Transcript Document

Dark Energy
Current theoretical issues and progress toward
future experiments
Andreas Albrecht (UC Davis)
LEPP Journal Club Seminar, Cornell University
December 1 2006
1
Cosmic acceleration
“Ordinary” non
accelerating
matter
 Amount of w=-1 matter (“Dark energy”)
Accelerating matter is required to fit current data
Preferred by
modern data
Supernova
 Amount
of “ordinary” gravitating matter
2
95% of the cosmic matter/energy is a mystery.
It has never been observed even in our best
laboratories
Ordinary Matter
(observed in labs)
Dark Energy
(accelerating)
Dark Matter
(Gravitating)
3
Dark energy appears to be the dominant component of the physical
Universe, yet there is no persuasive theoretical explanation. The
acceleration of the Universe is, along with dark matter, the observed
phenomenon which most directly demonstrates that our fundamental
theories of particles and gravity are either incorrect or incomplete.
Most experts believe that nothing short of a revolution in our
understanding of fundamental physics* will be required to achieve a
full understanding of the cosmic acceleration. For these reasons, the
nature of dark energy ranks among the very most compelling of all
outstanding problems in physical science. These circumstances
demand an ambitious observational program to determine the dark
energy properties as well as possible.
From the Dark Energy Task Force report (2006)
www.nsf.gov/mps/ast/detf.jsp,
astro-ph/0690591
*My emphasis
4
Dark energy appears to be the dominant component of the physical
Universe, yet there is no persuasive theoretical explanation. The
acceleration of the Universe is, along with dark matter, the observed
phenomenon which most directly demonstrates that our fundamental
theories of particles and gravity are either incorrect or incomplete.
Most experts believe that nothing short of a revolution in our
understanding of fundamental physics* will be required to achieve a
full understanding of the cosmic acceleration. For these reasons, the
nature of dark energy ranks among the very most compelling of all
outstanding problems in physical science. These circumstances
DETF = a HEPAP/AAAC
demand an ambitious observational
determineofthe dark
subpanelprogram
to guidetoplanning
energy properties as well as
possible.
future
dark energy experiments
From the Dark Energy Task Force report (2006)
www.nsf.gov/mps/ast/detf.jsp,
astro-ph/0690591
*My emphasis
5
Dark energy appears to be the dominant component of the physical
Universe, yet there is no persuasive theoretical explanation. The
acceleration of the Universe is, along with dark matter, the observed
phenomenon which most directly demonstrates that our fundamental
theories of particles and gravity are either incorrect or incomplete.
Most experts believe that nothing short of a revolution in our
understanding of fundamental physics* will be required to achieve a
full understanding of the cosmic acceleration. For these reasons, the
nature of dark energy ranks among the very most compelling of all
outstanding problems in physical science. These circumstances
DETF = a HEPAP/AAAC
demand an ambitious observational
determineofthe dark
subpanelprogram
to guidetoplanning
energy properties as well as
possible.
future
dark energy experiments
From the Dark Energy Task Force report (2006)
www.nsf.gov/mps/ast/detf.jsp,
astro-ph/0690591
*My emphasis
More info here
6
This talk
Part 1:
A few attempts to explain dark energy
- Motivations, Problems and other comments
 Theme: We may not know where this revolution is
taking us, but it is already underway:
(see e.g. Copeland et al 2006 review)
Part 2
Planning new experiments
(see e.g. DETF report and AA & Bernstein 2006)
7
This talk
Part 1:
A few attempts to explain dark energy
- Motivations, Problems and other comments
 Theme: We may not know where this revolution is
taking us, but it is already underway:
(see e.g. Copeland et al 2006 review)
Part 2
Planning new experiments
(see e.g. DETF report and AA & Bernstein 2006)
8
This talk
Part 1:
A few attempts to explain dark energy
- Motivations, Problems and other comments
 Theme: We may not know where this revolution is
taking us, but it is already underway:
(see e.g. Copeland et al 2006 review)
Part 2
Planning new experiments
(see e.g. DETF report and AA & Bernstein 2006)
9
Some general issues:
Properties:
Solve GR for the scale factor a of the Universe (a=1 today):
a
4 G


