A Cosmic Yardstick : Measuring Dark Energy with
Baryon Oscillations
Nikhil Padmanabhan1
w/ M. White, D.J. Schlegel, BOSS collaboration
1 Lawrence
Berkeley Labs
03-11-2009 / Hubble Symposium
NP, Schlegel, Seljak et al, 2007
NP & White, 2008
NP, White, Cohn 2009
NP & White, 2009, in prep
N. Padmanabhan (LBL)
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The Big Picture
Baryon oscillations are now an integral part of the dark energy
toolkit.
Extremely ambitious surveys are being planned, on promises
(hopes) of small systematic errors.
Real space, matter BAO look to be in good shape. Hope for
galaxies and redshift space.
Next generation of surveys are underway. Stay tuned for new
results.
N. Padmanabhan (LBL)
A Cosmic Yardstick
03-11-2009
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Outline
1
The Context : Dark Energy
2
Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
The Measurement
3
Nonlinear Evolution of BAO
4
Current and Future Observations
SDSS-III
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The Context : Dark Energy
Outline
1
The Context : Dark Energy
2
Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
The Measurement
3
Nonlinear Evolution of BAO
4
Current and Future Observations
SDSS-III
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The Context : Dark Energy
A Cosmological Standard Model
Multiple observations point to a concordance cosmological model.
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Cosmic Microwave Background
Large scale distribution of galaxies
Supernovae
Integrated Sachs Wolfe (ISW) measurements
Clusters
... and others
Matter content : ΩM ∼ 0.25, Ωb ∼ 0.05
Curvature : ΩK ∼ 0
ΩDE ∼ 0.75; an accelerating Universe!
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SNe, ISW
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The Context : Dark Energy
Probes of Dark Energy
The Homogeneous Universe
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Constrain scale factor a(t) as a function of time
Observations constrain dA (z), dL (z), H(z)
Geometrical probes
SNe – standard candles, baryon oscillations – standard rulers
Inhomogeneous Universe
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Constrain δ(t) – growth of fluctuations
Dynamical probes
Weak lensing, clusters, redshift space distortions
Standard rulers - completely analogous to standard candles!
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Baryon Oscillations : Basics
Outline
1
The Context : Dark Energy
2
Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
The Measurement
3
Nonlinear Evolution of BAO
4
Current and Future Observations
SDSS-III
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
A Toy Model : z = ∞
At z 1000, ∃ photon-baryon plasma
Consider an adiabatic point perturbation
Overpressured region drives out a sound wave
M. White
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
A Toy Model : z > 1000
√
Sound wave expands at cs ∼ c/ 3
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
A Toy Model : z ∼ 1000
At z ∼ 1000, T ∼ 0.3eV, neutral H forms.
cs → 0
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
A Toy Model
Photons begin to diffuse away
Baryon overdensity shell at L ∼ 150Mpc
Overdensities begin to grow
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
A Toy Model : z ∼ 0 − 10
Statistical effect only seen in the correlation function.
Non-linear evolution starts to smear out the peak.
Galaxies form in the overdensities.
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
The Linear Correlation Function
Use feature in matter correlation function as a standard ruler.
Use galaxies as a proxy for matter.
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
... and in Fourier Space
Feature transforms into oscillations.
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
A Robust Ruler
Simple underlying physics
Scale separation : rgal,nlin rBAO
Smooth effects on BAO scales, robust
probe
Expect small systematic errors
More later!
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Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
Cosmological “Experiments”
No dark energy, ΩM = 1
Ωb = 0.4 (contrast with current
observations Ωb ∼ 0.05)
Pronounced oscillations
rBAO ∼ 50Mpc/h; smaller errors,
larger nonlinear effects.
Extreme : effects are larger, rules
out accidental cancellations.
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Baryon Oscillations : Basics
The Measurement
dA (z) and H(z)
100 Mpc/h
Measure feature ⊥ and || to line of
sight
⊥ – constrain angular diameter
distance
dA
H
|| – constrain Hubble constant
Internal consistency test
More natural decomposition –
dilations and warping (NP & White,
2008)
O
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Baryon Oscillations : Basics
The Measurement
Systematics : How good do we need to be?
Next generation of surveys (WiggleZ, BOSS, HETDEX, PAU etc.)
will require systematics < 1%.
