Constraining light gravitino mass from cosmic microwave background

Toyokazu Sekiguchi

ICRR, Univ. of Tokyo

based on K. Ichikawa, M. Kawasaki, K. Nakayama, TS, & T. Takahashi, to appear

ICRR theory meeting (Dec 8-9, 2008)

Light gravitino: Why?

light gravitino: mass~1-100 eV‒free from cosmological gravitino problem Moroi, Murayama, Yamaguchi ‘93

‒compatible with thermal leptogenesis Fukugita, Yanagida ‘86-> realized in gauge mediated SUSY breaking (GMSB) scenarios

‒stability of vacuum -> lower bound

Dine, Fischler ’82, Alvarez-Gaumé, Claudson, Wise ‘82

gravitino: the supersymmetric partner of graviton

‒a lot of cosmological consequences (dark matter candidate(LSP), late-time decay, etc.)

‒less than the observed DM energy density-> upper bound

‒a consequence of local supersymmetry

-plenty of implications for supersymmetic models

• possible gravitino mass(m_3/2)

1 ! m3/2 ! 100 eV

Outline• Light gravitino: why?

• Effects on structure formation and CMB lensing

• A forecast for future CMB surveys Constraints on light gravitino mass Bayesian model selection analysis on light gravitino model

• Summary

Light gravitino in the early universeGravitino is in thermal equilibrium at early times

redshifted to momentum~massbecomes non-relativisticcontributes to dark matter => warm dark matter

-> 1/10 of single neutrino species

85 86 87 88 89 90 91 92 93 94

1 10 100

g *3/

2

m3/2 [eV]

!mess=200TeV!mess=100TeV!mess=50TeV

number density:

As temperature decreases, gravitino decouples from the plasma

!3/2h2(! !3/2) = 0.13

! m3/2

100eV

"cf. WMAP 5yr result

n3/2 =10.75g!3/2

n!0

g_* at decoupling

(only mild model-dep.)

g!3/2 ! 90

! 0.12 n!0

!dm!0.110± 0.06

Pagels & Primack ’82, Peebles ’82, Bond et al.’82, Olive & Turner ’82...

Structure formationHow light gravitino affects the structure formation ? basically same as WDM or massive neutrinos

suppresses the structure at small scales [perturbations evolution]

changing matter-radiation equality [background evolution]-> not significant for light gravitino; number density is small (∆N_eff~0.06)

•free streaming length

•energy fraction in DM

Rfs ! 20Mpc!m3/2

1eV

"!1

f3/2 !!3/2

!dm= 0.012

!m3/2

1eV

" ! !dm

0.110

"!1

=> scale of suppression

=> power of suppression

scale and power of suppression depends on the gravitino mass, m3/2

Matter power spectrum

100

1000

10000

0.01 0.1 1

P(k)

[h3 M

pc3 ]

k [h-1 Mpc-1]

m3/2= 0eVm3/2= 1eV

m3/2=10eVm3/2=86eV

for larger mass... free streaming length shortens

suppression powerincreases

Gravitino suppresses the matter power spectrum at small scale !!k!k!" = P (k)!kk!

At large scales, P(k) doesn’t change -> small scalelarge scale <-

Current constraints

Constraints from the Lyman alpha forestViel, Lesgourgues, Haehnelt, Matarrese, Riotto ‘05

Caveats: Larger amplitude than simulation? Systematics?

No small-scale suppression is seen in matter power spectrum from the Lyman alpha forest.

Other cosmological probe for light gravitino mass?

Light gravitino changes the matter power spectrum at small scales.Constraints comes from measurements of P(k) at small scales

=> constraint on Gravitino massindirect measurement of P(k) from absorption line of quasars

m3/2 ! 16 eV

lensing of CMB

lensing potential

: 2D projection of gravitational potential

CMB photons are deflected by gravitational potential generated by matter pertrubations

!(n) = !2! !!

0d"

"! ! "

"!"!("n, #0 ! ") !T (n) = !T (n +!"(n))

deflection angle

!T (n)

!(r, !)

