Download - Probing Dark Energy

1PASCOS – Sept. 10, 2006

Probing Dark Energy

Josh Frieman

PASCOS, Ohio State University, Sept. 10, 2006

PASCOS – Sept. 10, 2006 2

Brightness of distant Type Ia supernovae, along with CMB and galaxy clustering data, indicates the expansion of the Universe is accelerating, not decelerating.

This requires either a new form of stress-energy with negative effective pressure or a breakdown of General Relativity at large distances:

DARK ENERGY

Characterize by its effective equation of state: w = p/<1/3and its relative contribution to the present density of the Universe: DE

Special case: cosmological constant: w = 1

Dark Energy and the Accelerating Universe


What is the Nature of the Dark Energy?

Stress-Energy: G = 8G [T(matter) + T(dark energy)]

Gravity: G + f(g) = 8G T(matter) (e.g., branes)

Inhomogeneity:

Key Experimental Questions:

• Is DE observationally distinguishable from a cosmological

constant, for which T (vacuum) = g/3, i.e., w =—1?

• Can we distinguish between gravity and stress-energy?

Combine geometric with structure-growth probes

• Does dark energy evolve: w=w(z)?


• Probe dark energy through the history of the expansion rate:

and the growth of large-scale structure:

• Parametrize DE Evolution:

• Geometric tests:• Comoving distance Weak Lensing

• Standard Candles Supernovae • Standard Rulers Baryon Oscillations • Standard Population Clusters

Probing Dark Energy

€

H 2(z)

H02

= Ωm (1+ z)3 + ΩDE exp 3 (1+ w(z))d ln(1+ z)∫[ ] + 1− Ωm − ΩDE( ) 1+ z( )2

€

δ a( )ρ

€

w(z) = w0 + wa (1− a) + ...

€

r(z) = Fdz

H z( )∫ ⎡

⎣ ⎢

⎤

⎦ ⎥

dL z( ) = 1+ z( )r(z)

dA z( ) = 1+ z( )−1

r(z)

dV

dzdΩ=

r2(z)

H(z)


Constraints

on Constant

Dark Energy

Equation of State

CFHT SNLS+

SDSS BAO

Astier etal 05

Eisenstein etal 05

Assuming flat Universe and wa=0


Constraints

on

Time-varying

Dark Energy

3-parameter

Model

Substantially

weaker

Jarvis etal 05

Assumes flat

Universe


Scalar Field Dark Energy

If Dark Energy is due to a scalar field, , evolving in a potential, V():

Density & pressure:

)(

)(2

21

221

ϕϕ

ϕϕ

VP

V

−=

+=

&

&

'3 VH −=+ ϕϕ &&&

V

Scalar Field Dark Energy

Ultra-light particle: Dark Energy hardly clusters, nearly smoothEquation of state: usually, w > 1 and evolves in timeHierarchy problem: Why m/ϕ ~ 1061?Weak coupling: Quartic self-coupling ϕ < 10122

General features:

meff < 3H0 ~ 10-33 eV (w < 0)(Potential < Kinetic Energy)

V ~ m22 ~ crit ~ 10-10 eV4

~ 1028 eV ~ MPlanck

aka quintessence

V

1028 eV

(10–3 eV)4

The Coincidence Problem

Why do we live at the `special’ epoch when the dark energy density is comparable to the matter energy density?

matter ~ a-3

DE~ a-3(1+w)

a(t)Today

Scalar Field Models & Coincidence

VV

Runaway potentialsDE/matter ratio constant(Tracker Solution)

Pseudo-Nambu Goldstone BosonLow mass protected by symmetry

(Cf. axion) JF, Hill, Stebbins, Waga V() = M4[1+cos(/f)]

f ~ MPlanck M ~ 0.001 eV ~ m

e.g., e–ϕ or ϕ–n

MPl

Ratra & Peebles; Caldwell, Steinhardt,etal; Albrecht etal,…

`Dynamics’ models

(Freezing models)

`Mass scale’ models

(Thawing models)

Caldwell & Linder Goal for ~2015+: JDEM, LSST

Goal for ~2012: SPT+DES


Probing Dark EnergyPrimary Techniques identified by the Dark Energy Task Force report:

• Supernovae• Galaxy Clusters•Weak Lensing • Baryon Acoustic Oscillations

Multiple Techniques needed: complementary in systematics and in science reach


Type Ia SNPeak Brightnessas a calibrated`Standard’ Candle

Peak brightnesscorrelates with decline rate

Phillips 1993

After correction,~ 0.15 mag(~7% distance error)

Luminosity

Time

PASCOS – Sept. 10, 2006

Supernova

Hubble

Diagram

CFHT Supernova

Legacy Survey

Astier etal 05

Needed: more, better

data at low and

Intermediate redshift

KAIT, SNF, CSP, CfA

SDSSESSENCE, SNLS

16

Published Light Curves for Nearby Supernovae

More,

Better

needed

17

On-going SN surveys

Future Surveys:

PanSTARRS, DES, JDEM, LSST

(200)

(2000) (3000) (105)

high-z

Supernovae

Cf. Y.B.

18

Supernovae: the JDEM Future

• Goal: Determine w0 to ~5% and wa to ~20% (combined with CMB) • Statistical Requirement: ~1% relative distance measurements (2% flux) in z~0.1 redshift bins • Assume systematic error can be reduced to this level Kim, etal 04, Kim & Miquel 05 • Require ~3000 SNe spread over z ~ 0.3-1.7 and a well-observed sample at low z to anchor the Hubble diagram. Consequent requirements for NIR imaging and photometric stability lead to a space-based mission.

Proposals: SNAP, DESTINY, JEDI,…

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Probing Dark Energy Evolution: 2% Mag Systematic Error Floors

JF, Huterer, Linder, Turner 03

3000 SNe


e.g., Luminosity Evolution: We believe SNe Ia at z~0.5 are not intrinsically ~25% fainter than

nearby SNe (the basis for Dark Energy). Could SNe at z~1.5 be 2%

fainter/brighter than those nearby, in a way that leaves all other

observables fixed? Key: Many observables per SN; which needed?

Expectation: drift in progenitor population mix (progenitor mass,

age, metallicity, C/O, accretion rates, etc).

Control: the variety of host environments at low redshift spans a

larger range of metallicity, environment, than the median

differences between low- and high-z environments, so we can

compare high-z apples with low-z apples, using host info.,

LC shape, colors, spectral features & spectral evolution, and

assuming these exhaust the parameters that control Lpeak.

Can we get there? Systematics Concerns

Not (yet)guaranteedby SN theory

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SDSS II Supernova SurveySept-Nov. 2005-7

• Obtain ~200 high-quality SNe Ia light curves in the `redshift desert’ z~0.05-0.35: continuous Hubble diagram

• Probe Dark Energy in z regime less sensitive to evolution than, and complementary to, deeper surveys

• Study SN Ia systematics with high photometric accuracy

SDSS 2.5 meter Telescope

25

SN 2005 gb

z = 0.086, confirmed at ARC 3.5mPreliminary gri light curve and fit from low-z templates

Before After

Composite gri

images

26

SDSS II:~130

spectroscopically

confirmed

Type Ia

Supernovae

from the

Fall 2005

Season

First Results

aiming for

Jan. 07 AAS


Unusual SN: 2005gj

• Followed this object all semester with MDM

• 12 observations• Type Ia strongly interacting with CSM– Only 1 other object like this• 2002ic

• Prieto et al. 2006 (in preparation)– Spitzer observations

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.


Evolution of Structure

Robustness of the paradigm recommends its use as a Dark Energy probe

Price: additional cosmological and structure formation parameters

Bonus: additional structure formationParameters

Methods: WL, Clusters


Growth of Density Perturbations Volume Element

Flat, matter-dominated

w = -0.7w = –1

Raising w at fixed DE: decreases growth rate of

density perturbations and decreases volume surveyed


Clusters and Dark Energy

MohrVolume Growth(geometry)

Number of clusters above observable mass threshold

Dark Energy equation of state

€

dN(z)

dzdΩ=

dV

dz dΩn z( )

•Requirements1.Understand formation of dark matter halos 2.Cleanly select massive dark matter halos (galaxy clusters) over a range of redshifts 3.Redshift estimates for each cluster 4.Observable proxy that can be used as cluster mass estimate: O =g(M)

Primary systematic: Uncertainty in bias & scatter of mass-observable relation






€

dN(z)

dzdΩ=

dV

dz dΩn z( )




