Post on 25-Aug-2020
Jul. 12, 2017 @ DSU
Based on T. Binder, L. Covi, AK, H. Murayama, T. Takahashi, N. Yoshida, JCAP, 2016AK, K. Kohri, T. Takahashi, N. Yoshida, PRD, 2016AK, T. Takahashi. arXiv:1703.02338
1
Sudden kinetic decoupling of dark matter
Ayuki Kamada (IBS-CTPU)
see also talks by Pyungwon Ko & Joern Kersten
2
: chemical interactionthe number of DM is NOT conserved.the energy&momentum of DM are redistributed.
: kinetic interactionthe number of DM is conserved.the energy&momentum of DM are redistributed.
At the chemical decoupling,the number density of DM freezes out.
Observational consequence:relic abundance of DM
After the kinetic decoupling, DM streams freely.
Observational consequence: minimum mass of protohalo
Yiel
d
Time
DM-thermal bath interaction
DM DM
TP TP
3Fokker-Planck approximation
Fokker-Planck approximation: expanding the collision term w.r.t.i.e., the momentum change per collision the typical DM momentum
q/p ⌧ 1
T. Binder, L. Covi, AK, H. Murayama, T. Takahashi, N. Yoshida, JCAP, 2016
qp⌧
Bringmann et al., JCAP, 2007 Bringmann, New J. Phys, 2009
It is computationally challenging to follow the momentum redistribution through the kinetic interaction
Bertschinger, PRD, 2006 Gondolo et al., PRD, 2012
Boltzmann equation:
_____________________well-established
____hard to deal with
Ma et al., ApJ, 1995
⇥Pµ@
x
µ � �µ
�
PP�@P
µ
⇤f = C[f ]
4Fokker-Planck equation
__momentum transfer squared
______thermal momentum squared
differential cross section
MODEL-INDEPENDENT!
C[fDM] = mDM@
@pDMi
"�
✓mDMT
@fDM
@pDMi+ (pDMi �mDMui)fDM
◆#
� =1
6mDMT
X
sTP
Zd3pTP
(2⇡)3f eqTP(1⌥ f eq
TP)
Z 0
�4p2TP
dt(�t)d�
dtv
/ p2 / q2
T. Binder, L. Covi, AK, H. Murayama, T. Takahashi, N. Yoshida, JCAP, 2016Gondolo et al., PRD, 2012
Homogeneous and isotropic solution: Maxwell-Boltzmann distribution
with (coupled) → (decoupled) → (with monotonically decreasing faster than )
f0 =
n
g�
✓2⇡
m�T�0
◆3/2
exp
✓� q2
2a2m�T�0
◆
d ln(a2T�0)
d⌧= 2�0a
✓T0
T�0� 1
◆
: temperature : bulk velocityof thermal bath plasma
Tu
µ(x)
�/H > 1�/H < 1 T�0 / 1/a2
T�0 = T0 / 1/a
� 1/a Waldstein et al., PRD, 2017
→kinetic decoupling
temperature
�/H = 1
T kd
5
Evolution equations (synchronous gauge)
DM fluid variables: : density perturbation : bulk velocity potential : anisotropic inertia : entropy perturbation
DM perturbations
�✓�⇡
/: for Perfect fluid/: for Imperfect fluid
DM sound speed:
c2� =
T�0
m�
✓1� 1
3
d lnT�0
d ln a
◆
Fluid approximation - a closed set of equations
� = �✓ � 1
2h
✓ = � a
a✓ � k2� + k2(c2�� + ⇡) + �0a(✓TP � ✓)
� = �2a
a� � k
✓2T0
m�
◆3/2 ✓21
4f03 + f11
◆+
4
3
T0
m�✓ +
2
3
T0
m�(h+ 6⌘)� 2�0a�
⇡ = �2a
a⇡ +
5
4k
✓2T0
m�
◆3/2
f11 �1
a2d(a2c2�)
d⌧� �
✓5
3
T0
m�� c2�
◆✓ � 1
2
✓5
3
T�0
m�� c2�
◆h
�2�0a
⇡ � T1
m��✓
T0
m�� c2�
◆�
�+ 2�0a
✓T0
T�0� 1
◆T�0
m�
�1�0