   3 p 
a
3
3
Positive acceleration clearly requires
• w  p /   1/ 3
Universe) or
(unlike any known constituent of the
• a non-zero cosmological constant or
• an alteration to General Relativity.
10
Some general issues:
Numbers:
• Today,
 DE  10
120
M  10 eV 
4
P
3
4
• Many field models require a particle mass of
mQ  1031 eV  H0
from
mQ2 M P2  DE
11
Some general issues:
Numbers:
• Today,
 DE  10
120
M  10 eV 
4
P
3
4
• Many field models require a particle mass of
mQ  1031 eV  H0
from
mQ2 M P2  DE
Where do these come from and how are they
protected from quantum corrections?
12
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
Vacuum energy problem (we’ve gotten
“nowhere” with this)
=
10120
Vacuum Fluctuations
0
?
13
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
Vacuum energy problem (we’ve gotten
“nowhere” with this)
=
10120
Vacuum Fluctuations
0
?
See e.g. Tye & Wasserman, Csaki et al Flannagan et al (Braneworld)
14
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
 The string theory landscape (a radically
different idea of what we mean by a fundamental
theory)
KKLT, Tye etc
15
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
 The string theory landscape (a radically
different idea of what we mean by a fundamental
theory)
“Theory of Everything”
?
“Theory of Anything”
KKLT, Tye etc
16
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
 The string theory landscape (a radically
different idea of what we mean by a fundamental
theory)
Not exactly
a cosmological
constant
KKLT, Tye etc
17
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
 De Sitter limit: Horizon  Finite Entropy
Banks, Fischler, Susskind, AA & Sorbo etc
18
“De Sitter Space: The ultimate equilibrium for the
universe?
Horizon
S  A  H 2  1
Quantum effects: Hawking Temperature
8 G
T H 
 DE
3
19
“De Sitter Space: The ultimate equilibrium for the
universe?
Horizon
S  A  H 2  1
Quantum effects: Hawking Temperature
Does this imply (via
8 G
T H 
 DE
“ S  ln N “)
3
a finite Hilbert space for physics?
20
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
 De Sitter limit: Horizon  Finite Entropy 
Equilibrium Cosmology
Rare
Fluctuation
Banks, Fischler, Susskind, AA & Sorbo etc
21
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
 De Sitter limit: Horizon  Finite Entropy 
Equilibrium Cosmology
Rare
Fluctuation
“Boltzmann’s Brain” ?
Banks, Fischler, Susskind, AA & Sorbo etc
22
Specific ideas: i) A cosmological constant

• Nice “textbook” solutions BUT
• Deep problems/impacts re fundamental physics
 is not the “simple option”
23
Some general issues:
Alternative Explanations?:
Is there a less dramatic explanation of the data?
For example is supernova dimming due to
• dust? (Aguirre)
• γ-axion interactions? (Csaki et al)
• Evolution of SN properties? (Drell et al)
24
Some general issues:
Alternative Explanations?:
Is there a less dramatic explanation of the data?
For example is supernova dimming due to
• dust? (Aguirre)
• γ-axion interactions? (Csaki et al)
• Evolution of SN properties? (Drell et al)
Many of these are under increasing pressure from data, but
such skepticism is critically important.
25
Specific ideas: ii) A scalar field (“Quintessence”)
• Recycle inflation ideas (resurrect   0 dream?)
• Serious unresolved problems
 Explaining/ protecting mQ  1031 eV  H0
 5th force problem
 Vacuum energy problem
 What is the Q field? (inherited from inflation)
 Why now? (Often not a separate problem)
26
Quintessence: Model the dark energy by a
homogeneous scalar field obeying
With
dV
  3H  
0
d
 
and

p 
2
2

V
2
2
V
27
Why now? (Often not a separate problem)
today (t=14.5 Gyr). (not some other time)

1


0.5
rad
matter
DE

i
i
i 

c tot
0
-0.5 -20
10
10
a
0
28
Specific ideas: ii) A scalar field (“Quintessence”)
• Illustration: Pseudo Nambu Goldstone Boson
(PNGB) models
V  M cos( / f )  1
4
With f  1018GeV, M  10-3eV
PNGB:
Frieman,
Hill,
Stebbins, &
Waga 1995
PNGB mechanism protects M and 5th force issues
29
Specific ideas: ii) A scalar field (“Quintessence”)
• Illustration: Pseudo Nambu Goldstone Boson
(PNGB) models

