar
model:
The action
conformal transformation
the action in the Einstein frame
The scalar is directly coupled to matter
Background Dynamics
Jordan frame Vin the S Einstein Iframe
f(R) gravity
Einstein frame
conformal transformation
Second order equation
Two first order equations
GR: F=df/dR=1
=0
Physical meaning of
J.H.He, B.Wang, E.Abdalla, PRD(11)
The equation of motion under the transformation
where we have used D.20
in Wald’s book
for perfect fluid and drop pressure
the equation of motion
of particles with varying
mass
We have
introduce a scalar field Γ which satisfies
50
mass dilation rate due to the
conformal transformation.
Perturbation:
(Newtonian gauge)
Jordan frame
Einstein frame
f(R) gravity
Conformal
transformation
Equivalence
The equation of motion for a free particle
Jordan frame f(R) gravity
Action
Field
equations
Conformal
transformation
Action
Conformal
transformation
Field
equations
background
dynamics
Cosmological
perturbation
Conformal
transformation
background
dynamics
Cosmological
perturbation
Einstein frame Interaction between DE and DM
mass dilation
Summary
Cosmological Implications:
 Motivation to introduce the interaction between DE & DM
Observational Signatures:
CMB+SNIa+BAO+kSZ
Galaxy cluster scale tests
 Alleviate the coincidence problem
Theoretical Challenges:
 Understanding the interaction from field theory
 Relating the interaction model with modified gravity
Report on Progress in Physics
invited review 2015
Thanks!!!