Transcript Slide 1

What can we learn about dark energy?
Andreas Albrecht
UC Davis
December 17 2008
NTU-Davis meeting
National Taiwan University
1
Background
2
Cosmic acceleration
“Ordinary” non
accelerating
matter
 Amount of w=-1 matter (“Dark energy”)
Accelerating matter is required to fit current data
Preferred by
data c. 2003
Supernova
 Amount
of “ordinary” gravitating matter
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
How we think about the cosmic acceleration:
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.
5
Two “familiar” ways to achieve
Some general issues:
acceleration:
Properties:
1) Einstein’s cosmological constant
 1
 w Universe
and
relatives
Solve GR for the scale
factor
a of the
(a=1 today):
a
42)GWhatever drove
 inflation:

  3 p 

Dynamical,
Scalar
a
3
3 field?
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.
6
How we think about the cosmic acceleration:
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.
7
How we think about the cosmic acceleration:
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
Theory allows a multitude of possible
• a non-zero cosmological constant or
function w(a). How should we model
measurements of w?
• an alteration to General Relativity.
8
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
program
to determine
subpanel
to guide
planningthe
of dark
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
9
The Dark Energy Task Force (DETF)
 Created specific simulated data sets (Stage 2, Stage 3, Stage
4)
 Assessed their impact on our knowledge of dark energy as
modeled with the w0-wa parameters
w a   w0  wa 1 a 
10
The Dark Energy Task Force (DETF)
 Created specific simulated data sets (Stage 2, Stage 3, Stage
4)
 Assessed their impact on our knowledge of dark energy as
modeled with the w0-wa parameters
Followup questions:
 In what ways might the choice of DE parameters biased the
DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
11
The Dark Energy Task Force (DETF)
 Created specific simulated data sets (Stage 2, Stage 3, Stage
4)
 Assessed their impact on our knowledge of dark energy as
modeled with the w0-wa parameters
Followup questions:
New work,
relevant
to setting
a
 In what ways might the choice of DE parameters
biased
the
concrete threshold
DETF results?
for Stage 4
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
12
The Dark Energy Task Force (DETF)
 Created specific simulated data
setsTo
(Stage
2, Stage
3, Stage
NB:
make
concrete
4)
comparisons this work ignores
 Assessed their impact on our knowledge of dark energy as
possible improvements to the
modeled with the w0-wavarious
parameters
DETF data models.
(see for example J Newman, H Zhan et al
& Schneider et al)
 In what ways might the choice of DE parameters biased the
DETF results?
Followup questions:
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating DETF
power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
13
The Dark Energy Task Force (DETF)
 Created specific simulated data sets (Stage 2, Stage 3, Stage
4)
 Assessed their impact on our knowledge of dark energy as
modeled with the w0-wa parameters
Followup questions:
 In what ways might the choice of DE parameters biased the
DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
14
DETF
Review
15
wa
95% CL contour
w(a) = w0 + wa(1-a)
0
(DETF parameterization… Linder)
DETF figure of merit:
 1Area
1
w0
16
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)
DETF modeled
• SN
•Weak Lensing
•Baryon Oscillation
•Cluster data
17
Figure of merit Improvement over
Stage 2 
DETF Projections
Stage 3
18
Figure of merit Improvement over
Stage 2 
DETF Projections
Ground
19
Figure of merit Improvement over
Stage 2 
DETF Projections
Space
20
Figure of merit Improvement over
Stage 2 
DETF Projections
Ground + Space
21
A technical point: The role of correlations
Co
m
Technique #2
bi
na
t
io
n
Technique #1
22
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.
23
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
24
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
25
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
26
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
Sample w(z) curves for the EwP models
w
1
& flat
DE models can do this
(and much more)
0
-1
0
0.5
1
z
1.5
2
z
27
Try N-D stepwise constant w(a)
1
w  a  0
-1 -2
10
-1
0
10
10
1
10
z
N
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
28
found at http://www.physics.ucdavis.edu/Cosmology/albrecht/MoreInfo0608269/
Try N-D stepwise constant w(a)
1
w  a  0
-1 -2
10
-1
0
10
1
10
z
N
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

10
i
i 1

Used by
Huterer & Turner;
Huterer & Starkman;
Knox et al;
Crittenden & Pogosian
Linder; Reiss et al;
Krauss et al
de Putter & Linder;
Sullivan et al
AA & G Bernstein 2006 (astro-ph/0608269 ). More detailed info can be
29
found at http://www.physics.ucdavis.edu/Cosmology/albrecht/MoreInfo0608269/
Try N-D stepwise constant w(a)
1
w  a  0
-1 -2
10
-1
0
10
10
N
z
w(a)  1  w  a   1   wT
i  ai , ai 1 
i 1
1
10
 Allows greater
variety of w(a)
behavior
 Allows each
experiment to
9 parameters are coefficients of the “top “put its best foot
hat functions”
T ai , ai 1
forward”

