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Probing Dark Energy. Josh Frieman. PASCOS, Ohio State University, Sept. 10, 2006. Dark Energy and the Accelerating Universe. Brightness of distant Type Ia supernovae, along with CMB and galaxy clustering data, indicates the expansion of the Universe - PowerPoint PPT Presentation
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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.