T. Binder, L. Covi, AK, H. Murayama, T. Takahashi, N. Yoshida, JCAP, 2016Bertschinger, PRD, 2006 Ignoring the free
streaming after the kinetic decoupling
6Implications for structure formationVogelsberger et al., MNRAS, 2016
observed
cum
ulat
ive
num
ber o
f sub
halo
s
dim
ensi
onle
ss m
atte
r pow
er s
pect
rum
wave number
maximal circular velocity of subhalo
missing satellite problem
Suppressed matter density perturbations at galactic scales, → possible solution to the small scale issues in the standard CDM model
oscillation scale : comoving sound horizon at the
kinetic decoupling
T kd = O(1) keV
ks
7Question we have addresseddi
men
sion
less
mat
ter p
ower
spe
ctru
m
wave number
Damped oscillation
Acoustic damping≠ collisionless/free-streaming damping (SM neutrinos)≠ diffusion/Silk damping (baryons affected by the photon free-streaming)
What determines the damping scale?- collisionless/free-streaming damping→ free-streaming scale of DM- diffusion/Silk damping→free-streaming scale of radiation
Loeb et al., PRD, 2005
Vogelsberger et al., MNRAS, 2016
AK, K. Kohri, T. Takahashi, N. Yoshida, PRD, 2016AK, T. Takahashi. arXiv:1703.02338
8Electrically charged DM
10-15
10-10
10-5
100
105
P(k)
[h-3
Mpc
3 ]
mCh=1010 GeVmCh=1011 GeVmCh=1012 GeVstandard CDM
-1-0.5
0 0.5
1
10-4 10-3 10-2 10-1 100 101 102 103 104
P(k)
/P(k
) sta
ndar
d C
DM
-1
k [h Mpc-1]
recombination
e-+e+ pair annihilation
wave number
linea
r mat
ter p
ower
spe
ctru
m
AK, K. Kohri, T. Takahashi, N. Yoshida, PRD, 2016
Undamped oscillation!!
( ) 10-10
10-8
10-6
10-4
10-2
100
102
104
106
108
10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2
γ/H
a
mCh=108 GeVmCh=109 GeV
mCh=1010 GeVmCh=1011 GeVmCh=1012 GeV
e-+e+ pair annihilation
scale factorreac
tion
rate
per
Hub
ble
time
recombination
re-coupling
steep/sudden drop of at the kinetic decoupling
(n~20)
�/H
�/H / 1/an+4 �/H ⇡ 1
CHAMP (CHArged Massive Particle)
Rujula et al., Nucl. Phys B, 1990
9Simplified realization
Suppose a simplified model, where SM is extended with DM fermion ( ) and light Dirac fermions ( ) coupled to a mediator boson ( )
� ⌫�
LS � g����+ g⌫ ⌫�⌫
LV � g���µ��µ + g⌫ ⌫�
µ⌫�µ
LPS � ig����5�+ ig⌫ ⌫��
5⌫
χ φ νχφ ↔ χφ φ ↔ νν
for χ
χ φ νχφ ↔ χφ φ ↔ νν
for χ
Tν ≫ mφ
Tν ≪ mφ
time
χν ↔ χν
χν ↔ χν
for χ for φ
φ ↔ ννχφ ↔ χφ
for χ for φ
LPV � g���µ�5��µ + g⌫ ⌫�
µ�5⌫�µ
kinetic decoupling occurs when
and thusAK, T. Takahashi. arXiv:1703.02338
T⌫ < m�
n� / e�m�/T⌫
r = T⌫/T�
10Reaction rate & resultant matter power spectra
scale factorreac
tion
rate
per
Hub
ble
time
wave number
linea
r mat
ter p
ower
spe
ctru
m
�ϕ=� ���
�ϕ=�γ/�=�
�ν=�ϕ
αχ=�×��-�
�χ=� ����=��
��-� ��-� ��-� ��-� ��-���-����-����-���-���-���-���-������������������
�
γ/�
����ϕ=� ���αχ=�×��-�
�χ=� ���=��
��-���-���-���-���-���-���-���-���
�(�)
[���
� /�� ]
��� ���-���-������������������
� [�/�]
�(�)/�
���(�)-�
(Quasi-)undamped oscillation!!
