Revisiting CDM isocurvature perturbationsin curvaton scenario

Naoya Kitajima

3rd Korea-Japan Workshop on Dark Energy, KASI, Daejeon Apr. 4-8 2016

NK, D. Langlois, T. Takahashi, S. Yokoyama in prep

Single field inflation models are tightly constrained

ns = 0.968± 0.006 (68% CL), r < 0.12 (95% CL)

Small field model or R2 model seem good..

(One of) the next-to-simplest setup(s)

inflaton + extra scalar field

- light & subdominant during inflation

- decays after inflation

=> acquires quantum fluctuations

“Curvaton” :

Enqvist & Sloth / Lyth & Wands / Moroi & Takahashi (2001)

V

V

m Hinf ,

multiple origin for perturbations

Cosmic history in curvaton scenario

inflaton

curvaton

curvaton decay

radiationH =

H = m

inflation MD RD

time

ener

gy d

ensit

y

- Large non-gaussianity- Isocurvature perturbations

/ a4

/ a3

- Non-gaussianity

(68%CL, Planck Collaboration 2015)

Curvaton model:

! severely constrained

Curvaton should dominate the universe before decayin order not to give too large fNL

rs & 0.2

adiabatic perturbation

space space

/

CDM

photon

isocurvature perturbation

Curvaton has “Residual” CDM isocurvature perturbation

space

curvaton

radiation CDM

photon

- Isocurvature perturbations

SCDM = 3(CDM )

/

“intrinsic” such as axion

Planck collaboration 1502.02114

Constraint on isocurvature perturbations

iso

=PS

P + PS

[95% CL]

Planck 2015 constraint :

|S/| . 0.1

iso

(k0

) < 0.035 (uncorrelated), iso

(k0

) < 0.013 (correlated)

curvaton model is constrained

I. WIMP dark matter

Weakly Interacting Massive Particle

CDM isocurvature perturbation in curvaton scenario

ann > H

ann < H

— DM is in thermal equilibrium

— DM is decoupled from thermal bath

creation/annihilation rate for DM : ann = hannvinCDM

Thermally produced WIMP

DM

DM

SM

SM

thermal bath10-20

10-15

10-10

10-5

100

10-2 10-1 100 101 102 103

m/T

Yeq

Y

nCDM = n(eq)CDM

- “Sudden” freeze-out formalism -

before freeze-out after freeze-out

H = ann = hannvinCDM at N = Nfr

CDM freezes out suddenly at

non-relativistic limit —

to calculate isocurvature perturbation

“Residual” CDM isocurvature perturbation

DM is non-relativistic at freeze-out :

T

ann / nCDM / em/T

H

nCDM T

time

SCDM = 3(CDM ) =(nCDM/s)

nCDM/s

timing is different in each patch

freeze-out

radiation+

CDMradiation

CDM

case 1 — CDM freeze-out after curvaton decay

- single component

before freeze-out after freeze-out

H = ann ) 3M2P

2ann = r(Nfr)

case 2 — CDM freeze-out before curvaton decay

(consistent with Lyth, Wands astro-ph/0306500)NK, Langlois, Takahashi, Yokoyama in prep

non-relativistic limit :

↵,fr d lnann

d lnT

fr

r + = 3M2P

2ann

radiation-curvaton fluid(2-component)

before CDM freeze-out

radiation+

CDM

Curvaton

- Case A

radiation+

CDM

Curvaton

radiation

CDMCurvaton

- Case A

after CDM freeze-out

T nCDM

radiation+

CDM

Curvaton

radiation

CDMCurvaton

Curvaton

radiation

CDM

- Case A

before curvaton decayafter CDM freeze-out

T nCDM

radiation+

CDM

Curvaton

radiation

CDMCurvaton

Curvaton

radiation

CDM

radiation

CDM

- Case A

after curvaton decayafter CDM freeze-out

T T nCDM

ruled out!

- Case B

Curvaton

radiation+ CDM

before CDM freeze-out

- Case B

Curvaton

radiation+ CDM

before CDM freeze-out

Curvaton

radiation

CDM

T nCDM

- Case B

Curvaton

radiation+ CDM

before CDM freeze-out

Curvaton

radiation

CDM

Curvaton

radiation

CDM

before curvaton decay

T nCDM

- Case B

Curvaton

radiation+ CDM

before CDM freeze-out

Curvaton

radiation

CDM

Curvaton

radiation

CDM

radiation

CDM

after curvaton decay

T nCDM T

ruled out??