1

, w
0.5
r
m
D
w
0
-0.5
-1
-1.5
3
2
1
z
0
Hall et al 05 30
Dark energy and the ego test
31
Specific ideas: ii) A scalar field (“Quintessence”)
• Illustration: Exponential with prefactor (EwP)
models:


V ( )  V0   B   A exp   /  
2
AA & Skordis 1999
All parameters O(1) in Planck units,
 motivations/protections from extra dimensions &
quantum gravity Burgess &
collaborators
(e.g.
B  34
A  .005
 8
V0  1
)
32
Specific ideas: ii) A scalar field (“Quintessence”)
V prefactor

• Illustration: Exponential with
(EwP)
models:


V ( )  V0   B   A exp   /  
2
AA & Skordis 1999
All parameters O(1) in Planck units,

&
 motivations/protections from extra dimensions
quantum gravity
(e.g.
B  34
A  .005
Burgess &
collaborators
 8
V0  1
)
AA & Skordis 1999
33
Specific ideas: ii) A scalar field (“Quintessence”)
V prefactor

• Illustration: Exponential with
(EwP)
models:


V ( )  V0   B   A exp   /  
2
AA & Skordis 1999
All parameters O(1) in Planck units,

&
 motivations/protections from extra dimensions
quantum gravity
(e.g.
B  34
A  .005
Burgess &
collaborators
 8
V0  1
See also R. Bean
)
AA & Skordis 1999
34
Specific ideas: ii) A scalar field (“Quintessence”)
• Illustration: Exponential with prefactor (EwP)
models:

1

, w
0.5
r
m
D
w
0
-0.5
-1
-1.5 -20
10
10
a
0
AA & Skordis 199935
Specific ideas: iii) A mass varying neutrinos
(“MaVaNs”)
Faradon, Nelson & Weiner
• Exploit
m  
1/ 4
DE
3
 10 eV
• Issues
 Origin of “acceleron” (varies neutrino
mass, accelerates the universe)
 gravitational collapse
Afshordi et al 2005
Spitzer 2006
36
Specific ideas: iii) A mass varying neutrinos
(“MaVaNs”)
“
Faradon, Nelson & Weiner
• Exploit
m  
1/ 4
DE
3
 10 eV
”
• Issues
 Origin of “acceleron” (varies neutrino
mass, accelerates the universe)
 gravitational collapse
Afshordi et al 2005
Spitzer 2006
37
Specific ideas: iv) Modify Gravity
• Not something to be done lightly, but given our confusion
about cosmic acceleration, well worth considering.
• Many deep technical issues
e.g. DGP (Dvali, Gabadadze and Porrati)
Ghosts Charmousis et al
See e.g. Bean et al
38
This talk
Part 1:
A few attempts to explain dark energy
- Motivations, Problems and other comments
 Theme: We may not know where this revolution is
taking us, but it is already underway:
(see e.g. Copeland et al 2006 review)
Part 2
Planning new experiments
(see e.g. DETF report and AA & Bernstein 2006)
39
This talk
Part 1:
A few attempts to explain dark energy
- Motivations, Problems and other comments
 Theme: We may not know where this revolution is
taking us, but it is already underway:
(see e.g. Copeland et al 2006 review)
Part 2
Planning new experiments
(see e.g. DETF report and AA & Bernstein 2006)
40
Astronomy Primer for Dark Energy
Solve GR for the scale factor a of the Universe (a=1 today):
From
DETF
Positive acceleration clearly requires w  p /   1/ 3 unlike any known
constituent of the Universe, or a non-zero cosmological constant or an alteration to General Relativity.
 a  8 GN   k
  2
  