Large body of work (Huff et al, Angulo et al, 07; Sanchez et al, 08;
Seo et al, 08) argue this.
Future experiments will spectroscopically map large (∼ full sky)
volumes of the Universe.
Simple forecasts (mode counting, marginalizing over shape a la
Seo & Eisenstein, 08) suggest systematics <∼ 0.2%
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Baryon Oscillations : Basics
The Measurement
Fitting the acoustic scale
Analogous to line fitting in spectra.
Peak fitting - locate peak in ξ, or nodes in P(k ). However, sensitive
to broad band shape and therefore systematics + galaxy
properties. Therefore, undesirable!
Template fitting
P(k ) = B(k )Pwiggle (αk ) + A(k )
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(1)
Pwiggle is the BAO template.
α measures the acoustic scale relative to the fiducial scale
A(k ), B(k ) are smooth nuisance functions marginalizing over shape
etc. Polynomials, splines all work.
Calibration ≡ is α = 1 ?
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Nonlinear Evolution of BAO
Outline
1
The Context : Dark Energy
2
Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
The Measurement
3
Nonlinear Evolution of BAO
4
Current and Future Observations
SDSS-III
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Nonlinear Evolution of BAO
Nonlinear Evolution of BAO
Need a template
Change in broad-band shape –
marginalize over
Washed out oscillations – need to
be modeled
Linear theory is a bad template
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Nonlinear Evolution of BAO
Nonlinear Evolution of BAO : Matter, Real Space
Only need to track BAO;
large scales, simpler
problem.
Expand density in pert.
series.
(2)
100 Mpc/h
(1)
BAO dominant in δ1 ; only
nonlinearities transfer
BAO to δn>1
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Nonlinear Evolution of BAO
Erasure of Initial Conditions
Eisenstein, Seo & White 2007; Crocce & Scoccimarro 2007
Need to understand
(1)
hδ1 δ (2) i - the cross
correlation of the (linearly
evolved) initial density field
with final density field.
BAO ring will be smeared
out by non-coherent bulk
flows (on tens of Mpc) +
random motions.
(2)
100 Mpc/h
(1)
Smearing out the ring ≡
smoothing the correlation
function ≡ suppressing the
power spectrum.
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Nonlinear Evolution of BAO
Erasure of Initial Conditions
Consider relative
displacements on particles
separated by large
distances.
Zero mean. The variance
can be estimated from the
Zel’dovich approximation :
Z
1
dkP(k )
Σ→
3π 2
P1n = P11 exp(−Σ2 k 2 /4)
excellent
phenomenological
description.
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03-11-2009
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Nonlinear Evolution of BAO
The template : Adding Gaussian suppression
P(k ) ∼ Plin (αk )e(−k
2 Σ2 /2)
+ A(k )
Fit to 160 (Gpc/h)3 of
simulations
Marginalize over shape
A(k )
α − 1 ∼ 0.5% at z = 0 for
concordance cosmology
α − 1 ∼ 3% at z = 0 for toy
cosmology
Decreases with increasing
redshift D(z)2
Important clue : shift due to
2nd order perturbations?
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Nonlinear Evolution of BAO
Explaining the shifts : 2PT
After δ1 comes δ2 !
Consider P22 in standard
perturbation theory;
smooth (and incorrect)
piece does not matter.
R R
P
) ∼ P PF22 ∼
R 22 (k
P 2 (k /2) and is out of
phase with P(k ).
These oscillations also
smoothed.
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Nonlinear Evolution of BAO
The template : Adding P22
P(k ) ∼ Plin (αk )e(−k
2 Σ2 /2)
+ P22 (αk )e(−k
2 σ 2 /2)
+ A(k )
Significant reduction in
shifts
Mild overcorrection
Consistent with no shifts for
concordance cosmologies
Nonlinear evolution can be
modeled!
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03-11-2009
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Nonlinear Evolution of BAO
Undoing the smoothing : Reconstruction
Most of smoothing comes
from linear motions - can
be undone!
Eisenstein et al propose
using Zel’dovich in reverse
to undo smoothing.
Consider in Lagrangian
space (NP, White, Cohn 09)
Analytically show that
smoothing is reduced.
