Yun Wang, 3/2011

Baryon Acoustic Baryon Acoustic Oscillations and DE Figure Oscillations and DE Figure

of Meritof Merit

Yun WangYun Wang WFIRST SDT #2, March 2011WFIRST SDT #2, March 2011

• BAO as a robust dark energy probe• Forecasting DE FoM from BAO

Yun Wang, 3/2011

How We Probe Dark EnergyHow We Probe Dark Energy

• Cosmic expansion history HCosmic expansion history H((zz) or DE density ) or DE density XX((zz):):

tells us whether DE is a cosmological constanttells us whether DE is a cosmological constant

H2(z) = 8 G[m(z) + r(z) +X(z)]/3 k(1+z)2

• Cosmic large scale structure growth rate function fCosmic large scale structure growth rate function fgg((zz), ), or or

growth history Ggrowth history G((zz):):

tells us whether general relativity is modifiedtells us whether general relativity is modified

fg(z)=dln/dlna, G(z)=(z)/(0)

=[m-m]/m

Yun Wang, 3/2011

Current Current Dark Dark

Energy Energy ConstraintConstraint

ss

Wang (2009)

1 yoctogram=10-24 g

Yun Wang, 3/2011

Observational Methods for Observational Methods for Probing Dark Energy Probing Dark Energy

• Measure two functions of redshift Measure two functions of redshift zz: : – cosmic expansion ratecosmic expansion rate H H((zz) ) tells us whether dark energy is a tells us whether dark energy is a

cosmological constantcosmological constant– growth rate of cosmic large scale structuregrowth rate of cosmic large scale structure f fgg((zz) ) [or growth [or growth

factorfactor G G((zz))] tells us whether gravity is modified, given ] tells us whether gravity is modified, given HH((zz)) • Use three main methods:Use three main methods:

– SNe Ia (Standard Candles):SNe Ia (Standard Candles): method through which DE was discovered; independent of clustering of matter, probes H(z).

– Baryon Acoustic Oscillations (Standard Ruler): Baryon Acoustic Oscillations (Standard Ruler): calibrated by CMB, probes H(z). Redshift-space distortions from the same data probe fg(z).

– Weak Lensing Tomography and Cross-Correlation Weak Lensing Tomography and Cross-Correlation Cosmography:Cosmography: probe a combination of G(z) and H(z).

Yun Wang, 3/2011

The Origin of BAOThe Origin of BAO

• At the last scattering of CMB photons, the acoustic oscillations in the photon-baryon fluid became frozen and imprinted on – CMB (acoustic peaks in the CMB)– Matter distribution (BAO in the galaxy power spectrum)

• The BAO scale is the sound horizon scale at the drag epoch – The drag epoch occurred shortly after decoupling of

photons, when photon pressure could no longer prevent gravitational instability of baryons.

– WMAP data give s = 153.2 1.7 Mpc, zd = 1020.5 1.6

(Komatsu et al. 2010)

Yun Wang, 3/2011

Δr┴ = DAΔθΔr|| = (c/H)Δz

BAO“wavelength” in radial direction in slices of z : H(z)

BAO “wavelength” in transverse direction in slices of z : DA(z)

BAO systematics:BiasRedshift-space distortionsNonlinear effects

Δr|| = Δr┴ = 148 Mpc = standard ruler

BAO as a Standard BAO as a Standard RulerRuler Blake & Glazebrook 2003

Seo & Eisenstein 2003

Yun Wang, 3/2011

DifferentiatingDifferentiatingdark energy dark energy

and and modified gravitymodified gravity

Measuring redshift-space distortions (z) and bias b(z) allows us to measure fg(z)=(z)b(z)

[fg=dln/dlna]

H(z) and fg(z) allow us to differentiate dark energy and modified gravity.

Wang (2008)

Yun Wang, 3/2011

BAO Avantages and BAO Avantages and ChallengesChallenges

• Advantages:– Observational requirements are least demanding among

all methods (redshifts and positions of galaxies are easy to measure).

– Systematic uncertainties (bias, nonlinear clustering, redshift-space distortions) can be made small through theoretical progress in numerical modeling of data.

• Challenges:– Full modeling of systematic uncertainties

– Translate forecasted performance into reality

Yun Wang, 3/2011

BAO Systematic Effect: BAO Systematic Effect: Galaxy Clustering BiasGalaxy Clustering Bias

• How galaxies trace mass distribution– Could be scale-dependent– Only modeled numerically for a given galaxy sample selection (Angulo et

al. 2008)

Ratio of galaxy power spectrum over linear matter power spectrumHorizontal lines: no scale dependence in bias. Dashed lines: model

Yun Wang, 3/2011

BAO Systematic Effect: BAO Systematic Effect:

Redshift Space DistortionsRedshift Space Distortions • Artifacts not present in real space

– Small scales: smearing due to galaxy random motion (“Finger of God” effect)– Large scales: coherent bulk flows (out of voids and into overdense regions).