AA & G Bernstein 2006

 Any signal
rejects Λ
30
Try N-D stepwise constant w(a)
1
w  a  0
-1 -2
10
-1
0
10
10
N
z
w(a)  1  w  a   1   wT
i  ai , ai 1 
i 1
1
10
 Allows greater
variety of w(a)
behavior
 Allows each
experiment to
9 parameters are coefficients of the “top “put its best foot
hat functions”
T ai , ai 1
forward”

AA & G Bernstein 2006

 Any signal
“Convergence”
rejects Λ
31
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
32
Q: How do you describe error ellipsis in 9D space?
A: In terms of 9 principle axes f i and
corresponding 9 errors  i :
Principle component
analysis
2D illustration:
1
f1  Axis 1
f2  Axis 2
2
33
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   ci fi
i
The ci are independently
measured qualities with
errors  i
34
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   ci fi
i
The ci are independently
measured qualities with
errors  i
35
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
z-=4
0.3
0.4
z =1.5
0.5
0.6
a
a
0.7
0.8
z =0.25
0.9
1
z =0
36
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
z-=4
0.3
0.4
z =1.5
0.5
0.6
a
a
0.7
0.8
z =0.25
0.9
1
z =0
37
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
z-=4
0.3
0.4
z =1.5
0.5
0.6
a
a
0.7
“Convergence”
0.8
0.9
1
z =0.25
z =0
38
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
39
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
40
Stage 2  Stage 4 = 3 orders of magnitude (vs 1 for DETF)
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 (related to higher
dimensional parameter space).
4) DETF FoM is fine for most purposes (ranking,
value of combinations etc).
41
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 (related to higher
dimensional parameter space).
4) DETF FoM is fine for most purposes (ranking,
value of combinations etc).
42
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 (related to higher
dimensional parameter space).
4) DETF FoM is fine for most purposes (ranking,
value of combinations etc).
43
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 (related to higher
dimensional parameter space).
4) DETF FoM is fine for most purposes (ranking,
value of combinations etc).
44
Upshot of 9D FoM:
1) DETF underestimates impact of expts
2) DETF underestimates relative value of Stage 4 Inverts
vs Stage 3
cost/FoM
3) The above can be understood approximately inEstimates
S3 vs S4
terms of a simple rescaling
4) DETF FoM is fine for most purposes (ranking,
value of combinations etc).
45
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).
 A nice way to gain insights into data (real or
imagined)
46
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
47
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
A: Only by an overall (possibly important) rescaling
48
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
49
How well do Dark Energy Task Force
simulated data sets constrain
specific scalar field quintessence
models?
Augusta Abrahamse
Brandon Bozek
+
Michael Barnard
DETF
Simulated data
Mark Yashar
+AA
+
Quintessence
potentials
+
MCMC
See also Dutta & Sorbo 2006, Huterer and Turner 1999
& especially Huterer and Peiris 2006
50
The potentials
Exponential (Wetterich, Peebles & Ratra)
PNGB aka Axion (Frieman et al)
Exponential with prefactor (AA & Skordis)
Inverse Power Law (Ratra & Peebles, Steinhardt et al)
51
The potentials
Exponential (Wetterich, Peebles & Ratra)
V ( )  V0e
PNGB aka Axion (Frieman et al)
V ( )  V0 (cos( /  )  1)
Exponential with prefactor (AA & Skordis)


V ( )  V0        e
2
Inverse Power Law (Ratra & Peebles, Steinhardt et al)

m
V ( )  V0  
 
52
The potentials
Exponential (Wetterich, Peebles & Ratra)
V ( )  V0e
Stronger than
average
motivations &
interest
PNGB aka Axion (Frieman et al)
V ( )  V0 (cos( /  )  1)
Exponential with prefactor (AA & Skordis)


V ( )  V0        e
2
Inverse Power Law (Ratra & Peebles, Steinhardt et al)

m
V ( )  V0  
 
53
The potentials
Exponential (Wetterich, Peebles & Ratra)
V ( )  V0e
PNGB aka Axion (Frieman et al)
ArXiv Dec 08,
PRD in press
V ( )  V0 (cos( /  )  1)
Exponential with prefactor (AA & Skordis)