!T (n)

unlensed anisotropy

large scale structure

observed, lensed anisotropy

=>

Since it reflects the changes in the matter power spectrum, it can be a good probe for light gravitino.How does gravitino change ?

• angular spectra: !!T !

!m"!!m!" + (c.c.) = 2CT"! !!!!!mm!!!!

!m!!!m!" = C""! "!!!"mm! ,

C!!" & CT!

1e-07

1e-06

1e-05

0.0001

0.001

0.01

10 100 1000l3 C

lT! [µ

K]l

m3/2= 0eVm3/2= 1eV

m3/2=10eVm3/2=86eV

1e-09

1e-08

1e-07

1e-06

10 100 1000

l4 Cl!!

l

m3/2= 0eVm3/2= 1eV

m3/2=10eVm3/2=86eV

Angular spectra of lensing potential

To constrain light gravitino, precise measurements of lensing potential is needed. However, current sensitivities are not sufficiently high.

-> Forecast for Future CMB surveys

suppression via free streaming

-> small scalelarge scale <- -> small scalelarge scale <-

Analysis method

Sampling of posterior distribution(PD): MultiNest Feroz, Hobson & Bridges ‘08

Mock data:• Planck

without precise measurements of lensing potential, we cannot constrain m3/2 from current

CMB surveys. To forecast constraints on light gravitino from future CMB surveys, we make

use of following three surveys in this paper, the Planck [14], PolarBeaR [15] and CMBpol [16]

surveys. Their parameters for instrumental design is summarized in Table I, where !FWHM

is the size of Gaussian beam2 at FWHM and "T ("P ) is the temperature (polarization) noise.

surveys fsky bands [GHz] !FWHM [arcmin] "T [µK] "P [µK]

Planck [14] 0.65 100 9.5 6.8 10.9

143 7.1 6.0 11.4

217 5.0 13.1 26.7

PolarBeaR [15] 0.03 90 6.7 1.13 1.6

150 4.0 1.70 2.4

220 2.7 8.00 11.3

CMBpol [16] 0.65 100 4.2 0.84 1.18

150 2.8 1.26 1.76

220 1.9 1.84 2.60

TABLE I: CMB surveys and their instrumental parameters used in our analysis. !FWHM is Gaussian

beam width at FWHM, "T and "P are temperature and polarization noise, respectively. For the

Planck and PolarBeaR surveys, we assume 1-year duration of observation and for the CMBpol

survey, we assumed 4-year duration.

In this paper, to generate the Bayesian posterior distributions of cosmological parame-

ters, we make use of the public code MultiNest [17] integrated in the vastly used Markov

chain Monte Carlo (MCMC) sampling code COSMOMC [18]. While COSMOMC samples the pos-

terior distributions via the Markov chain sampling method, MultiNest is based on the

nested-sampling method [19], which is not a MCMC sampling. Use of MultiNest has sev-

eral advantages in our analysis. One of the greatest advantages is that it enables e!cient

exploring of multi-modal/highly-degenerated likelihood surface, which is indeed the case for

light gravitino models, as have been investigated in the previous section. Also it provides

2 We assume Gaussian beam and neglect the any anisotropies in beam and distortion arising from the scanstrategy.

10

• PolarBeaR• CMBpol

‒ efficient sampling of PD for multimodal/highly-degenerate likelihood‒ calculation of “Bayes factors” -> “Bayesian model selection analysis”

using TT, TE, EE, φφ, Tφ spectra (l < 2500)

assuming power-law flat LWCDM (CDM+WDM) universealso we assume massless neutrino species -> comments are in Summary

Parameter space:

(!b,!dm, "s, #, f3/2, ns, As)

fiducial values are WMAP 5yr result(besides f_3/2 & N_3/2)

Sensitivities

Planck: large sky coverage, low resolution (compared with other two)PolarBeaR: small sky coverage, high resolutionCMBpol: large sky coverage, very high resolution survey

1e-08

1e-07

10 100 1000

PlanckPolarBeaR

CMBpol

m3/2= 0eV (f3/2=0) m3/2= 1eV (f3/2=0.0013)m3/2= 10eV (f3/2=0.013) m3/2= 86eV (f3/2=1)

l4 C l!!

l

Forecasts for constraints

Planck alone/PolarBeaR alone suffer from degeneracies in and (-> next slide).