These boost BAO; can be used to probe growth rate fg(z)

Left: Ratio of redshift-space and real-space power spectra. Horizontal lines: coherent bulk flows only. Dashed lines: model (Angulo et al. 2008)

Yun Wang, 3/2011

BAO Systematic Effect:BAO Systematic Effect:Nonlinear Gravitational Nonlinear Gravitational

ClusteringClustering• Mode-coupling

– Small scale information in P(k) destroyed by cosmic evolution due to mode-coupling (nonlinear modes); intermediate scale P(k) also altered in shape

– Its effect can be reduced by: (1) Density field reconstruction (Eisenstein et al. 2007) (2) Extracting “wiggles only” constraints (discard P(k) shape info)

(3) Full modeling of correlation function (Sanchez et al. 2008)

–mostly untested on real data

Ratio of nonlinear and linear P(k)Horizontal line: no nonlinearityDashed lines: modelDark matter only (Augulo et al. 2008)

Yun Wang, 3/2011

2D Galaxy Clustering of SDSS 2D Galaxy Clustering of SDSS LRGsLRGs

Okumura et al. (2008) Chuang & Wang, arXiv:1102.2251

Yun Wang, 3/2011

First Measurements of H(z) and First Measurements of H(z) and DDAA(z) from Data(z) from Data

Average of 160 LasDamas mock catalogs SDSS LRG catalog

Chuang & Wang, arXiv:1102.2251

)(zH

Mpc 916)26.0(

Mpcs km 2.78)26.0(4645

112.43.4

zD

zH

A

Yun Wang, 3/2011

DETF FoMDETF FoM• DETF figure of merit

= 1/[area of 95% C.L. w0-wa error ellipse],for wX(a) = w0+(1-a)wa

• Pivot Value of a:At a=ap, wp= w0 + (1-ap)wa.

Making wpwa=0 gives 1-ap= – w0wa/ wa2:

DETF FoM = 1/[6.17(wa)(wp)]

• FoMr = 1/[(wa)(wp)]

• ap is different for each survey, thus wp refers to a different property of DE in each survey.

Yun Wang, 3/2011

• Given a set of DE parameters, what is the Given a set of DE parameters, what is the simplest, intuitive, and meaningful way to simplest, intuitive, and meaningful way to define a FoM?define a FoM?

• What are the sets of minimal DE What are the sets of minimal DE parameters that we should use in parameters that we should use in comparing different DE projects?comparing different DE projects?

Yun Wang, 3/2011

Generalized FoMGeneralized FoM• For parameters {fi}:

FoMr = 1/[det Cov(f1, f2 , f3, …)]1/2

• Can be easily applied to both real and simulated data

• DETF FoMr = 1/[(wa)(wp)] = 1/[det Cov(w0wa)]1/2

Wang (2008)

Yun Wang, 3/2011

What Parameters to What Parameters to Use:Use:

• Two considerations:– Simple, clear, intuitive physical meaning– Minimally correlated

• 2 Parameter Test: {w0, w0.5}

wX(a) = 3w0.5-2w0+3(w0-w0.5)a

w0 = wX(z=0), w0.5 = wX(z=0.5)

• 3 Parameter Test: {X0.5, X1.0, X1.5}

value of X(z) = X(z)/X(z=0) at z = 0.5, 1.0, 1.5simplest smooth interpolation: polynomial

Wang (2008)

Yun Wang, 3/2011

DE Forecasting from DE Forecasting from BAOBAO• Propagate the measurement errors in lnPg(k) into measurement

errors for the parameters pi:

lnPg(k) [Veff(k)]-1/2

=k·r/kr

3

3

)2(2

d)(

)(ln)(lnmax

min k

kkk

effj

g

i

gk

kij V

pP

pP

F

surveyg

g

g

geff

VknP

knP

kPn

kPndV

2

23

1),(

),(

1),()(

),()()(

r

rrk

04/20/23Yun Wang, 3/2011

Euclid slitless spectroscopy:

Veff ≈ 19 h-3 Gpc3 ≈ 75x largerthan now (i.e. SDSS) !

dwp, dwa ~ 1.5-1.9%, 6-14% (with Planck) (FoM≈370-1115)

FoM(imaging+spectroscopy+Planck)> 1500 log10(0.2)=-0.7(~ 100x better than now !)

only 20%of the survey !