V ( )  V0        e
2
Inverse Tracker (Ratra & Peebles, Steinhardt et al)

m
V ( )  V0  
 
In prep.
54
…they cover a
variety of behavior.
-0.5
PNGB
EXP
IT
AS
-0.6
w(a)
-0.7
-0.8
-0.9
-1
0.2
0.4
0.6
a
0.8
1
55
Challenges: Potential parameters can have very
complicated (degenerate) relationships to
observables
Resolved with good parameter choices (functional
form and value range)
56
DETF stage 2
DETF stage 3
DETF stage 4
57
DETF stage 2
(S2/3)
DETF stage 3
Upshot:
DETF stage 4
Story in scalar field parameter
space very similar to DETF story
in w0-wa space.
(S2/10)
58
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
59
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
A: Very similar to DETF results in w0-wa space
60
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
61
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
Michael Barnard et al arXiv:0804.0413
62
Problem:
Each scalar field model is defined in its own parameter
space. How should one quantify discriminating power
among models?
Our answer:
Form each set of scalar field model parameter values,
map the solution into w(a) eigenmode space, the space
of uncorrelated observables.
 Make the comparison in the space of uncorrelated
observables.
63
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
0
0.3
0.4
0.5
f1 0.6 Axis 0.7
1
0.8
1
i
w   ci 4fi
1
1
-1
0.2
i
0.9
5
6
1
a
1
f's
Principle Axes
f's
1
0
-1
0.2
z-=4
f2  Axis 2
0.3
0.4
z =1.5
0.5
0.6
a
a
0.7
2
0.8
z =0.25
7
8
9
0.9
1
z =0
64
Concept: Uncorrelated data points
(expressed in w(a) space)
2
■
■
Y
■
■
■
■ ■
●
■
■
●
0
0
■ Theory 1
■ Theory 2
■
●
●
1
●
● Data
5
10
15
X
65
Starting point: MCMC chains giving distributions for each
model at Stage 2.
66
DETF Stage 3 photo [Opt]
67
w   ci fi
DETF Stage 3 photo [Opt]
i
c2 /  2
c1 /  1
68
DETF Stage 3 photo [Opt]
 Distinct model locations
 mode amplitude/σi “physical”
 Modes (and σi’s) reflect
specific expts.
c2 /  2
c1 /  1
69
DETF Stage 3 photo [Opt]
c2 /  2
c1 /  1
70
DETF Stage 3 photo [Opt]
c4 /  4
c3 /  3
71
Eigenmodes:
z=4
z=2
z=1
z=0.5
z=0
Stage 3
Stage 4 g
Stage 4 s
72
Eigenmodes:
z=4
z=2
z=1
z=0.5
z=0
Stage 3
Stage 4 g
Stage 4 s
N.B. σi
change too
73
DETF Stage 4 ground [Opt]
74
DETF Stage 4 ground [Opt]
75
DETF Stage 4 space [Opt]
76
DETF Stage 4 space [Opt]
77
The different kinds of curves correspond to different
“trajectories” in mode space (similar to FT’s)
-0.5
PNGB
EXP
IT
AS
-0.6
w(a)
-0.7
-0.8
-0.9
-1
0.2
0.4
0.6
a
0.8
1
78
DETF Stage 4 ground
 Data that reveals a
universe with dark
energy given by “ “
will have finite minimum
2
“distances” to other
quintessence models
 powerful
discrimination is
possible.
79
Consider discriminating power
of each experiment (look at
units on axes)
80
DETF Stage 3 photo [Opt]
81
DETF Stage 3 photo [Opt]
82
DETF Stage 4 ground [Opt]
83
DETF Stage 4 ground [Opt]
84
DETF Stage 4 space [Opt]
85
DETF Stage 4 space [Opt]
86
Quantify discriminating power:
87
Stage 4 space Test Points
Characterize each model distribution
by four “test points”
88
Stage 4 space Test Points
Characterize each model distribution
by four “test points”
(Priors: Type 1 optimized for conservative results re discriminating power.)
89
Stage 4 space Test Points
90
•Measured the χ2 from each one of the test points
(from the “test model”) to all other chain points (in the
“comparison model”).
•Only the first three modes were used in the
calculation.
•Ordered said χ2‘s by value, which allows us to plot
them as a function of what fraction of the points have
a given value or lower.
•Looked for the smallest values for a given model to
model comparison.
91
Model Separation in Mode Space
99% confidence at 11.36
Test point 1