3
3 a
a
The second basic equation is
2
8 GN 0 
Today we have H 02   a  
 k
3
3
a
2
41
Hubble Parameter
We can rewrite this as
1
8GN 0

k


     k
2
2
2
3H 0
3H 0 H 0
To get the generalization that applies not just now (a=1), we need
to distinguish between non-relativistic matter and relativistic matter.
We alsogeneralize  to dark energy with a constant w,
not necessarily equal to -1:
non-rel. matter
curvature
rel. matter
Dark Energy
42
What are the observable quantities?
Expansion factor a is directly observed by redshifting of emitted
photons: a=1/(1+z), z is “redshift.”
Time is not a direct observable (for present discussion). A measure
of elapsed time is the distance traversed by an emitted photon:
This distance-redshift relation is one of the diagnostics of dark energy.
Given a value for curvature, there is 1-1 map between D(z) and w(a).
Distance is manifested by changes in flux, subtended angle, and sky
densities of objects at fixed luminosity, proper size, and space density.
These are one class of observable quantities for dark-energy study.
43
Another observable quantity:
The progress of gravitational collapse is damped by expansion of the
Universe. Density fluctuations arising from inflation-era quantum
fluctuations increase their amplitude with time. Quantify this by the
growth factor g of density fluctuations in linear perturbation theory.
GR gives:
This growth-redshift relation is the second diagnostic of dark energy.
If GR is correct, there is 1-1 map between D(z) and g(z).
If GR is incorrect, observed quantities may fail to obey this relation.
Growth factor is determined by measuring the density fluctuations in
nearby dark matter (!), comparing to those seen at z=1088 by WMAP.
44
What are the observable quantities?
Future dark-energy experiments will require percent-level precision on
the primary observables D(z) and g(z).
45
Dark Energy with Type Ia Supernovae
• Exploding white dwarf
stars: mass exceeds
Chandrasekhar limit.
• If luminosity is fixed,
received flux gives
relative distance via
Qf=L/4D2.
• SNIa are not
homogeneous events.
Are all luminosityaffecting variables
manifested in observed
properties of the
explosion (light curves,
spectra)?
Supernovae Detected in HST
GOODS Survey (Riess et al)
46
Dark Energy with Type Ia Supernovae
Example of SN data:
HST GOODS Survey (Riess et al)
Clear evidence of acceleration!
47
Riess et al astro-ph/0611572
48
Dark Energy with Baryon Acoustic Oscillations
•Acoustic waves propagate in the baryonphoton plasma starting at end of inflation.
•When plasma combines to neutral
hydrogen, sound propagation ends.
BAO seen in CMB
(WMAP)
•Cosmic expansion sets up a predictable
standing wave pattern on scales of the
Hubble length. The Hubble length
(~sound horizon rs) ~140 Mpc is imprinted
on the matter density pattern.
•Identify the angular scale subtending rs
then use s=rs/D(z)
•WMAP/Planck determine rs and the
distance to z=1088.
•Survey of galaxies (as signposts for dark
matter) recover D(z), H(z) at 0<z<5.
•Galaxy survey can be visible/NIR or 21cm emission
BAO seen in SDSS
Galaxy correlations
(Eisenstein et al)
49
Dark Energy with Galaxy Clusters
•Galaxy clusters are the largest
structures in Universe to undergo
gravitational collapse.
•Markers for locations with
density contrast above a critical
value.
•Theory predicts the mass
function dN/dMdV. We observe
dN/dzd.
Optical View
(Lupton/SDSS)
•Dark energy sensitivity:
•Mass function is very sensitive
to M; very sensitive to g(z).
•Also very sensitive to misestimation of mass, which is not
directly observed.
Cluster method probes both D(z) and g(z)
50
Dark Energy with Galaxy Clusters
Optical View
(Lupton/SDSS)
X-ray View
(Chandra)
30 GHz View
(Carlstrom et al)
Sunyaev-Zeldovich effect
51
Galaxy Clusters from ROSAT X-ray surveys
From Rosati et al, 1999:
ROSAT cluster surveys yielded ~few
100 clusters in controlled samples.
Future X-ray, SZ, lensing surveys
project few x 10,000 detections.
52
Dark Energy with Weak Gravitational Lensing
•Mass concentrations in the
Universe deflect photons from
distant sources.
•Displacement of background
images is unobservable, but their
distortion (shear) is measurable.
•Extent of distortion depends
upon size of mass concentrations
and relative distances.
•Depth information from redshifts.
Obtaining 108 redshifts from
optical spectroscopy is infeasible.
“photometric” redshifts instead.
Lensing method probes both D(z) and g(z)
53
Dark Energy with Weak Gravitational Lensing
In weak lensing, shapes
of galaxies are measured.
