Transcript Document

Course on Dark Energy
Cosmology at the Beach 2009
Eric Linder
University of California, Berkeley
Lawrence Berkeley National Lab
JDEM constraints
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Outline
Lecture 1: Dark Energy in Space
The panoply of observations
Lecture 2: Dark Energy in Theory
The garden of models
Lecture 3: Dark Energy in your Computer
The array of tools – Don’t try this at home!
In theory, there is no difference between theory
and practice. In practice, there is. - Yogi Berra
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Solving the Equation of Motion
Klein-Gordon equation
Transform to new variables
Autonomous
system
where
Copeland, Liddle, Wands 1998
Phys. Rev. D 57, 4686
Transform solution to
Can add equation for EOS dynamics
Caldwell & Linder 2005
Phys. Rev. Lett 95, 1413013
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Equation of State Dynamics
For robust solutions, pay attention to initial
conditions, shoot forward in time, use 4th order
Runge-Kutta.
For monotonic , can switch to  as time variable, defining
present as, e.g. =0.72.
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Asymptotic Behaviors
Asymptotic behaviors can be physically interesting.
Solve for critical points x(xc,yc)=0, y(xc,yc)=0.
Check stability by sign of eigenvalues p=Mp. p={x,y}
Copeland, Liddle, Wands 1998
Phys. Rev. D 57, 4686
Relevant to fate of universe.
Crossing w=-1:
Phantom fields roll up potential
so V>0, so wtot∞<-1. Cannot
cross w=-1 even with coupling.
Quintessence can cross with
coupling since w<wtot.
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From Data to Theory (and back)
Fisher matrix gives lower limit for Gaussian
See: Tegmark et al. astro-ph/9805117
likelihoods, quick and easy.
Dodelson, “Modern Cosmology”
Fij = d2(- ln L) / dpi dpj = O(dO/dpi) COV-1 (dO/dpj)
(pi) 1/(Fii)1/2
Example: O=dlum(z=0.1,0.2,…1), p=(m,w), COV=(d/d)d ij
Fw=k(dOk/d)(dOk/dw)k-2
F=
(
F
Fw
Fw
Fww
)
C=
F-1
=
2()
COV(,w)
COV(,w)
2(w)
(
)
Also called information matrix. Add independent
data sets, or priors, by adding matrices.
e.g. Gaussian prior on m=0.280.03 via 2 = (m-0.28)2/0.032 66
Survival of the Fittest
Fisher estimates give a N-dimension ellipsoid.
Marginalize (integrate over the probability distribution) over
parameters not of immediate interest by crossing out their
row/column in F-1.
Fix a parameter by crossing out row/column in F.
1 (68.3% probability enclosed) joint contours have 2=2.30 in 2-D
(not 2=1). Read off 1 errors by projecting to axis and dividing by
1.52=2.30.
Orientation/ellipticity of ellipse
shows degree of covariance
(degeneracy).
Different types of observations
can have different degeneracies
(complementarity) and combine
to give tight constraints.
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Bias from Systematics
Fisher estimation calculated around fiducial model,
but can also compute bias due to offset
(systematic).
Bias p in parameter p is related to offset O in
observable, through U=O/p and covariance matrix
C=O O. For diagonal covariance, simplifies to:
In statistics, often combine uncertainty and bias into
Risk parameter:
R(p) = [2(p)+p2]1/2
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Design an Experiment
Precision in measurement is not enough - one
must beware degeneracies and systematics.
.
p2
*
p1
Degeneracy:
e.g.
Aw0+Bwa=const
Degeneracy:
hypersurface, e.g.
covariance with m
or Systematic: floor
to precision, e.g.
calibration
Systematic: offset
error in data or
model, e.g. evolution9
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Orthogonal Basis Analysis
Eigenmodes: w(z) =  i ei(z) For orthogonal basis,
errors (i) are uncorrelated. “Principal components”.
Start with parameters {wi} in z bins.
Diagonalize Fisher matrix F=ETDE: D is diagonal, rows
of E give eigenvectors.
NOTE: basis differs with model, experiment, and probe
-- cannot directly compare.
Huterer & Starkman 2003
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Decorrelated Bins
Bandpowers or decorrelated redshift bins diagonalize
sqrt{F} to try to localize w(zi). Unlike for LSS, for dark
energy they do not localize well, and confuse interpretation.
Also depends strongly on assumption of w(z>zmax)
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Principal Component Analysis
The uncertainties (i) have no physical meaning -must interpret the signal-to-noise, not just the noise.
Even next generation experiments have only 2
components with S/N>3. Almost all models have
97-100% of the information in first 2 components.
Eigenmode analysis does not improve over w0-wa.
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Common Mistakes
• Neglecting M or S (SN or BAO absolute scale).
• Neglecting systematics.
• Claiming systematics, but still  ’ing down errors.
• Thinking “self calibration” covers systematics;
“self calibration” = “assuming a known form”.
• Using noise, not S/N, for PCA.
• Fixing w=-1 at high redshift.