2
Fraction of compared
model within given χ2
of test model’s test
point
Where the curve meets the
axis, the compared model is
ruled out by that χ2 by an
observation of the test point.
This is the separation seen in
the mode plots.
2
Test point 4
92
Model Separation in Mode Space
99% confidence at 11.36
Test point 1
Fraction of compared
model within given χ2
of test model’s test This gap…
point
Where the curve meets the
axis, the compared model is
ruled out by that χ2 by an
observation of the test point.
This is the separation seen in
the mode plots.
2
Test point 4
…is this gap
93
Comparison Model
DETF Stage 3 photo
Test Point Model
[4 models] X [4 models] X [4 test points]
94
DETF Stage 3 photo
Test Point Model
Comparison Model
95
DETF Stage 4 ground
Test Point Model
Comparison Model
96
DETF Stage 4 space
Test Point Model
Comparison Model
97
DETF Stage 3 photo
A tabulation of χ2 for each
graph where the curve
crosses the x-axis (= gap)
For the three parameters
used here,
95% confidence χ2 = 7.82,
99%  χ2 = 11.36.
Light orange > 95% rejection
Dark orange > 99% rejection
PNGB
PNGB
Exp
IT
AS
Point 1
0.001
0.001
0.1
0.2
Point 2
0.002
0.01
0.5
1.8
Point 3
0.004
0.04
1.2
6.2
Point 4
0.01
0.04
1.6
10.0
Point 1
0.004
0.001
0.1
0.4
Point 2
0.01
0.001
0.4
1.8
Point 3
0.03
0.001
0.7
4.3
Point 4
0.1
0.01
1.1
9.1
Point 1
0.2
0.1
0.001
0.2
Point 2
0.5
0.4
0.0004
0.7
Point 3
1.0
0.7
0.001
3.3
Point 4
2.7
1.8
0.01
16.4
Point 1
0.1
0.1
0.1
0.0001
Point 2
0.2
0.1
0.1
0.0001
Point 3
0.2
0.2
0.1
0.0002
Point 4
0.6
0.5
0.2
0.001
Exp
IT
AS
Blue: Ignore these because
PNGB & Exp hopelessly
similar, plus self-comparisons
98
DETF Stage 4 ground
A tabulation of χ2 for each
graph where the curve
crosses the x-axis (= gap).
For the three parameters
used here,
95% confidence χ2 = 7.82,
99%  χ2 = 11.36.
Light orange > 95% rejection
Dark orange > 99% rejection
PNGB
PNGB
Exp
IT
AS
Point 1
0.001
0.005
0.3
0.9
Point 2
0.002
0.04
2.4
7.6
Point 3
0.004
0.2
6.0
18.8
Point 4
0.01
0.2
8.0
26.5
Point 1
0.01
0.001
0.4
1.6
Point 2
0.04
0.002
2.1
7.8
Point 3
0.01
0.003
3.8
14.5
Point 4
0.03
0.01
6.0
24.4
Point 1
1.1
0.9
0.002
1.2
Point 2
3.2
2.6
0.001
3.6
Point 3
6.7
5.2
0.002
8.3
Point 4
18.7
13.6
0.04
30.1
Point 1
2.4
1.4
0.5
0.001
Point 2
2.3
2.1
0.8
0.001
Point 3
3.3
3.1
1.2
0.001
Point 4
7.4
7.0
2.6
0.001
Exp
IT
AS
Blue: Ignore these because
PNGB & Exp hopelessly
similar, plus self-comparisons
99
DETF Stage 4 space
A tabulation of χ2 for each
graph where the curve
crosses the x-axis (= gap)
For the three parameters
used here,
95% confidence χ2 = 7.82,
99%  χ2 = 11.36.
Light orange > 95% rejection
Dark orange > 99% rejection
PNGB
PNGB
Exp
IT
AS
Point 1
0.01
0.01
0.4
1.6
Point 2
0.01
0.05
3.2
13.0
Point 3
0.02
0.2
8.2
30.0
Point 4
0.04
0.2
10.9
37.4
Point 1
0.02
0.002
0.6
2.8
Point 2
0.05
0.003
2.9
13.6
Point 3
0.1
0.01
5.2
24.5
Point 4
0.3
0.02
8.4
33.2
Point 1
1.5
1.3
0.005
2.2
Point 2
4.6
3.8
0.002
8.2
Point 3
9.7
7.7
0.003
9.4
Point 4
27.8
20.8
0.1
57.3
Point 1
3.2
3.0
1.1
0.002
Point 2
4.9
4.6
1.8
0.003
Point 3
10.9
10.4
4.3
0.01
Point 4
26.5
25.1
10.6
0.01
Exp
IT
AS
Blue: Ignore these because
PNGB & Exp hopelessly
similar, plus self-comparisons
100
DETF Stage 4 space
2/3 Error/mode
A tabulation of χ2 for each
graph where the curve
crosses the x-axis (= gap).
For the three parameters
used here,
95% confidence χ2 = 7.82,
99%  χ2 = 11.36.
Light orange > 95% rejection
Dark orange > 99% rejection
Many believe it is realistic
for Stage 4 ground and/or
space to do this well or
even considerably better.
(see slide 5)
PNGB
PNGB
Exp
IT
AS
Point 1
0.01
0.01
.09
3.6
Point 2
0.01
0.1
7.3
29.1
Point 3
0.04
0.4
18.4
67.5
Point 4