Noh, NP, White
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Current and Future Observations
Outline
1
The Context : Dark Energy
2
Baryon Oscillations : Basics
Linear Theory – Constructing a Standard Ruler
The Measurement
3
Nonlinear Evolution of BAO
4
Current and Future Observations
SDSS-III
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Current and Future Observations
Surveys : Detecting the Ruler
Need a 3D map of the Universe
Galaxy redshift surveys
Galaxy redshift + cosmology = distance
Spectroscopic surveys
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Redshifts from features in galaxy
spectra.
Accurate redshifts
Slower
Photometric surveys (eg. LSST)
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Redshifts from fitting multi-band
photometry of galaxies
Redshifts less accurate; dependent on
galaxy type.
Faster.
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A Cosmic Yardstick
Michael Blanton
03-11-2009
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Current and Future Observations
Spectroscopy vs Photometry?
Photo-z’s smear out positions (and the BAO
feature) along the LOS.
Lose all H(z) information; degrade DA as
well.
Spec. FoM ∼ 5x Photo. FoM
Erase all redshift space distortion
information
Reduce number of modes sampled, larger
errors on P(k ).
Good news: Astrophysical floor on redshift
accuracy of ∼ 10 Mpc.
Do not require very precise redshifts.
Previous redshift surveys significantly above
spec.
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A Cosmic Yardstick
03-11-2009
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Current and Future Observations
Next Generation Experiments
WiggleZ : 1-2% distance measurements, 0.5 < z < 1.0, half
completed
BOSS :
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1% distance measurements, 0 < z < 0.6
1.5% distance measurements, 2 < z < 3, new method
Started
HETDEX : 1% distance measurements, 2 < z < 4
PAU : 1% distance measurements, 0 < z < 1, photo-z++
....
Note : the next challenge is the 1% distance measurement.
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Current and Future Observations
SDSS-III
BOSS : A next generation BAO experiment
How to do a precision
z < 1 BAO expt.?
After SDSS, then what?
SDSS imaging detects red
galaxies to z ∼ 0.8
(2SLAQ, AGES)
The SDSS spectrograph
still is one of the best wide
field MOS.
Percival et al, 2006
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Current and Future Observations
SDSS-III
BOSS in overview
Ω = 10,000 deg2
Fill in SDSS stripes in the south; 8500deg2 in North, 3000deg2 in South
Galaxies : z ∼ 0.1 − 0.7
QSOs (Lyman-α forest) : z ∼ 2.3 − 3.3
1% dA , 2% H at z ∼ 0.35, 0.6
1.5% dA , H at z ∼ 2.5
Leverage existing hardware/software where possible
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Current and Future Observations
SDSS-III
Imaging status
SDSS-II
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Current and Future Observations
SDSS-III
Imaging status
BOSS
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Current and Future Observations
SDSS-III
What’s next for BOSS?
July 15, 2008: SDSS-II ended, SDSS-III began.
Completed ∼ 3000 deg2 on imaging in the South in Fall 2008.
Upgrade spectrographs Summer 08/09.
Gal/QSO spectroscopy Fall 2009 - 2014
At which point, we should know....
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wp = −??.?? ± 0.03, wa =??.?? ± 0.28
h = 0.?? ± 0.008, ΩK = 0.?? ± 0.002
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Current and Future Observations
SDSS-III
What’s next for BOSS?
July 15, 2008: SDSS-II ended, SDSS-III began.
Completed ∼ 3000 deg2 on imaging in the South in Fall 2008.
Upgrade spectrographs Summer 08/09.
Gal/QSO spectroscopy Fall 2009 - 2014
At which point, we should know....
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wp = −??.?? ± 0.03, wa =??.?? ± 0.28
h = 0.?? ± 0.008, ΩK = 0.?? ± 0.002
N. Padmanabhan (LBL)
A Cosmic Yardstick
03-11-2009
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Current and Future Observations
SDSS-III
The Big Picture, reprised
Baryon oscillations are now an integral part of the dark energy
toolkit.
Extremely ambitious surveys are being planned, on promises
(hopes) of small systematic errors.
Real space, matter BAO look to be in good shape. Hope for
galaxies and redshift space.
Next generation of surveys are underway. Stay tuned for new
results.
N. Padmanabhan (LBL)
A Cosmic Yardstick
03-11-2009
37 / 37