Cosmology with WFMOSCosmology with WFMOS

Jan 14, 09 @NAOJ

Masahiro Takada (IPMU)

Precision CosmologyPrecision CosmologyΛΛCDM structure formation scenarioCDM structure formation scenario

mh2=0.12770.008 etc

• ~96% of the Universe is dark, unknown:

• Dark Matter + Dark Energy

From WMAP website

>0.1% Neutrinos

Most ImportantMost Important ProblemsProblems• What is dark matter?

– The nature of DM, neutrino masses

• What is the cause of cosmic acceleration?

– Dark energy or Modification of gravity

• What is the beginning of Big-Bang?

– The nature of inflation (early-time DE)

WFMOS+HSC provide breakthrough data sets for addressing these fundamental problems with unprecedented accuracies

DE mystery: Coincidence problemDE mystery: Coincidence problem

• Late-time DE becomes dominant in the cosmic energy budget, only recently during the cosmic history

ln(i(a))

scale factor: a

BBN CMB Now

radiation (a^-4)

matter (a^-3)

DE (a^~0)？

€

de ~ a−3(1+w )

(w ~ −1)

Note: DE Effect on CMBNote: DE Effect on CMB

DE effect on CMB is small

(Suto, MT, Aihara 07 ）

€

de(z*)

ρ m (z*)<<1 (e.g.10^−9)

Cosmic AccelerationCosmic Acceleration• Cosmological principles: homogeneous and isotropic• Gravity theory: e.g., Einstein gravity

Hubble expansion

€

H 2(z) ≡˙ a

a

⎛

⎝ ⎜

⎞

⎠ ⎟2

= H02 Ωm0(1+ z)3 + Ωde0(1+ z)3(1+w )[ ]€

Gμν = 8πG Tμν (space-time curvature)=(matter)

Matter (CDM ＋ baryon) Dark Energy

• Cosmological distances (SNe, BAO: baryon acoustic oscillation)

cosmoclogical const. (w=-1) ： infinite expansion (z-1)H(t)=const. a(t)exp(Ht) (the late-time inflation)

€

DL (z) = (1+ z) d ′ z 1

H( ′ z ), DA (z) = (1+ z)−2 DL (z)

0

z

∫

Structure Formation- Growth of fluctuations -

From WMAP

€

δT

T(z =10^3) ~ 10−5

€

δ

(z ~ 0) ~ 1

Gravity Cosmic Expansion

Growth of cosmic structuresGrowth of cosmic structures

€

δm (x,z) ≡ρ m (x,z) − ρ m (z)

ρ m (z)= D(z)δm (x,z ≈1000)

€

˙ ̇ D + 2H ˙ D − 4πGρ mD = 0

• The density fluctuation field of total matter (mainly CDM) in the linear regime

• The 2nd-order diff. eqn. to govern the redshift evolution of density pert.: (FRW eqns ＋ linearized Einstein eqns.)

• Cosmic acceleration the density growth is suppressed€

H 2(z) ≡˙ a

a

⎛

⎝ ⎜

⎞

⎠ ⎟2

= H02 Ωm0(1+ z)3 + Ωde0(1+ z)3(1+w )[ ]

matter(CDM ＋ baryon+) Dark energy

where

€

(Ωm0 + Ωde0 =1)

€

δGμν = 8πGδTμν

Friction due to cosmic exp. Gravitational instability

Growth RateGrowth Rate

• The initial conditions on the perturbations are well constrained by the CMB

• A variant in DE changes the growth of density perturbations

• A test of gravity theory on cosmological scale

CMB(z~1000)

WFMOS (0.5<z<1.3,z~3)

Weak Lensing(0.2<z<1)

SCDM CDM

Jenkins+99

CDM scenario (bottom-up): P(k)CDM scenario (bottom-up): P(k)

CMB

Galaxy Survey(WFMOS)

k3 P(k

,z)/

22 ~

<δ2

>R

~1/k

WL(HSC)

Length scales + Time evolution

Caution: “light” is biased tracers of massCaution: “light” is biased tracers of mass

From

the V

irgo C

on

sortiu

m85

Mpc

/h

Different types of galaxies (and clusters) trace the total matter (mostly DM) distribution in different ways

Dark Energy ProbesDark Energy Probes• Type-Ia SNe

– Standard candle ：　 DL(z)

– pros ： established cons ： empirical, different pops

• Galaxy clustering statistics (redshift: WFMOS)– Standard ruler + structure formation ：　 DA(z), H(z), + D(z)

– pros ： smaller systematics cons ： galaxy bias…..