Dominant noise source is
the (random) intrinsic
shape of galaxies. LargeN statistics extract lensing
influence from intrinsic
noise.
54
55
Choose your background photon source:
Faint background galaxies:
Hoekstra et al 2006:
Use visible/NIR imaging to
determine shapes.
Photometric redshifts.
Photons from the CMB:
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Use mm-wave highresolution imaging of CMB.
(lensing not yet detected)
All sources at z=1088.
21-cm photons:
Use the proposed Square
Kilometer Array (SKA).
Sources are neutral H in
regular galaxies at z<2, or
the neutral Universe at z>6.
(lensing not yet detected)
56
Q: Given that we know so little about the cosmic
acceleration, how do we represent source of this
acceleration when we forecast the impact of future
experiments?
Consensus Answer: (DETF, Joint Dark Energy Mission
Science Definition Team JDEM STD)
• Model dark energy as homogeneous fluid  all
information contained in w a   p  a  /   a 
• Model possible breakdown of GR by inconsistent
determination of w(a) by different methods.
57
Q: Given that we know so little about the cosmic
acceleration, how do we represent source of this
acceleration when we forecast the impact of future
experiments?
Consensus Answer: (DETF, Joint Dark Energy Mission
Science Definition Team JDEM STD)
• Model dark energy as homogeneous fluid  all
information contained in w a   p  a  /   a 
• Model possible breakdown of GR by inconsistent
determination of w(a) by different methods.
Also: Std cosmological parameters including
curvature
58
wa
95% CL contour
w(a) = w0 + wa(1-a)
0
(DETF parameterization… Linder)
DETF figure of merit:
 1Area
1
w0
59
The DETF stages (data models constructed for each
one)
Stage 2: Underway
Stage 3: Medium size/term projects
Stage 4: Large longer term projects (ie JDEM, LST)
60
A technical point: The role of correlations
Co
m
Technique #2
bi
na
t
io
n
Technique #1
61
Figure of merit Improvement over
Stage 2 
DETF Projections
Stage 3
62
Figure of merit Improvement over
Stage 2 
DETF Projections
Ground
63
Figure of merit Improvement over
Stage 2 
DETF Projections
Space
64
Figure of merit Improvement over
Stage 2 
DETF Projections
Ground + Space
65
A technical point: The role of correlations
Co
m
Technique #2
bi
na
t
io
n
Technique #1
66
From the DETF Executive Summary
One of our main findings is that no single technique can
answer the outstanding questions about dark energy:
combinations of at least two of these techniques must be
used to fully realize the promise of future observations.
Already there are proposals for major, long-term (Stage IV)
projects incorporating these techniques that have the
promise of increasing our figure of merit by a factor of ten
beyond the level it will reach with the conclusion of current
experiments. What is urgently needed is a commitment to
fund a program comprised of a selection of these projects.
The selection should be made on the basis of critical
evaluations of their costs, benefits, and risks.
67
From the Executive Summary
Success in reaching our ultimate goal will depend on the
development of dark-energy science. This is in its infancy.
Smaller, faster programs (Stage III) are needed to provide
the experience on which the long-term projects can build.
These projects can reduce systematic uncertainties that
could otherwise impede the larger projects, and at the same
time make important advances in our knowledge of dark
energy.
68
How good is the w(a) ansatz?
w(a)  w0  wa 1 a 
Sample w(z) curves in w0-wa space
w
0
w0-wa can only do these
-2
-4
0
0.5
1
1.5
2
2.5
Sample w(z) curves for the PNGB models
w
1
w0
-1
0
0.5
1
1.5
2
DE models can do this
(and much more)
Sample w(z) curves for the EwP models
w
1
0
-1
0
0.5
1
z
1.5
2
z
69
How good is the w(a) ansatz?
w(a)  w0  wa 1 a 
Sample w(z) curves in w0-wa space
w
0
w0-wa can only do these
-2
-4
0
0.5
1
1.5
2
2.5
Sample w(z) curves for the PNGB models
w
1
w0
-1
0
0.5
1
1.5
2
DE models can do this
(and much more)
Sample w(z) curves for the EwP models
w
1
0
-1
0
0.5
1
z
1.5
2
z
70
How good is the w(a) ansatz?
w(a)  w0  wa 1 a 
Sample w(z) curves in w0-wa space
w
0
w0-wa can only do these
-2
-4
0
0.5
1
1.5
2
2.5
Sample w(z) curves for the PNGB models
NB: Better than
1
w
w(a)  w0
w0
-1
0
0.5
1
1.5
2
DE models can do this
(and much more)
Sample w(z) curves for the EwP models
w
1
0
-1
0
0.5
1
z
1.5
2
z
71
Try 9D stepwise constant w(a)
1
w  a  0
-1 -2
10
-1
0
10
10
9
1
10
z
w(a)  1  w  a   1   wT
i  ai , ai 1 
i 1
9 parameters are coefficients of the “top
hat functions”
T a ,a