Clusters form hierarchically

z = 7 z = 5 z = 3

z = 1 z = 0.5 z = 0

5 Mpc

dark matterdark matter

timetime

Kravtsov


Theoretical Abundance of Dark Matter Halos

Warren et al ‘05

Warren etal

€

n(z) = (dn /d ln M)d ln MM min

∞

∫






€

dN(z)

dzdΩ=

dV

dz dΩn z( )




Cluster Selection

• 4 Techniques for Cluster Selection:

• Optical galaxy concentration

• Weak Lensing

• Sunyaev-Zel’dovich effect (SZE)

• X-ray

38PASCOS – Sept. 10, 2006Holder






€

dN(z)

dzdΩ=

dV

dz dΩn z( )




Photometric Redshifts

• Measure relative flux in four filters griz: track the 4000 A break

• Estimate individual galaxy redshifts with accuracy (z) < 0.1 ~0.02 for clusters

• Precision is sufficient for Dark Energy probes, provided error distributions well measured.

Elliptical galaxy spectrum


DESgriz filters10 Limiting Magnitudes g 24.6 r 24.1 i 24.0 z 23.9

+2% photometric calibrationerror added in quadrature

Key: Photo-z systematic errors under control using existing spectroscopic training sets to DES photometric depth

Galaxy Photo-z Simulations

+VDES JK

Improved Photo-z & Error Estimates and robust methods of outlier rejection

DES

Cunha, etal

DES + VDES on

ESO VISTA 4-m

enhances science reach






€

dN(z)

dzdΩ=

dV

dz dΩn z( )




Precision Cosmology with Clusters?

Effect of Uncertainty inmass-observable relation

Sensitivity to Mass Threshold

€

dN(z)dzdΩ

= cH z( )

dA2 1+z( )2 dM

dnM,z( )

dMf M( )

0

∞∫ Mass

threshold


Cluster Mass Estimates

4 Techniques for Cluster Mass Estimation:

• Optical galaxy concentration

• Weak Lensing

• Sunyaev-Zel’dovich effect (SZE)

• X-ray • Cross-compare these techniques to

reduce systematic errors• Additional cross-checks:

shape of mass function; cluster

correlations


SZE vs. Cluster Mass: Progress toward Realistic

Simulations

Motl, etalIntegrated SZE flux decrement depends only on cluster mass: insensitive to details of gas dynamics/galaxy formation in the cluster core robust scaling relations

Nagai

SZE

flu

x

Adiabatic∆ Cooling+Star Formation

SZE

Obs

erva

ble

Kravtsov

small (~10%) scatter


Gravitational Lensing by Clusters

Weak Lensing of Faint Galaxies: distortion of shapes

BackgroundSourceshape

ForegroundCluster

Weak Lensing of Faint Galaxies: distortion of shapes


Note: the effect has been greatly exaggerated here

ForegroundCluster

Lensing of real (elliptically shaped) galaxies

Co-add signal around a number of Clusters



Statistical Weak Lensing by Galaxy Clusters

Mean

Tangential

Shear

Profile

in Optical

Richness

(Ngal) Bins

to 30 h-1Mpc

Sheldon,

Johnston, etal

SDSS


Statistical Weak Lensing CalibratesCluster Mass vs. Observable Relation

Cluster Massvs. Number of galaxies they contain

Future:use this to independently calibrate, e.g., SZE vs. Mass

Johnston, Sheldon, etal, in preparation

Statistical Lensing eliminates projection effectsof individual cluster massestimates

Johnston, etalastro-ph/0507467

SDSS DataPreliminaryz<0.3


Dark Energy Survey + South Pole Telescope

10-m South Pole Telescope: 4000 sq. deg. SZE Survey

Dec 2005

Blanco 4-m Optical Telescope at CTIO: 5000 sq. deg. Dark Energy Survey

See also: APEX, ACT,…


The Dark Energy Survey• Study Dark Energy using 4 complementary* techniques: I. Cluster Counts II. Weak Lensing III. Baryon Acoustic

Oscillations IV. Supernovae

• Two multiband surveys: 5000 deg2 g, r, i, z 40 deg2 repeat (SNe)

• Build new 3 deg2 camera and Data management sytem Survey 2009-2015 (525 nights) Response to NOAO AO

