Observational Probes Observational Probes ofof

Dark EnergyDark Energy Yun Wang Yun Wang

Univ. of OklahomaUniv. of Oklahoma

The Dark Side of the Universe VIII The Dark Side of the Universe VIII Buzios, Brazil, June 12, 2012 Buzios, Brazil, June 12, 2012

Beware of the dark side …

Master Yoda

Yun Wang, DSU 2012

How do we know there is How do we know there is dark energy?dark energy?

We infer its existence via its We infer its existence via its influence on the expansion influence on the expansion

history of the universe.history of the universe.

Yun Wang, DSU 2012

First Evidence for Dark First Evidence for Dark Energy Energy in the Hubble Diagrams of in the Hubble Diagrams of

SupernovaeSupernovae [ [ddLL((zz)] )] (Schmidt et al. 1998, Perlmutter et al. (Schmidt et al. 1998, Perlmutter et al. 1999)1999)faint

bright

Yun Wang, DSU 2012

Alternative Analysis of First EvidenceAlternative Analysis of First EvidenceFlux-averaged and combined data of 92 SNe Ia from Schmidt et al. (1998) and Perlmutter et al. (1999). [Wang 2000b, ApJ ]

Deceleration parameter

q0 =m/2-

Data favor q0 <0: cosmic

accelerationYun Wang, DSU 2012

Hubble diagram of 472 SNe Ia compiled by Conley et al. (2011)

Yun Wang, DSU 2012

Wang, Chuang, & Mukherjee (2012) [See Wang & Tegmark (2005) for the method to derive uncorrelated estimate of H(z) using SNe.]

H(z) = [da/dt]/a

Cosmic Acceleration

Today Past

Yun Wang, DSU 2012

w(z) = w0+wa(1-a); w(z)=w0(3a-2)+3w0.5(1-a) 1+z = 1/a; z: cosmological redshift; a: cosmic scale factor

CMB: WMAP7 (Komatsu et al. 2011)H0=73.82.4 km/s/Mpc (Riess et al. 2011) GRBs (compiled by Wang 2008)SNe: 472 SNe Ia (compiled by Conley et al. 2011)GC: [H(z=0.35), DA(z=0.35)] from SDSS LRGs (Chuang & Wang 2011)

(Wang, Chuang, & Mukherjee 2012)

Yun Wang, DSU 2012

Model-independent constraints on dark Model-independent constraints on dark energyenergy

(as proposed by Wang & Garnavich 2001)(as proposed by Wang & Garnavich 2001)

1 yoctogram=10-24g Wang, Chuang, & Mukherjee (2012)

Yun Wang, DSU 2012

Some Candidates for Dark Some Candidates for Dark EnergyEnergy

cosmological constant (Einstein 1917)

quintessence (Freese, Adams, Frieman, Mottola 1987; Linde 1987; Peebles & Ratra 1988; Frieman et al. 1995; Caldwell, Dave, & Steinhardt 1998; Dodelson, Kaplinghat, & Stewart 2000)

k-essence: (Armendariz-Picon, Mukhanov, & Steinhardt 2000)

Modified Gravity Vacuum Metamorphosis (Sahni & Habib 1998; Parker & Raval 1999) Modified Friedmann Equation (Freese & Lewis 2002)Phantom DE from Quantum Effects (Onemli & Woodard 2004)Backreaction of Cosmo. Perturbations (Kolb, Matarrese, & Riotto 2005)

Emergent Gravity (Padmanabhan 2009)

Yun Wang, DSU 2012

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/a2

• Growth history of cosmic large scale structure [growth Growth history of cosmic large scale structure [growth rate frate fgg(z) or growth factor G(z) or growth factor G((zz)])]

tells us whether general relativity is modified, given tells us whether general relativity is modified, given HH((zz))

Yun Wang, DSU 2012

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

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

– Galaxy Cluster Statistics:Galaxy Cluster Statistics: probes H(z)– Other MethodsOther Methods

Yun Wang, DSU 2012

Supernovae as Standard CandlesSupernovae as Standard Candles

The SNe Ia lightcurves (left) are very different from that of SNe II (below).

Measuring the apparent peak Measuring the apparent peak brightness and the redshift of SNe Ia brightness and the redshift of SNe Ia gives gives ddLL((zz), hence ), hence HH((zz))

Yun Wang, DSU 2012

Theoretical understanding of SNe Theoretical understanding of SNe IaIa

Binary C/O white dwarf near Chandrasekher limit (~ 1.4 MSun) explosion radioactive decay of 56Ni and 56Co: observed brightness

• explosion: carbon burning begins as a turbulent deflagration, then makes a transition to a supersonic detonation

• earlier transition: cooler explosion less 56Ni produced: dimmer SN Ialower opacity faster decline of the SN brightness

Wheeler 2002 (resource letter)

Yun Wang, DSU 2012

Calibration of SNe IaCalibration of SNe Ia Phillips 1993 Riess, Press, & Kirshner 1995

Brighter SNe IaBrighter SNe Iadecline more slowlydecline more slowly make a correction make a correction to the brightness based to the brightness based on the decline rate.on the decline rate.