i
i 1

AA & G Bernstein 2006 (astro-ph/0608269 ). More detailed info can be
72
found at http://www.physics.ucdavis.edu/Cosmology/albrecht/MoreInfo0608269/
Try 9D stepwise constant w(a)
1
w  a  0
-1 -2
10
-1
0
10
10
z
9
w(a)  1  w  a   1   wT
i  ai , ai 1 
i 1
1
10
 Allows
greater variety
of w(a)
behavior
9 parameters are coefficients of the “top  Allows each
experiment to
hat functions”
T ai , ai 1
“put its best
foot forward”

AA & G Bernstein 2006

73
Try 9D stepwise constant w(a)
1
w  a  0
-1 -2
10
-1
0
10
10
9
z
w(a)  1  w  a   1   wT
i  ai , ai 1 
i 1
1
10
 Allows
greater variety
of w(a)
behavior
9 parameters are coefficients of the “top  Allows each
experiment to
hat functions”
T ai , ai 1
“put its best
foot forward”
“Convergence”
AA & G Bernstein 2006


74
Q: How do you describe error ellipsis in 9D space?
A: In terms of 9 principle axes f i and
corresponding 9 errors  i :
2D illustration:
1
f1  Axis 1
f2  Axis 2
2
75
Q: How do you describe error ellipsis in 9D space?
A: In terms of 9 principle axes f i and
corresponding 9 errors  i :
2D illustration:
1
f1  Axis 1
f2  Axis 2
2
Assuming Gaussian
distributions for this
discussion
76
Q: How do you describe error ellipsis in 9D space?
A: In terms of 9 principle axes f i and
corresponding 9 errors  i :
NB: in general the f i s form
a complete basis:
2D illustration:
1
f1  Axis 1
f2  Axis 2
2
w  i fi
i
The i are independently
measured qualities with
errors  i
77
Characterizing 9D ellipses by principle axes and
Stage 2 ; lin-a
N
= 9, z
= 4, Tag = 044301
corresponding
errors
DETF stage 2
Grid
max
2
i
i
1
0
1
2
3
4
5
6
7
8
9
fi
f's
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
i
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
1
f's
Principle Axes
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
a
0.7
0.8
0.9
1
78
Characterizing 9D ellipses by principle axes and
Stage 4 Space WLcorresponding
Opt; lin-a N
= 9, z
= 4, Tag
= 044301
errors
WL Stage 4 Opt
Grid
max
5
6
2
i
i
1
0
1
2
3
4
7
8
9
fi
f's
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
i
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
1
f's
Principle Axes
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
a
0.7
0.8
0.9
1
79
Characterizing 9D ellipses by principle axes and
Stage 4 Space WLcorresponding
Opt; lin-a N
= 16, z
= 4, errors
Tag = 054301
WL Stage 4 Opt
Grid
max
2
i
i
1
0
0
2
4
6
8
10
12
14
16
18
f's
fi
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
i
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
1
f's
Principle Axes
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
a
0.7
“Convergence”
0.8
0.9
1
80
DETF Figure of Merit:
FDETF 
1
1 2
9D Figure of Merit:
F9D 
1
9
If
 i  1 we set  i  1
i
i 1
81
FDETF/9D
Grid Linear in a zmax = 4 scale: 0
DETF(-CL)
Stage 3
Stage 4 Ground
9D (-CL)
1e4
1e4
1e3
1e3
100
100
10
10
1
BAOp BAOs SNp
SNs
WLp ALLp
1
Stage 4 Space
Stage 4 Ground+Space
1e4
1e4
1e3
1e3
100
100
10
10
1
BAO
SN
WL
S+W S+W+B
Bska Blst Slst Wska Wlst Aska Alst