rs 1

More realistic analysis

sudden decay approximationr

time

! r

r,inf + 4Hr,inf = 0

r,curv + 4Hr,curv =

r + 4Hr = 0

+ 3H = 0until decay

r !time

r,inf

r,curv

“dilution plasma”

it is not valid in some cases e.g. T-dependent decay rate

ΝΚ,Langlois,Takahashi,Takesakoand Yokoyama 1407.5148

(numerical analysis)

w/ dilution plasma

see e.g. Kolb & Turner

w/o dilution plasma :

curvaton

radiation r,curv r,inf

curvaton

radiationT

time

r,inf

r,curv

freeze-out nCDM r,inf

Primordial radiation vs dilution plasma

r,curv < r,inf

time

r,inf

r,curv

freeze-out nCDM r,curv

Primordial radiation vs dilution plasma

r,curv > r,inf

r,inf r,curv ) SCDM/ ' 0

Numerical calculations

(+ CDM annihilation)

N =

ZHdt, i = N +

1

3(1 + wi)ln

ii

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-14 -12 -10 -8 -6 -4 -2 0 2

−S

CD

M/ζ

Nfr−Ndec

numericalanalytic

w/o dilute gas

w/ dilute gasPreliminar

y

— Analytic & Numerical results —

r,curv > r,inf

NK, Langlois, Takahashi, Yokoyama in prep

Isocurvature vanishes if axion starts to oscillate after dilute gas exceeds primordial radiation

sudden freeze-out seems OK!

σ∗/Mpl

10-6

10-5

10-4

10-3

10-2

10-1

10-31

10-32

10-33

10-34

10-35

10-36

10-37

σ∗/Mpl

10-31

10-32

10-33

10-34

10-35

10-36

10-37

10-6

10-5

10-4

10-3

10-2

10-1

w/o dilution plasma w/ dilution plasma

tfr = tdectfr = tdec

tfr < tdec

rs > 0.1 rs > 0.1

|SCDM/| > 0.1

Preliminar

y

Preliminar

y

Allowed region is broadened for rs 1

Allowed parameter regionNK, Langlois, Takahashi, Yokoyama in prep

II. Axion dark matter

CDM isocurvature perturbation in curvaton scenario

— Axion dark matter —

axion

ma(T ) '(ma(Tcr/T ) for T > Tcr

ma for T < Tcr

ma(T ) '

8>>><

>>>:

4.05 1042QCD

Fa

T

QCD

3.34

T > 0.26QCD

3.82 1022QCD

FaT < 0.26QCD

QCD axion :

axion mass :

Fa = 109 1012 GeV, QCD ' 400 MeV

H = ma(Tosc

)

Hma(T )

T

time

“Sudden” beginning of oscillation at

na T

na

s

t>t

osc

=na(Tosc

)

s(Tosc

)

10-3

10-2

10-1

100

-10 -8 -6 -4 -2 0 2

N−Ndec

ΩσΩr

ΩrσW/WfH/ma

ma(T)/ma

W = nae3N

oscillation

SCDM

/ = 3

,osc

rs

3 +

4 + 2 ,osc 1

case 1 — Axion oscillation after curvaton decay

- single componentH = ma(Tosc

) ) 3M2

Pm2

a(Tosc

) = r(Nosc

)

case 2 — Axion oscillation before curvaton decay

r + = 3M2

Pm2

a(Tosc

)

(consistent with Lyth, Wands astro-ph/0306500)

Numerical calculations

N =

ZHdt, i = N +

1

3(1 + wi)ln

ii

a+ 3Ha+m2a(T )a = 0 (axion)

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-14 -12 -10 -8 -6 -4 -2 0 2

−S

CD

M/ζ

Nosc−Ndec

rs = 0.999analytic

Preliminar

y

analytic & numerical results

Isocurvature vanishes if axion starts to oscillate after dilute gas exceeds primordial radiation

NK, Langlois, Takahashi, Yokoyama in prep

10-6

10-4

10-2

100

102

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1

Γ σ/m

a

σi/MP

Preliminar

y

Allowed parameter region

tfr = tdec

rs > 0.1

|SCDM/| > 0.1

Allowed region is broadened for rs 1

NK, Langlois, Takahashi, Yokoyama in prep

— Summary —

We revisited isocurvature perturbations in curvaton model.“Residual” CDM isocurvature perturbations can be produced in this model In previous thought, it becomes large (S/ζ = -3 — -3/2) and it is already ruled out by observations unless CDM produced after curvaton decay.

Detailed analysis beyond sudden decay approximation (including dilution plasma from gradual decay of the curvaton) shows that CDM isocurvature can be suppressed even if curvaton decays after CDM production (freeze-out of WIMP/beginning of axion oscillation).

constraint from isocurvature is relaxedgood news or bad news?