( )
steep/sudden drop of at the kinetic decoupling
(n~10)
�/H / 1/an+4 �/H ⇡ 1
�/H
: perfect fluid : perfect fluid dark radiation⌫� see the paper
AK, T. Takahashi. arXiv:1703.02338
11Evolution of adiabatic perturbations
wave number
linea
r mat
ter p
ower
sp
ectru
m ra
tio to
the
stan
dard
CD
M m
odel
����ϕ=� ���αχ=�×��-�
�χ=� ���=��
��-���-���-���-���-���-���-���-���
�(�)
[���
� /�� ]
��� ���-���-������������������
� [�/�]
�(�)/�
���(�)-�
��
δχ
θχ/�(×��)
θν/�(×��)
�=�� �/���
�ϕ=� ���αχ=���×�-�
�χ=� ���=��
��-� ��-�-�
-�
-��
�
��
�
�
�
��
δχ
θχ/�(×��)
θν/�(×��)
�=��� �/��
�ϕ=� ���αχ=���×�-�
�χ=� ���=��
��-� ��-� ��-�-�
-��
-��
�
��
��
�
�
intermittent collision - effectively taken an average
over many oscillation
AK, T. Takahashi. arXiv:1703.02338
12Damping scale
wave numberlinea
r mat
ter p
ower
sp
ectru
m ra
tio to
the
stan
dard
CD
M m
odel
����ϕ=� ���αχ=�×��-�
�χ=� ���=��
��-���-���-���-���-���-���-���-���
�(�)
[���
� /�� ]
��� ���-���-������������������
� [�/�]
�(�)/�
���(�)-�
These observations infer the following criterion for the damping scale of dark acoustic oscillation: : sound speed , of the plasma (usually )
1
�0/H
d(�0/H)
dt
����0=H
=kdampcs
a
cs
1/p3
Analytical approaches (see the paper) implies for ,
which is concordant with the above criterion (up to )
�/H / 1/an+4
2/⇡
kdamp =2(n+ 4)
⇡ks
(n~10)
( )�/H / 1/an+4 �/H ⇡ 1
ks kdamp
_________________(duration of the kinetic decoupling)-1
_______(oscillation period)-1
AK, T. Takahashi. arXiv:1703.02338
13Summary and conclusion
- Kinetic decoupling of DM leaves dark acoustic oscillation on the matter distribution of the Universe, which provides an invaluable hint on the nature of DM.
- The density perturbations at peak wavenumbers can be larger than those in the standard CDM model.The damping scale is determined by equating the duration of the kinetic decoupling and acoustic oscillation period.
- Imprints of such enhanced dark acoustic oscillation on the non-linear matter distribution are worth investigating by performing N-body simulations in future work.
15Effects of collisionless damping of DM
wave number
linea
r mat
ter p
ower
spe
ctru
m
��������� ��� �������� ��� �ϕ=� ���αχ=���×��-�
�χ=� ���→��� ���
�=��
��� �����-���-���-���-���-���-���-���-���
� [�/���]
�(�)
[���
� /�� ]
: perfect fluid dark radiation⌫
The collisionless damping of DM does not spoil the dark acoustic oscillation, but introduce an additional damping scale
16Effects of collisionless damping of radiation
linea
r mat
ter p
ower
spe
ctru
m
wave number
���������-�� ����� �� ��ϕ=� ��αχ=���×��-�
�χ=� ��=��
��� �����-���-���-���-���-���-���-���-���
� [�/���]
�(�)
[���
� /�� ]
: perfect fluid�
The collisionless damping of radiation completely changes the dark acoustic oscillation
17
10�3 10�2 10�1 100
k [Mpc�1]
101
102
103
104
105
P(k,
z=0)
[Mpc
3 ]
SDSS DR7 (Reid et al. 2010)LyA (McDonald et al. 2006)ACT CMB Lensing (Das et al. 2011)ACT Clusters (Sehgal et al. 2011)CCCP II (Vikhlinin et al. 2009)BCG Weak lensing(Tinker et al. 2011)ACT+WMAP spectrum (this work)
pow
er s
pect
rum
wave number
Hlozek et al., ApJ, 2012
ΛCDM (linear)
Large scale structure of the Universe
The ΛCDM model reproduces wellthe large scale (>Mpc) structure of the Universe
+non-linear evolution
18
10�3 10�2 10�1 100
k [Mpc�1]
101
102
103
104
105
P(k,
z=0)
[Mpc
3 ]
SDSS DR7 (Reid et al. 2010)LyA (McDonald et al. 2006)ACT CMB Lensing (Das et al. 2011)ACT Clusters (Sehgal et al. 2011)CCCP II (Vikhlinin et al. 2009)BCG Weak lensing(Tinker et al. 2011)ACT+WMAP spectrum (this work)
Cold Dark Matter?
