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
3PASCOS – Sept. 10, 2006
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)?
4PASCOS – Sept. 10, 2006
• 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)
5PASCOS – Sept. 10, 2006
Constraints
on Constant
Dark Energy
Equation of State
CFHT SNLS+
SDSS BAO
Astier etal 05
Eisenstein etal 05
Assuming flat Universe and wa=0
6PASCOS – Sept. 10, 2006
Constraints
on
Time-varying
Dark Energy
3-parameter
Model
Substantially
weaker
Jarvis etal 05
Assumes flat
Universe
7PASCOS – Sept. 10, 2006
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
12PASCOS – Sept. 10, 2006
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
13PASCOS – Sept. 10, 2006
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
14PASCOS – Sept. 10, 2006
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,…
19
Probing Dark Energy Evolution: 2% Mag Systematic Error Floors
JF, Huterer, Linder, Turner 03
3000 SNe
PASCOS – Sept. 10, 2006
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
21PASCOS – Sept. 10, 2006
22
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
24
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
27
28PASCOS – Sept. 10, 2006
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.
29PASCOS – Sept. 10, 2006
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
30PASCOS – Sept. 10, 2006
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
31PASCOS – Sept. 10, 2006
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
32PASCOS – Sept. 10, 2006
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
33PASCOS – Sept. 10, 2006
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
34PASCOS – Sept. 10, 2006
Clusters form hierarchically
z = 7 z = 5 z = 3
z = 1 z = 0.5 z = 0
5 Mpc
dark matterdark matter
timetime
Kravtsov
35PASCOS – Sept. 10, 2006
Theoretical Abundance of Dark Matter Halos
Warren et al ‘05
Warren etal
€
n(z) = (dn /d ln M)d ln MM min
∞
∫
36PASCOS – Sept. 10, 2006
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
37PASCOS – Sept. 10, 2006
Cluster Selection
• 4 Techniques for Cluster Selection:
• Optical galaxy concentration
• Weak Lensing
• Sunyaev-Zel’dovich effect (SZE)
• X-ray
38PASCOS – Sept. 10, 2006Holder
39PASCOS – Sept. 10, 2006
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
40PASCOS – Sept. 10, 2006
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
41PASCOS – Sept. 10, 2006
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
42PASCOS – Sept. 10, 2006
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
43PASCOS – Sept. 10, 2006
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
44PASCOS – Sept. 10, 2006
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
45PASCOS – Sept. 10, 2006
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
46PASCOS – Sept. 10, 2006
Gravitational Lensing by Clusters
Weak Lensing of Faint Galaxies: distortion of shapes
BackgroundSourceshape
ForegroundCluster
Weak Lensing of Faint Galaxies: distortion of shapes
BackgroundSourceshape
Note: the effect has been greatly exaggerated here
ForegroundCluster
Lensing of real (elliptically shaped) galaxies
Co-add signal around a number of Clusters
BackgroundSourceshape
50PASCOS – Sept. 10, 2006
Statistical Weak Lensing by Galaxy Clusters
Mean
Tangential
Shear
Profile
in Optical
Richness
(Ngal) Bins
to 30 h-1Mpc
Sheldon,
Johnston, etal
SDSS
51PASCOS – Sept. 10, 2006
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
52PASCOS – Sept. 10, 2006
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,…
53PASCOS – Sept. 10, 2006
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
PASCOS – Sept. 10, 2006
The DES Instrument: DECam
3556 mm
1575 mm
Hexapod
Optical Lenses
F8 Mirror
CCDRead out
Filters Shutter
55PASCOS – Sept. 10, 2006
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
56PASCOS – Sept. 10, 2006
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
57PASCOS – Sept. 10, 2006
Weak lensing: shear and mass
Jain
58PASCOS – Sept. 10, 2006
•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
PASCOS – Sept. 10, 2006
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
PASCOS – Sept. 10, 2006
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
….
63PASCOS – Sept. 10, 2006
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
64PASCOS - Sept. 10, 2006
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.
68PASCOS - Sept. 10, 2006
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
70PASCOS – Sept. 10, 2006
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.