Yun Wang, 3/2011

Two Approaches:Two Approaches:

• “Full P(k)” method:

parametrize P(k) using

[H(zi), DA(zi), fg(zi)8m(zi), 8g(zi), Pshoti, nS, mh2, bh2]

• BAO “wiggles only”:

P(k) P(k0.2,|z)[sin(x)/x]·exp[-(ks)1.4-k2 nl2/2]

x=(k2s2+ k//

2s//2)1/2

p1=ln s

-1=ln(DA/s); p2=ln s //=ln(sH).

-- Assumes that the shape of P(k) (and BAO) are fixed by CMB

-- Inclusion of growth info is precluded by construction

Yun Wang, 3/2011

FoM(wFoM(w00,w,waa))

P(k) +Planck P(k)+fg +PlanckEuclid 48.25 369.58 148.93 1114.91Euclid+BOSS 52.22 386.53 166.62 1165.83

Euclid-NIS+Planckdw0 dwa dwp FoM(w0,wa)

P(k) 0.067 0.140 0.0193 369.58P(k)+fg 0.023 0.061 0.0148 1114.91

Wang et al. (2010)

Yun Wang, 3/2011

FoM(XFoM(X0.670.67,X,X1.331.33,X,X22))

P(k) +Planck P(k)+fg +PlanckEuclid 421.26 3487.41 2979.51 26659.23Euclid+BOSS 449.85 3639.72 3206.81 27664.98

Wang et al. (2010)

FoM{f1,f2,…}= {det[Cov(f1,f2,…}]} -1/2

Yun Wang, 3/2011

EuclidBaseline: f>410-16 erg s-1 cm-2

(deg)2

0.5<z<2z/(1+z)=0.001

z/(1+z)>0.01:Photo-z regime

Wang et al. (2010)Y. Wang

Figure of Merit vs redshift accuracy

Yun Wang, 3/2011

0.5<z<2

Wang et al. (2010)

20,000 deg2

F(Hα) > 5x10-16 erg s-1 cm-2

0.3 < z < 1.7BAO+Planck

Y. Wang

Figure of Merit vs survey area

Yun Wang, 3/2011

BOSS + slitless zmin<z< 2

Wang et al. (2010)

20,000 deg2

F(Hα) > 5x10-16 erg s-1 cm-2

0.3 < z < 1.7BAO+Planck

Y. Wang

Figure of Merit vs redshift range

Yun Wang, 3/2011

z/(1+z)=0.001

Wang et al. (2010)

20,000 deg2

F(Hα) > 5x10-16 erg s-1 cm-2

0.3 < z < 1.7BAO+Planck

Y. Wang

Figure of Merit vs forecast method

Yun Wang, 3/2011

0.5<z<2

Wang et al. (2010)

Y. Wang

Figure of Merit vs flux limit

Yun Wang, 3/2011

0.5<z<2

Wang et al. (2010)

Y. Wang

FoM(X0.67,X1.33,X2)vs flux limit

Yun Wang, 3/2011

The EndThe End

Yun Wang, 3/2011

The Drag EpochThe Drag Epoch

• The BAO scale is the sound horizon scale at the drag epoch, when photon pressure can no longer prevent gravitational instability in baryons.– Epoch of photon-decoupling: (z*)=1

– Drag epoch: b(zd)=1, zd<z*

– The higher the baryon density, the earlier baryons can overcome photon pressure.

• Rb = (3b)/(4) =31500bh2/[(1+z)(TCMB/2.7K)4]

• zd=z* only if Rb=1

• Our universe has low baryon density: Rb(z*)< 1, thus zd<z*

(Hu & Sugiyama 1996)

Yun Wang, 3/2011

Puzzle: SDSS Large-Scale Clustering: Puzzle: SDSS Large-Scale Clustering: Sample Variance or Unknown Systematics?Sample Variance or Unknown Systematics?

04/20/23Yun Wang, 3/2011

Full Power Spectrum P(k)Primordial fluctuationsModels of inflationNeutrino massComplementary to CMB

More cosmology with the ENIS dataset

Redshift Space DistortionsAnisotropy of radial vs tangential clusteringImpossible with photometric redshifts !Test of Modified Gravity theoriesBreak degeneracies for models with same H(z)

SDSS

2dFGRS

SDSSLRGs

2SLAQVVDS

ENISslitless

only 20%of the survey !

Yun Wang, 3/2011

0.5<z<2

20,000 deg2

F(Hα) > 5x10-16 erg s-1 cm-2

0.3 < z < 1.7BAO+Planck

Y. Wang

FoM(X0.5,X1,X1.5,X2)vs flux limit