• Weak gravitational lensing (imaging: HSC)– Structure formation + geometrical: DA(z), D(z)

– pros ： mapping DM cons ： shape, photo-z….

• Cluster abundance (optical: WL, X-ray, SZ)– Structure formation + geometrical: DA

2(z)/H(z), D(z)

– pros ： well-behaved bias cons ： mass-observable relation

Larg

e-s

cale

str

uct

ure

pro

bes

Dark Energy Task ForceDark Energy Task Force

A. Albrecht (UC Davis)

G. Bernstein (Penn)

R. Chan (LBNL)

W. Freedman (Carnegie)

J. Hewitt (MIT)

W. Hu (Chicago)

J. Huth (Harvard)

M. Kamionkonski (Caltech)

E. Kolb (Chair, Chicago)

L. Knox (UC Davis)

J. Mather (Goddard)

S. Staggs (Princeton)

N. Suntzeff (Texas A&M) astro-ph/0609591

The DETF ReportThe DETF Report

WFMOS BAOWFMOS BAO(see Taruya-san’s talk)(see Taruya-san’s talk)

rdV

dV• Measure galaxy

clustering strengths:

2pt correlations (or P(k))

€

dP = n g2 1+ ξ g(r)[ ]dV 2

Eisenstein et al 05

rBAO~150Mpc

DA(z)

• Find a tiny excess in the galaxy clustering strengths

€

rBAO = DA (z)θobs

Capability of WFMOS for BAOCapability of WFMOS for BAO• The combination of the 8.2 aperture, the wide field

(1.5sqdeg), high multiplex gain (~3000) gives WFMOS the unique capability: no competition before ~2020

• Target galaxies– 0.5<z<1.3 (~2000deg^2): red ellipticals and blue spirals, based

on the DEEP2 survey (e.g., BRI cut; r_AB<24)

– 2.5<z<3.5 (~300 deg^2): LBGs or LEAs; U-band needed

– nP~1 defines an optimal number of fibers (3000 fibers)

• A cosmological survey requires to cover a larger comoving volume (>1Gpc^3): deep and wide– Enables to cover a larger volume at higher redshifts with a

fixed solid angle

– Galaxy clustering information is cleaner at higher redshifts, more in the linear regime

Our observable universe

z=1100

z=50

z=10

z=5 z=3 z=2

z=1

共同座標スケール

21cm tomography

Subaru HSC/WFMOS Survey

Cosmic sampling varianceCosmic sampling variance

• The measurement errors for CMB, galaxy P(k), WL,… are limited by the statistical errors, rather than the systematics

• A larger surveyed volume allows the higher precision– CMB(z~1000): all-sky map already obtained,

d_LSS~15Gpc– SDSS 2.5m (z<0.4, ~10^4 deg^2): d_SDSS/d_LSS~0.1– Subaru 8.2m (HSC: <z>~1, WFMOS z~1+3):

d_Subaru/d_LSS~0.5– Ultimately: 21cm survey (z~10, SKA): d_21/d_LSS~0.7

• A wide redshift coverage (CMB+galaxy surveys+)

€

σ (P)

P

⎡ ⎣ ⎢

⎤ ⎦ ⎥

2

∝1

surveyed volume+ systematics

z=50 z=10

z=5 z=3 z=2 z=1

z=1100

LSS

Expected Performance of WFMOSExpected Performance of WFMOS• WFMOS allows to

measure D_A(z) and H(z) at each redshift slice to a few % accuracies

• The expected DE constraints:

σ(w)≈0.06

• A wide redshift coverage: w≠-1 at any z

a big discovery

Synergy of HSC and WFMOS (I)Synergy of HSC and WFMOS (I)

main galaxy sample: r<17.77

Luminous Red Galaxies (LRGs; r<19.5 ) (Eisenstein et al. 01)

From Tegmark

• The multi-color data sets of HSC would be valuable to find target galaxies for WFMOS (r_AB<24)

• A similar-type galaxy sample across redshifts would be most useful to trace the LSS (like LRGs in SDSS)

Synergy of HSC and WFMOS (II)Synergy of HSC and WFMOS (II)

• HSC: WL – DM distribution

in the LSS

• WFMOS: galaxy clustering– View the LSS

via biased tracers

present

past

• Calibrating systematics: for WL, photo-z errors

• For BAO, a direct measurement of galaxy bias

• WL+BAO allows a stringent test of gravity theory

Complementarity btw WL and BAO Complementarity btw WL and BAO

• Cosmological parameter constraints can be improved by combining BAO and WL, because the two have different dependences on cosmo paras.