Planck and PolarBeaR combined

CMBpol

1d marginalized PD for gravitino fraction(f_3/2)

m3/2 ! 3.0 eV (95% C.L.)

m3/2 = 1.04+0.25!0.22 eV

gravitino mass can be constrained!

‒ cannot constrain light gravitino f3/2 ! 0

f3/2 !!3/2

!dm= 0.012

!m3/2

1eV

" ! !dm

0.110

"!1

1

more stringent constraint

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Post

erio

r

f3/2

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06f3/2

related to gravitino mass

Planck alonePolarBeaR alone

Planck&PolarBeaRcombinedCMBpol

DegeneraciesPlanck and PolarBeaR suffers from degeneracies and f3/2 ! 0 f3/2 ! 1

1e-08

1e-07

10 100 1000

PlanckPolarBeaR

CMBpol

m3/2= 0eV (f3/2=0) m3/2= 1eV (f3/2=0.0013)m3/2= 10eV (f3/2=0.013) m3/2= 86eV (f3/2=1)

l4 C l!!

lFor large mass streaming length is small, so that anisotropies are same as

m_3/2=0 except for (noise dominated) small scales

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Post

erio

r

f3/2

Planck alonePolarBeaR alonePlanck&PolarBeaRcombinedCMBpol

Evidence of gravitino? How strong?Bayesian model selection analysis (1)

•model likelihood (Bayesian evidence)

<- balances fit of data, and model complexity (Occam’s razor)•Bayes factor

A general question: Do data favor/disfavor a model against another? If so, then how strongly?

Bayesian model selection analysis

=> Jeffreys’ scale (this is a rule of thumb)

(This is one way, and of course there’re a number of other methods)likelihood prior probatility

: model parameters

E(Model)(= P (Data|Model)) =!

d!L(!|Data) "(!|Model)

!

evidence for a model, M1 against another, M2

! ln E12 Interpretation< 1.2 Very slight< 2.3 Slight< 4.6 Strong> 4.6 Decisive

Table 1: the Ja"reys’ Prior

1

! lnE12 = ln(E(M1)/E(M2))

•using mock data of CMBpol with gravitino of mass 1eV

In the Jaffreys’ scale, • “Strong” evidence for mass=1eV. • For larger mass, evidence can be “Decisive”.

GMSB models predict gravitino mass>1eV. -> With the future CMBpol survey, detection/exclusion of light gravitino is possible in almost whole interesting range of mass.

Light gravitino model vs conventional CDM model

Evidence of gravitino? How strong?Bayesian model selection analysis (2)

! ln E12 Interpretation< 1.2 Very slight< 2.3 Slight< 4.6 Strong> 4.6 Decisive

Table 1: the Ja"reys’ Prior

1

M1: light gravitino model M2: CDM model

! lnE12 ! 4.2lnE1 = !28.3± 0.2 lnE2 = !32.3± 0.2

Conclusion

Caveats: Neutrino masses can degrade the deterministic power on gravitino mass.They can be pre-determined from tritium beta decay, neutrinoless double beta decay, and/or other experiments/observations. Quantitative arguments in progress.

We forecasted constraints on the light gravitino model with future CMB surveys, and shown the most of the deterministic power comes from correlation of lensing potential itself/with temperature anisotropy.

With Planck/PolarBeaR alone, constraints suffer from strong degeneracies arising between and .

When Planck and PolarBeaR are combined, they complementarily covers small and large scale anisotropies, and enables us to constrain as gravitino mass<3eV.

With CMBpol, high resolution, low noise level and whole-sky survey, we can constrainalmost all possible gravitino mass, and detect/exclude the light gravitino models.

f3/2 ! 0 f3/2 ! 1