1
[SSBlstW lst] [BSSlstW lst] Alllst [SSW SBIIIs ] Ss W lst
82
FDETF/9D
Grid Linear in a zmax = 4 scale: 0
DETF(-CL)
Stage 3
Stage 4 Ground
9D (-CL)
1e4
1e4
1e3
1e3
100
100
10
10
1
BAOp BAOs SNp
SNs
WLp ALLp
1
Bska Blst Slst Wska Wlst Aska Alst
Stage 2  Stage 3 = 1 order of magnitude (vs 0.5 for DETF)
Stage 4 Space
Stage 4 Ground+Space
1e4
1e4
1e3
1e3
100
100
10
10
1
BAO
SN
WL
S+W S+W+B
1
[SSBlstW lst] [BSSlstW lst] Alllst [SSW SBIIIs ] Ss W lst
83
Stage 2  Stage 4 = 3 orders of magnitude (vs 1 for DETF)
Define the “scale to 2D” function
S2D F   F
S2D  F  
2/ De
1
2
 ave
The idea: Construct an effective 2D FoM by assuming
two dimensions with “average” errors (~geometric mean
of 9D errors)
 Purpose: Separate out the impact of higher
dimensions on comparisons with DETF, vs other
information from the D9 space (such relative
comparisons of data model).
84
Stage 3
Stage 4 Ground
DETF(-CL)
20
20
10
10
5
3
2
5
3
2
1
1
9D (-CL)-Scaled to 2D
Bp
Bs
Sp
Ss
Wp ALLp
De=2.5 for Stage 2
B
LST
S
lst
W
ska
20
10
10
5
3
2
5
3
2
1
1
W
SW
W
lst
A
ska
A
lst
Stage 4 Ground+Space
20
S
B
De=3 for Stage 3
Stage 4 Space
B
ska
SWB
[SSBlstWlst] [BSSlstWlst] Alllst [SSWSBIIIs ] Ss Wlst
85
De= 4 for Stage 4 Pes, ; De= 4.5 for Stage 4 Opt,
Discussion of cost/benefit analysis should take
place in higher dimensions (vs current standards)
DETF
1
f1  Axis 1
f2  Axis 2
“form” Frieman’s talk
2
86
An example of the power of the principle component
analysis:
Q: I’ve heard the claim that the DETF FoM is unfair to
BAO, because w0-wa does not describe the high-z
behavior which to which BAO is particularly sensitive.
Why does this not show up in the 9D analysis?
87
FDETF/9D
Grid Linear in a zmax = 4 scale: 0
DETF(-CL)
Stage 3
Stage 4 Ground
9D (-CL)
1e4
1e4
1e3
1e3
100
100
10
10
1
BAOp BAOs SNp
SNs
WLp ALLp
1
Stage 4 Space
1e4
Stage 4 Ground+Space
1e4
Specific
1e3 Case:
1e3
100
100
10
10
1
Bska Blst Slst Wska Wlst Aska Alst
BAO
SN
WL
S+W S+W+B
1
[SSBlstW lst] [BSSlstW lst] Alllst [SSW SBIIIs ] Ss W lst
88
BAO
Stage 4 Space BAO Opt; lin-a NGrid = 9, z max = 4, Tag = 044301
i
2
1
0
1
2
3
4
5
6
7
8
9
f's
1
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
89
SN
Stage 4 Space SN Opt; lin-a NGrid = 9, z max = 4, Tag = 044301
i
2
1
0
1
2
3
4
5
6
7
8
9
f's
1
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
90
BAO
DETF  ,
Stage 4 Space BAO
1 Opt;2 lin-a NGrid = 9, z max = 4, Tag = 044301
i
2
1
0
1
2
3
4
5
6
7
8
9
f's
1
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
91
SN
 ,
Stage 4 Space SN
1 Opt;2lin-a NGrid = 9, z max = 4, Tag = 044301
i
2
1
0
1
2
3
4
5
6
7
8
9
f's
1
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
92
SN
w0-wa analysis shows two
parameters measured on
average as well as 3.5 of these
Stage 4 Space SN Opt; lin-a NGrid = 9, z max = 4, Tag = 044301
i
2
1
0
1
2
3
4
5
6
7
8
9
f's
1
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
4
5
6
0
-1
0.2
0.3
DETF
f's
1
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8