26 SNe Ia with Bmax-Vmax 0.20 fromthe Calan/Tololo sample[Hamuy et al. 1996, AJ, 112, 2398]

Yun Wang, DSU 2012

SNe Ia as Cosmological Standard SNe Ia as Cosmological Standard CandlesCandles

Systematic effects: dust: can be constrained using multi-color data (Riess et al.

1998; Perlmutter et al. 1999)

gray dust: constrained by the cosmic far infrared background. (Aguirre & Haiman 2000)

gravitational lensing: its effects can be reduced by flux-averaging. (Wang 2000; Wang, Holz, & Munshi 2002)

SN Ia evolution (progenitor population drift):Once we obtain a large number of SNe Ia at high z

(z > 1), we can disregard SN Ia events that have no counterparts at high z, and only compare like with like. (Branch et al., astro-ph/0109070)

Yun Wang, DSU 2012

Weak Lensing of SNe IaWeak Lensing of SNe Ia Kantowski, Vaughan, & Branch 1995 Frieman 1997 Wambsganss et al. 1997 Holz & Wald 1998 Metcalf & Silk 1999 Wang 1999

WL of SNe Ia can be modeled by a Universal Probability Distribution for Weak Lensing Magnification (Wang, Holz, & Munshi 2002)

The WL systematic of SNe Ia can be removed by flux averaging (Wang 2000; Wang & Mukherjee 2003)

Yun Wang, DSU 2012

Impact of Supernova systematic Impact of Supernova systematic errorserrors

The large effect of flux-averaging of SNe (which minimizes the weak lensing systematic effect) indicates the presence of unknown systematic errors.

Wang, Chuang, & Mukherjee (2012)

Yun Wang, DSU 2012

SNe+CMB+HSNe+CMB+H00+GRB+GRB

Yun Wang, DSU 2012

Wang, Chuang, & Mukherjee (2012)

SNe+GC+CMB+HSNe+GC+CMB+H00+GRB+GRB

Yun Wang, DSU 2012

Flux-averaging of SNe increases their concordance with other data.Wang, Chuang, & Mukherjee (2012)

Getting the most distant SNe Getting the most distant SNe Ia:Ia: critical for measuring the evolution in dark energy density:

Wang & Lovelave (2001)Yun Wang, DSU 2012

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

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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, DSU 2012

Challenge in 2D: Challenge in 2D: Proper Modeling of SDSS DataProper Modeling of SDSS Data

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

Yun Wang, DSU 2012

First Measurements of H(z) & DFirst Measurements of H(z) & DAA(z) from (z) from DataDataLasDamas mock catalog SDSS LRG catalog

xh(z) =H(z)s = 0.04339 0.00178 (4.1%); xd(z) = DA(z)/s= 6.599 0.263 (4.0%)r(xh,xd) = 0.0604 (z=0.35, s: BAO scale, i.e., sound horizon at the drag epoch)

Chuang & Wang, arXiv:1102.2251

Yun Wang, DSU 2012

Evaluating the ModelingEvaluating the ModelingAverage of 160 LasDamas mock catalogs

Chuang & Wang, arXiv:1102.2251

Yun Wang, DSU 2012

Different analyses of Different analyses of GC/BAOGC/BAO

Yun Wang, DSU 2012

GC results from Chuang & Wang (2011) favors w = -1, while the results from some other groups favor w < -1. Wang, Chuang, & Mukherjee (2012)

Use galaxy Use galaxy clustering to clustering to differentiate differentiate

dark energy and dark energy 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, DSU 2012

xh=H(z)s, xd=DA(z)/s z=0.1 Wang (2012)

Yun Wang, DSU 2012

Weak Lensing Tomography Weak Lensing Tomography and Cross-Correlation and Cross-Correlation

CosmographyCosmography

Yun Wang, DSU 2012

• Weak Lensing Tomography:Weak Lensing Tomography: compare observed cosmic shear correlations with theoretical/numerical predictions to measure cosmic large scale structure growth history G(z) and H(z) [Wittman et al. 2000]

• WL Cross-Correlation WL Cross-Correlation CosmographyCosmography measure the relative shear signals of galaxies at different distances for the same foreground mass distribution: gives distance ratios dA(zi)/dA(zj) that can be used to obtain cosmic expansion history H(z) [Jain & Taylor 2003]Yun Wang, DSU 2012

Measurements of cosmic shear Measurements of cosmic shear (WL image distortions of a few percent)(WL image distortions of a few percent)

left:top-hat shear variance; right: total shear correlation function. 8=1 (upper); 0.7 (lower). zm=1.