pow
er s
pect
rum
wave number
?Small scale matter density fluctuations, especially their deviations from the ΛCDM model, contain imprints of the nature of DM
cold dark matter:null thermal velocityonly gravitationally interacting
particle physics DM candidates:finite (sizable) thermal velocityinteracting in many ways
hypothetical Hlozek et al., ApJ, 2012
19
missing satellite problem
maximal circular velocity of subhalo
cum
ulat
ive
num
ber o
f sub
halo
s
Vmax≃208 km/sVmax≃160 km/s
Kratsov, Advances in Astronomy, 2010
N-body (DM-only) simulations in the ΛCDM model → Milky Way-size halos host O(10) times larger number of subhalos than that of observed dwarf spheroidal galaxies
Small scale crisis I
When N-body simulations in the ΛCDM model and observations are compared, problems appear at (sub-)galactic scales: small scale crisis
V 2circ(r) =
GM(< r)
r
circular velocity
20
α=1 (NFW)
α=0 (isothermal)
field dwarf spheroidal galaxies~109 Msun
Oh et al., AstroJ, 2011
Small scale crisis IIcusp vs core problem
NFW profile
N-body (DM-only) simulations in ΛCDM model → Universal DM profile independent of halo size: NFW profile
⇢DM(r) =⇢s
r/rs(1 + r/rs)2
⇢DM(r) / r�↵
isothermal profile
Observations infer core profile in the inner region rather than cuspy NFW profile
⇢DM(r) = ⇢0DM
(1 (r ⌧ r0)
(r0/r)2 (r � r0)
inner profile
norm
aliz
ed m
ass
dens
ity
normalized radius
21
Boylan-Kolchin et al., MNRAS, 2011
too big to fail problem
Small scale crisis III
N-body (DM-only) simulations in ΛCDM model →~10 subhalos with deepest potential wells in Milky Way-size halos do not have observed counterparts (dwarf spheroidal galaxies)
circ
ular
vel
ocity
of s
ubha
los
MW-like halos
radius
22
Baryonic processes
too dim
Sawala et al., MNRAS, 2016Possible solution IAbove Discussions are based onN-body (DM-only) simulations in the ΛCDM model
Gravitational potentials are shallower at smaller scales →Baryonic heating and cooling processes may be important
- heating from ionizing photons - ionizing photons emitted and spread around reionization of the Universe heat and evaporate gases
- mass loss by supernova explosions - supernova explosions blow gases from inner region -> DM redistribute along shallower potential
cum
ulat
ive
num
ber o
f sat
ellit
es/s
ubha
los
stellar mass of satellite, mass of subhalo
23
Possible solution II
alternative models ↔ nature of DM- Warmness - thermal velocities induce pressure of DM fluid and prevent gravitational growth (Jeans analysis)
- Interactions with relativistic particles - DM fluid couples to relativistic particles in a direct/indirect manner
- Self-interaction - induced heat transfer of DM fluid heats DM particles in inner region and flatten inner profile
Above Discussions are based onN-body (DM-only) simulations in the ΛCDM model
24Physical meaning
Fokker-Planck equation - diffusion equation:
- random walk in the momentum space
The collision term vanishes in equilibrium - detailed balance
C[fDM]
mDM=
@
@pDMi
"D
✓@fDM
@pDMi+
pDMi/mDM � ui
TfDM
◆#
C[fDM] = 0fDM = f eqDM = exp
✓� (pDM �mDMu)2
2m�T� µDM
T
◆
The derived reaction rate reproduces that of Thomson scattering� =
1
6meT
X
s�
Zd3p�
(2⇡)3f eq� (1⌥ f eq
� )
Z 0
�4p2�
dt(�t)d�T
dtv =
4⇢�3⇢b
ane�T
D =1
6hq2�elvinTP =
1
6
(�p)2
�t
25
~
Important subtlety
Fokker-Planck approximation: expanding the collision term w.r.t. q/p
A systematic expansion of w.r.t. q (mass dimension one!) is studied and found in the literature
C[f ]
Bringmann et al., New J. Phys, 2009DARK SUSY Bringmann et al., JCAP, 2007
� =1
6mDMT
X
sTP
Zd3pTP
(2⇡)3f eqTP(1⌥ f eq
TP)
Z 0
�4p2TP
dt(�t)d�
dtv~t ! 0
forward scattering
Suppose a simplified model, where SM is extended with DM fermion ( ) and light Dirac fermions ( ) coupled to a mediator boson ( )
� ⌫�
A scalar mediator
CANNOT archive a late kinetic decoupling from in the literature
Tdec = O(keV)
LS � g����+ g⌫ ⌫�⌫
← the leading term is subdominant!!