1  2    i 
 1

0.4
0.5
0.6
a
9
0.7
0.8
2 /  De  3.5 
0.9
1
7
8
9
0.9
9D
1
93
Upshot of 9D FoM:
1) DETF underestimates impact of expts
2) DETF underestimates relative value of Stage 4
vs Stage 3
3) The above can be understood approximately in
terms of a simple rescaling
4) DETF FoM is fine for most purposes (ranking,
value of combinations etc).
94
Dark energy appears to be the dominant component of the physical
Universe, yet there is no persuasive theoretical explanation. The
acceleration of the Universe is, along with dark matter, the observed
phenomenon which most directly demonstrates that our
fundamental theories of particles and gravity are either incorrect or
incomplete. Most experts believe that nothing short of a revolution
in our understanding of fundamental physics will be required to
achieve a full understanding of the cosmic acceleration. For these
reasons, the nature of dark energy ranks among the very most
compelling of all outstanding problems in physical science. These
circumstances demand an ambitious observational program to
determine the dark energy properties as well as possible.
From the Dark Energy Task Force report (2006)
www.nsf.gov/mps/ast/detf.jsp
& to appear on the arXiv.
95
Dark energy appears to be the dominant component of the physical
Universe, yet there is no persuasive theoretical explanation. The
acceleration of the Universe is, along with dark matter, the observed
phenomenon which most directly demonstrates that our
fundamental theories of particles and gravity are either incorrect or
incomplete. Most experts believe that nothing short of a revolution
in our understanding of fundamental physics will be required to
achieve a full understanding of the cosmic acceleration. For these
reasons, the nature of dark energy ranks among the very most
compelling of all outstanding problems in physical science. These
circumstances demand an ambitious observational program to
determine the dark energy properties as well as possible.
From the Dark Energy Task Force report (2006)
www.nsf.gov/mps/ast/detf.jsp
& to appear on the arXiv.
96
Dark energy appears to be the dominant component of the physical
Universe, yet there is no persuasive theoretical explanation. The
acceleration of the Universe is, along with dark matter, the observed
phenomenon which most directly demonstrates that our
fundamental theories of particles and gravity are either incorrect or
incomplete. Most experts believe that nothing short of a revolution
in our understanding of fundamental physics will be required to
achieve a full understanding of the cosmic acceleration. For these
reasons, the nature of dark energy ranks among the very most
compelling of all outstanding problems in physical science. These
circumstances demand an ambitious observational program to
determine the dark energy properties as well as possible.
From the Dark Energy Task Force report (2006)
www.nsf.gov/mps/ast/detf.jsp
& to appear on the arXiv.
97
END
98
Extra material
99
sigMax = 4 sigMin = 0 OneModel = 0 OneVersionP1 = 0 OneRun = 0 EigenSR14 AllSolsV2 2
4
2
0
-2
-4
-6
-8
Markers label different
scalar field models
-10
-12
mode 2
 Coordinates are first three
-14
-16
in
0
100
200
mode 1
300
400
500
600
100
sigMax = 4 sigMin = 0 OneModel = 0 OneVersionP1 = 0 OneRun = 0 EigenSR14 AllSolsV2 2
4
Implication:
New experiments will have very significant
2
discriminating power among actual scalar field models.
0
(See Augusta Abrahamse, Michael Barnard, Brandon Bozek & AA, to
appear-2 soon)
-4
-6
-8
Markers label different
scalar field models
-10
-12
mode 2
 Coordinates are first three
-14
-16
in
0
100
200
mode 1
300
400
500
600
101
Stage 4 Space WL Opt; lin-a NGrid = 9, z max = 4, Tag = 044301
i
2
1
0
1
2
3
4
5
6
7
8
9
f's
1
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
102
Stage 4 Space WL Opt; lin-a NGrid = 16, z max = 4, Tag = 054301
i
2
1
0
0
2
4
6
8
10
12
14
16
18
f's
1
1
2
3
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
4
5
6
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
f's
1
7
8
9
0
-1
0.2
0.3
0.4
0.5
0.6
a
0.7
0.8
0.9
1
103