First conclusive detection of cosmic shear was made in 2000.

Yun Wang, DSU 2012

Cosmological parameter constraints from WLCosmological parameter constraints from WL

L: 8 from analysis of clusters of galaxies (red) and WL (other). [Hetterscheidt et al. (2006)]

R: DE constraints from CFHTLS Deep and Wide WL survey. [Hoekstra et al. (2006)]

Yun Wang, DSU 2012

Measurements of cosmic shear Measurements of cosmic shear (WL image distortions of a few percent)(WL image distortions of a few percent)

Two-point shear correlationfunction measured from thecombined 57 pointings of theCFHTLS by Fu et al. (2008)

First conclusivedetection of cosmicshear was made in 2000.

Yun Wang, DSU 2012

Comparison between CFHTLS (blue) andWMAP3 (green).

Fu et al. (2008)

Yun Wang, DSU 2012

Most recent WL measurements:Most recent WL measurements:

*Same raw SDSS data over area of SDSS II SN survey; analyzed by two groups

Yun Wang, DSU 2012

ref instrument Area (deg2)

# of galaxies

8

Fu et al. (2008) CFHT/MegaCam 57 1.7M 8(m/0.3)0.64=0.700.04

Schrabback et al. (2010)

HST/ACS 1.64 195K 8(m/0.3)0.51=0.750.08

Huff et al. (2011) SDSS* 168 1.3M 8=0.636+0.109 0.154; @m=0.265

Lin et al. (2011) SDSS* 275 4.5M 8(m/0.3)0.7=0.64+0.080.12

Growth history of structure from WLGrowth history of structure from WL

Cosmic shear signal on fixed angular scales as a function of redshift.[Massey et al. (2007)]

Yun Wang, DSU 2012

WL systematics effectsWL systematics effects• Bias in photometric redshift distribution• PSF correction• Bias in selection of the galaxy sample• Intrinsic distortion signal (intrinsic

alignment of galaxies)

Yun Wang, DSU 2012

DE constraints from WL depend on the DE constraints from WL depend on the accuracy of photometric redshiftsaccuracy of photometric redshifts

Huterer et al. (2006)Yun Wang, DSU 2012

WL forecasts for a LSST-like WL forecasts for a LSST-like surveysurvey

Knox, Song, & Tyson (2006)Yun Wang, DSU 2012

Future Dark Energy Surveys Future Dark Energy Surveys (an incomplete list)(an incomplete list)

• ESO VISTA (2005?-?): few hundred SNe, z < 0.5• Pan-STARRS (2006-?): all sky WL, 100’s SNe y, z < 0.3, 6

bands, t = 10d

• BOSS (2011-?): 10,000 sq deg galaxy redshift survey, 0.1<z<0.7• Dark Energy Survey (2012?): clusters at 0.1<z<1.3, 5000 sq deg

WL, up to 4000 SNe at 0.05<z<1.2• HETDEX(2012?): 420 sq deg BAO, 1.9 < z < 3.5

• LSST (2019?): 0.5-1 million SNe Ia y, z < 0.8, > 2 bands, t = 4-7d; 20,000 sq deg WL & BAO with photo-z

• Euclid (2019): 15,000 sq deg WL and galaxy redshift survey• WFIRST (2022?): SNe, WL (?), galaxy redshift survey (?)

Yun Wang, DSU 2012

How many methods should we How many methods should we use?use?

• The challenge to solving the DE mystery will not be the statistics of the data obtained, but the tight control of systematic effects inherent in the data.

• A combination of the three most promising methods (SNe, GC/BAO, WL), each optimized by having its systematics minimized by design, provides the tightest control of systematics.

Yun Wang, DSU 2012

ConclusionsConclusions Unraveling the nature of DE is one of the most

important problems in cosmology today. Current data (SNe Ia, CMB, and GC) are consistent with a constant X(z) at 68% confidence. However, the reconstructed X(z) still has large uncertainties at z > 0.5.

DE probing methods’ checklist: 1) Supernovae as standard candles; 2) Galaxy clustering (inc. baryon acoustic oscillations); 3) Weak lensing tomography and cosmography. A combination of different methods carried out in

ambitious surveys is required to achieve accurate and precise constraints on the time dependence of X(z) , and to test gravity. This will have a fundamental impact on particle physics and cosmology.

Yun Wang, DSU 2012