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.

14

Backup slides

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

3000

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

20

30

40

50

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)!