Reductio ad absurdum:
1 SN/sec, 10 y survey gives d(z) to 0.003%
Every acoustic mode gives d(z) to 0.1%
Full sky space WL takes 1% shears to 310-6 level
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Controlling Systematics
Controlling systematics is the name of the game.
Finding more objects is not.
Forthcoming experiments
may deliver 100,000s of
objects. But uncertainties
do not reduce by 1/N.
Must choose cleanest
probe/data, mature method,
with multiple crosschecks.
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Battle Royale
Astronomer Royal (Airy):
“I should not have believed it if I had not seen it!”
Astronomer Royal (Hamilton):
“How different we are! My eyes have too
often deceived me. I believe it because I have
proved it.”
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What makes SN measurement special?
Control of systematic uncertainties
Each supernova is “sending” us a rich stream of
information about itself.
Images
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Redshift & SN Properties
Nature of
Dark Energy
Spectra
data
analysis
physics
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Astrophysical Uncertainties
For accurate and precision cosmology,
need to identify and control systematic uncertainties.
Systematic
Control
Host-galaxy dust
extinction
Wavelength-dependent absorption identified with high S/N
multi-band photometry.
Supernova evolution
Supernova subclassified with high S/N light curves and peakbrightness spectrum.
Flux calibration error
Program to construct a set of 1% error flux standard stars.
Malmquist bias
Supernova discovered early with high S/N multi-band
photometry.
K-correction
Construction of a library of supernova spectra.
Gravitational lensing
Measure the average flux for a large number of supernovae in
each redshift bin.
Non-Type Ia
contamination
Classification of each event with a peak-brightness spectrum.
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Controlling Systematics
Same SN, Different z  Cosmology
Same z, Different SN  Systematics Control
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Fitting Subsets
perfect
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Depth + Width + Resolution
Subaru - best ground
HST - space
Weak lensing signal
Bacon, Ellis, Refregier 2000
Kasliwal, Massey, Ellis, Miyazaki, Rhodes 2007
Weak lensing noise
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Cluster Abundances
Clusters -- largest bound objects. DE + astrophysics.
Uncertainty in mass of 0.1 dex gives wconst~0.1
[M. White],
w~?
Optical: light  mass
Xray: hot gas  gravitational
potential  mass
Traditional
Difficult for z>1
Detects light, not mass
Mass of what?
Clean detections
Difficult for z>1
Need optical survey for redshift
Detects flux, not mass
Only cluster center
Assumes simple: ~ne2
Sunyaev-Zel’dovich: hot escatter CMB  mass
Clean detections
Indepedent of redshift
Need optical survey for redshift
Detects flux, not mass
Assumes ~simple: ~neTe
Weak Lensing: gravity distorts
images of background galaxies
Detect mass directly
Can go to z>1
Line of sight contamination
Efficiency reduced
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Heterogeneous Data
Offsets due to different instruments, filters, sources
can be a serious source of bias. “Stitching
together” surveys, even with modest overlap, may
give precision cosmology, but inaccurate results.
No need to stitch in z>2
– no leverage.
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Design an Experiment
How to design an experiment to explore dark energy?
• Choose clear, robust, mature techniques
• Rotate the contours thru choice of redshift span
• Narrow the contours thru systematics control
• Break degeneracies thru multiple probes
• Use homogeneous data set
With a strong experiment, we can even test the
framework of physics. Recall {,w0,wa,,g*}.
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Discovery Space
Dark energy may be a decades long mystery.
Space wide-field surveys maximize the
discovery space. 40 trillion pixels on sky!
20x ground.
Fundamental physics of inflation:
• Weak lensing - ns primordial perturbation spectrum
• Cluster abundances - non-Gaussianity
Dark Matter maps -
“the skeleton of the universe”
Imagine COSMOS x 2000!
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Dark Energy – The Next Generation
wide
104  the Hubble Deep Field area (and deeper)
plus 107  HDF (almost as deep)
deep
Mapping 10 billion years / 70% age of universe
colorful
Optical + IR to see thru dust, to high redshift
Euclid (ESA)
Launch ~2015
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The Next Physics
What is dark
energy?
Current
data
do not tell us  is the answer (or
What is the fate of the universe?
anything
about dark energy at z>1).
How many dimensions are there?
How are quantum
gravity
unified?it.
Odds against : Einstein+us
failedphysics
for 90 and
years
to explain
Experiments to reveal dynamics (w-w) are essential
to reveal physics. Space is the low risk option for
dependable answers.
Expansion plus growth (e.g. SN+WL) is critical
combination. We can test GR and can test geometry.
Space imaging mission gives optical-NIR and low-high z
measurements, high resolution and low systematics;
multiple probes and rich astronomical resources.
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Dark Energy Pessimism
[2008 STScI Symposium: “We shall never be able
to know the composition of dark energy”
-- pessimistic physicist]
1835: “We shall never be able to know the
composition of stars” -- Comte
1849: Kirchhoff discovers that the spectrum of
electromagnetic radiation encodes the composition
[2022? Cosmology on the Beach: Fiji has talks
revealing the true nature of dark energy
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“Acceleration”
to the tune of The Beatles’ “Revolution”
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