Bringmann et al., PRL, 2012
�
⌫⌫ ⇠ m⌫ +O(q)
subgalactic damping
26Scalar and vector operators
The argument in the literature seems a consequence of an inappropriate expansion of C[f ]
We show the scalar operator CAN achieve a subgalactic damping as well as the vector operator LV � g���
µ��µ + g⌫ ⌫�µ⌫�µ
← not-suppressed by a small fermion mass⌫�µ⌫ ⇠ pµ⌫ ⇠ T
Estimate of the minimum halo mass from in our formalismVector:
Scalar:
�
(Mcut)S = 6.6⇥ 108 M�
✓r
r0
◆9/2 ✓N⌫
6
↵⌫
10�5
↵�
0.17
◆3/4 ⇣ m�
1TeV
⌘�3/4 ⇣ m�
1MeV
⌘�3
(Mcut)V = 6.8⇥ 108 M�
✓r
r0
◆9/2 ✓N⌫
6
↵⌫
10�4
↵�
0.035
◆3/4 ⇣ m�
1TeV
⌘�3/4 ⇣ m�
1MeV
⌘�3
27Linear perturbation theory
Evolution equation in the Fourier space (synchronous gauge):
Fokker-Planck operator:
Expansion with the eigenfunctions:
___
LFP[f ] =@
@qi
qif + a2m�T0
@
@qif
�
LFP�n `m = �(2n+ `)�n `m
�n `m = e�ySn`(y)Y`m(q)Sn `(y) = y`/2L`+1/2
n (y)
f1(k,q, ⌧) =1
(2⇡a2m�T0)3/2e�y
1X
n,`=0
(�i)`(2`+ 1)Sn `(y)P`(kiqi)fn`(k, ⌧)
f1 +ikiqi
am�f1 � �0aLFP[f1] = ⌘
q2
2a2m�T�0f0 �
h+ 6⌘
2k2(kiqi)
2 1
2a2m�T�0f0 �
ikiqi
aT�0�0a
✓TP
k2f0
+
�1a
✓T0
T�0� 1
◆+ �0a
T1
T�0
�✓q2
2a2m�T�0� 3
◆f0
28
(coupled) → , , the others vanish (decoupled) → , the others are tiny
Boltzmann hierarchy
Boltzmann hierarchy of (synchronous gauge):
with , ,
fn`(k, ⌧)
fn` + (2n+ `)(�0a+R)fn` � 2nRfn�1`
+k
s2T0
m�
⇢`+ 1
2`+ 1
✓n+ `+
3
2
◆fn`+1 � nfn�1`+1
�+
`
2`+ 1(fn+1`�1 � fn`�1)
�
= �`0
⇢�1
2Anh+
1
3Bnh� 2Bn
�1a
✓T0
T�0� 1
◆+ �0a
T1
T�0
��
+�`11
3Ank
r2m�
T0�0a
✓TP
k2+ �`2
2
15
T�0
T0An(h+ 6⌘)
R =d ln(aT 1/2
0 )
d⌧An =
✓1� T�0
T0
◆n
Bn = nT�0
T0
✓1� T�0
T0
◆n�1
�/H > 1
�/H < 1
A0 = 1 B1 = 1
An = 1
Only low multipole (& when ) components couple to the gravity
` = 0, 1, 2 n = 0, 1 �/H > 1
29DM imperfect fluid
Low multipole components are related with the primitive variables of DM imperfect fluid:mass density , bulk velocity potential ,pressure , anisotropic inertia
⇢ ✓P �
, , ,� = f00 ✓ = 3k
sT0
2m�f01 � = 5
T0
m�f02
⇢(1 + �) = �T 00 = a�4
X
s�
Zd3q
(2⇡)3m� f
(⇢+ P )� = �✓kikj �
1
3�ij
◆T i
j = �a�4X
s�
Zd3q
(2⇡)3q2
m�
(kiqi)
2 � 1
3
�f
P + �P =1
3T i
i = a�4X
s�
Zd3q
(2⇡)3q2
3m�f
(⇢+ P )✓ = ikiTi0 = a�4
X
s�
Zd3q
(2⇡)3ikiqi f
�P =T0
T�0P (f00 � f10) = ⇢(c2�� + ⇡)
DM sound speed:c2� =
T�0
m�
✓1� 1
3
d lnT�0
d ln a
◆
30Linear matter power spectra
Scalar vs Vector operators
10-10
10-8
10-6
10-4
10-2
100
10 100
P(k)
[(M
pc/h
)3 ]
Wavenumber k [h/Mpc]
Non-Interacting DM -Vector-DM -Scalar-DM
The scalar operator CAN achieve a subgalactic damping as well as the vector operator
Set parameters such that
Mcut = 6.4⇥ 108 M�
Perfect fluid
31Validity of perfect fluid description