Blanco 4-meter at CTIO

*in systematics & in cosmological parameter degeneracies*geometric+structure growth: test Dark Energy vs. Gravity


The DES Instrument: DECam

3556 mm

1575 mm

Hexapod

Optical Lenses

F8 Mirror

CCDRead out

Filters Shutter


Observer

Dark matter halos

Background sources

Statistical measure of shear pattern, ~1% distortion Radial distances depend on geometry of Universe Foreground mass distribution depends on growth of structure

Weak Lensing: Cosmic Shear


Weak lensing: shear and mass

Jain


•Cosmic Shear Angular Power Spectrum in 4 Photo-z Slices

•Future: Shapes of 108-109 galaxies

•Primary Systematics: photo-z’s, PSF anisotropy, shear calibration

Weak Lensing Tomography

Huterer

Statistical errorsshown


Weak Lensing Systematics:

Anisotropic PSF

• Whisker plots for three BTC camera exposures; ~10% ellipticity• Left and right are most extreme variations, middle is more typical.• Correlated variation in the different exposures: PCA analysis --> can use stars in all the images: much better PSF interpolation

Focus too lowFocus (roughly) correctFocus too high

Jarvis and Jain


PCA Analysis: Improved Systematics Reduction

• Remaining ellipticities are essentially uncorrelated.• Measurement error is the cause of the residual shapes.• 1st improvement: higher order polynomial means PSF accurate to smaller scales• 2nd: Much lower correlated residuals on all scales!

Focus too lowFocus (roughly) correctFocus too high

Jarvis and Jain

61PASCOS - Sept. 10, 2006

Reducing WL Shear Systematics

DECam+Blancohardwareimprovements that will reduce raw lensing systematics

Red: expected signal

Results from 75 sq. deg. WLSurvey with Mosaic II and BTCon the Blanco 4-mBernstein, etal

DES: comparable depth: source galaxies well resolved & bright:low-risk

(improved systematic)

(signal)

(old systematic)

Cosmic Shear

62

The Large Synoptic Survey Telescope

(LSST)

Time-Domain Astronomy

survey visible sky every few

nights

Weak Lensing

Cluster Counts

Galaxy Clustering

….


Baryon Acoustic Oscillations (BAO) in the CMB

Characteristic angular scale set by sound horizon at recombination: standard ruler (geometric probe).

Sound Waves in the Early Universe

Before recombination: Universe is ionized. Photons provide enormous

pressure and restoring force.

Perturbations oscillate as acoustic waves.

After recombination: Universe is neutral. Photons can travel

freely past the baryons. Phase of oscillation at

trec affects late-time amplitude.

Big

Bang T

oday

Recombinationz ~ 1000

~400,000 yearsIonized Neutral

Time

Sound Waves Each initial overdensity (in

dark matter & gas) is an overpressure that launches a spherical sound wave.

This wave travels outwards at 57% of the speed of light.

Pressure-providing photons decouple at recombination. CMB travels to us from these spheres.

Sound speed plummets. Wave stalls at a radius of 150 Mpc.

Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies. Preferred separation of 150 Mpc.

Eisenstein

A Statistical Signal

The Universe is a super-position of these shells.

The shell is weaker than displayed.

Hence, you do not expect to see bullseyes in the galaxy distribution.

Instead, we get a 1% bump in the correlation function.


Baryon Acoustic Oscillations: CMB & Galaxies

CMBAngularPowerSpectrum

SDSS galaxycorrelation function

Acoustic series in P(k) becomes a single peak in (r)

Bennett, etal

Eisenstein etal

BaryonOscillationsIn theMatter PowerSpectrum

Future:HETDEXWFMOS`SDSS III’

Seo &Eisenstein

Hu &Haiman


Conclusions• Excellent prospects for increasing the precision on Dark Energy parameters from a sequence of increasingly complex and ambitious experiments over the next 5-15 years: DES+SPT, PANSTARRS,…, followed by LSST and JDEM

• Exploiting complementarity of multiple probes will be key: we don’t know what the ultimate systematic error floors for each method will be. Combine geometric with structure-growth probes to help distinguish modified gravity from dark energy.

• What parameter precision is needed to stimulate theoretical progress? It depends in large part on what the answer is.

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