An example of measuring galaxy bias An example of measuring galaxy bias Galaxy-galaxy lensing (spec-z gals – background imaging gals)

2D m

ass

den

sity

pro

file

[M

sun

/pc^

2]

radius from galaxy center [kpc/h]

Red: early-typeBlue: late-type

SDSS results(Mandelbaum+05)

• More luminous and late-type galaxies reside in more massive halos

State of the WorldState of the World

• JDEM– Announcement of Opport.

(selected mid 09)

– WL+BAO+SNe (SNAP concept reset)

– NIR infrared + optical

– Spectroscopic (likely in NIR) + imaging

– Launched in 2016

– ~$1 billion

• Euclid– R&D study since mid 2008

– WL+BAO(+SNe)

– NIR + optical

– Spectroscopic + imaging

– Launched in 2017

– ~$1 billion

USA(NASA/DOE) EU(ESA Cosmic Vision)

BOSS (09-), HETDEX (10-): don’t have synergetic WL survey partner HSC(11-)+WFMOS (15-) are unique: a window prior to JDEM/EUCLID

Guaranteed Science: Neutrino Mass Guaranteed Science: Neutrino Mass • A mixed DM model: Structure formation is induced by the

density fluctuations of total matter

• The neutrinos slow down LSS on small scales– On large scales >fs, the neutrinos can grow together with CDM

– On small scales <fs, the neutrinos are smooth, δ=0, therefore weaker gravitational force compared to a pure CDM case

)(xδ

Total matter perturbations can grow!

CDM CDM

< fs > fs

Suppresses growth of total matter perturbations

€

˙ ̇ δ cb + 2H ˙ δ cb − 4πGρ m(1− fν )δcb = 0, δν ≈ 0

€

δm =ρ cδc + ρ bδb + ρ ν δν

ρ c + ρ b + ρ ν≡ fcδc + fbδb + fν δν

€

δc = δb = δν

Effect of m_nu on nonlinear P(k)Effect of m_nu on nonlinear P(k)

WFMOS achieves a few % accuracy in measuring P(k) at each k bins over k=[0.03,1] The suppression effect on P(k) due to neutrinos is enhanced in the weakly nonlinear regime

Saito, MT, Taruya, PRL, 2008

€

m

Σm

ν [e

V]

WMAP5+SN+BAO: m_nu<0.75eV

An example: WL constraints on m_nuAn example: WL constraints on m_nu

WMAP5: m_nu<1.1 eV(95%CL)

WL+WMAP5+SN+BAO: m_nu<0.54eV

flat LambdaCDM + total neutrino mass

Ichiki, MT, Takahashi 09 PRD in press

Forecast for WFMOSForecast for WFMOS Saito, MT, Taruya, PRL, 08M

argi

nali

zed

erro

r: σ

(f_ν

)

Neu

trin

o to

tal m

ass:

σ(M

_ν)[

eV]

0.05

0.1

0.2

0.5

Power spectrum amplitude @k=k_max: Δ^2(k_max;z)0.01 0.1 1

Linear

Non-Linear (PT)

σ(M_ν)~0.13eV

σ(M_ν)~0.1eV

SummarySummary • WFMOS delivers a very powerful data set for

developing our understanding of cosmology– Constraining the nature of DE (BAO), neutrino masses,

inflation models, the primordial non-Gaussianity

• A valuable synergy of WFMOS and HSC– Unique complementarity btw WL(LSS: HSC) and galaxy

clustering methods (geometrical: WFMOS)

– Improve cosmological constraints and calibrate systematic errors inherent in each methods

– Opens a window to test gravity theory on cosmological scales

– A golden opportunity; prior to $1 billion projects, JDEM and EUCLID (launched around 2017)

The recent update of cluster The recent update of cluster abundance methodabundance method

• Vikhlinin et al. 08: use the improved mass estimates based on the Chandra observations of 36 and 49 clusters at <z>=0.55 and 0.05, respectively

Vikhlinin et al. 08Vikhlinin et al. 08