The effects of the higher order terms are suppressed by
Perfect vs imperfect fluid approximations
10-10
10-8
10-6
10-4
10-2
100
10 100
P(k)
[(M
pc/h
)3 ]
Wavenumber k [h/Mpc]
Non-Interacting DMPerfect Fluid
Imp. Fluid, m = 1 TeVImp. Fluid, m = 1 GeV
k
aH
sT0
m�
The perfect fluid description is expected to be trustworthy atk ⌧ 430 /Mpc⇥
✓r
r0
◆�1/2 ⇣ m�
GeV
⌘1/2
Mismatching of the two approximations DOES NOT NECESSARILY means that the imperfect fluid description is better, but it means that we need to follow the full Boltzmann hierarchy
32Application to electrically charged DMCHAMP (CHArged Massive Particle): DM particle carries the electromagnetic chargepositive charge ( ): ,
Dimopoulos et al., PRD, 1990
TeV
PeV
EeV
_
_
_: thermal relic_: Pioneer 11_: improved to mCh > 108 GeV
_: more stringent mCh > 106 GeV from Catalyzed BBN
___
_____
____
____
_________
Verkerk et al., PRL, 1992
(X�4He) + D ! 6Li +X�
quasi-stable: τCh > 1010 yr (age of the Universe)
direct detection: mCh > 1022 GeV (LUX)
Above the Planck scale!!
Kohri et al., PLB, 2010(X�4He)X+YCh ⌧ Y4He
33
Analytic estimate from A. De Rujula, S. L. Glashow (!), and U. Sarid, Nucl. Phys. B, 1990
Caveats
The severer terrestrial constraints are NOT applicable IF
the Galactic magnetic field expels CHAMPs from the the Galactic disk (Fermi acceleration)& prevents CHAMPs from crossing the Galactic disk (a small gyroradius) 105 GeV < mCh < 1011 GeV
Chuzoy et al., JCAP, 2009
CHAMP decays to a neutral particle (DM at present) at some point
Impacts on CMB if τCh > 105 yr (recombination) ?
_________
True in elaborate and modern analysis ? AK, K. Kohri, T. Takahashi, N. Yoshida, arXiv:1604.07926t-averaging is important d�
dt
���t!0
! 1
34Effects on CMB temperature and polarization spectra
0
1000
2000
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4000
5000
6000
7000
500 1000 1500 2000 2500
l(l+1
)ClTT
/(2π)
[µK2 ]
l
mCh=1010 GeVmCh=1011 GeVmCh=1012 GeVstandard CDM
Planck 2015
-20
-10
0
10
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500 1000 1500 2000 2500
l(l+1
)ClEE
/(2π)
[µK2 ]
l
mCh=1010 GeVmCh=1011 GeVmCh=1012 GeVstandard CDM
Planck 2015EE
-cor
rela
tion
multipole
TT-c
orre
latio
n
multipole
The EE-correlation is MORE sensitive to the re-coupling of CHAMP when compared to the TT-correlation
CHAMP effects:baryon drag - CHAMPs and baryons compress (heat) the primordial plasmaearly Integrated Sachs-Wolfe (ISW)- CHAMPs cannot sustain the gravitational potential → photons obtains a net energy
baryon drag
early ISW
mCh > 1011 GeV (modern)coincides with the analytic estimate of DGS (1990)!