0.09
0.4
24.1
84.1
Point 1
0.04
0.01
1.4
6.4
Point 2
0.1
0.01
6.6
30.7
Point 3
0.3
0.01
11.8
55.1
Point 4
0.7
0.05
18.8
74.6
Point 1
3.5
2.8
0.01
4.9
Point 2
10.4
8.5
0.01
18.4
Point 3
21.9
17.4
0.01
21.1
Point 4
62.4
46.9
0.2
129.0
Point 1
7.2
6.8
2.5
0.004
Point 2
10.9
10.3
4.0
0.01
Point 3
24.6
23.3
9.8
0.01
Point 4
59.7
56.6
23.9
0.01
Exp
IT
AS
101
Comments on model discrimination
•Principle component w(a) “modes” offer a space in which
straightforward tests of discriminating power can be made.
•The DETF Stage 4 data is approaching the threshold of
resolving the structure that our scalar field models form in the
mode space.
102
Comments on model discrimination
•Principle component w(a) “modes” offer a space in which
straightforward tests of discriminating power can be made.
•The DETF Stage 4 data is approaching the threshold of
resolving the structure that our scalar field models form in the
mode space.
103
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
A:
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach
104
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
A:
Structure in mode
space
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach
105
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
A:
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach
106
Followup questions:
 In what ways might the choice of DE parameters have skewed
the DETF results?
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
 To what extent can these data sets deliver discriminating power
between specific DE models?
 How is the DoE/ESA/NASA Science Working Group looking at
these questions?
107
DoE/ESA/NASA JDEM Science Working Group
 Update agencies on figures of merit issues
 formed Summer 08
 finished ~now (moving on to SCG)
 Use w-eigenmodes to get more complete picture
 also quantify deviations from Einstein gravity
 For today: Something we learned about normalizing
modes
108
NB: in general the f i s form
a complete basis:
w   ci fi
Define
i
The ci are independently
measured qualities with
errors  i
fi D  fi / a
which obey continuum
normalization:
D
D
f
a
f
 i  k  j  ak  a  ij
k
then
w   ciD fi D
i
where
ciD  ci  a
109
Q: Why?
D
f
A: For lower modes, j
has typical grid independent
“height” O(1), so one can
more directly relate values
D
of  i   i  a
to one’s
thinking (priors) on  w
Define
fi D  fi / a
which obey continuum
normalization:
D
D
f
a
f
 i  k  j  ak  a  ij
w   ci fi   ciD fi D
i
i
k
then
w   ciD fi D
i
where
ciD  ci  a
110
DETF= Stage 4 Space Opt All
f k=6 = 1, Pr = 0
4
i
2
0
2
4
6
8
10
12
14
16
18
20
2
Mode 1
Mode 2
Principle Axes
0
-2
0
fi
0.2
0.5
1
z
2
2
4
0
-2
1
Mode 3
0.8
0.6
0.4
0.2
a
2
0
-2
0
0
Mode 4
0.2
0.5
1
z
2
4
111
DETF= Stage 4 Space Opt All
f k=6 = 1, Pr = 0
2
0
-2
0
Mode 5
0.2
0.5
1
z
Principle Axes
2
2
4
0
fi
-2
1
Mode 6
0.8
0.6
0.4
0.2
a
2
0
-2
0
Mode 7
0.2
0.5
2
1
z
2
4
0
-2
0
0
Mode 8
0.2
0.5
1
z
2
4
112
Upshot: More modes are interesting (“well measured” in a
grid invariant sense) than previously thought.
113
Summary
 In what ways might the choice of DE parameters have skewed
the DETF results?
A: Only by an overall (possibly important) rescaling
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
A: Very similar to DETF results in w0-wa space
To what extent can these data sets deliver discriminating power
between specific DE models?
A:
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach (AA) 114
Summary
 In what ways might the choice of DE parameters have skewed
the DETF results?
A: Only by an overall (possibly important) rescaling
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
A: Very similar to DETF results in w0-wa space
To what extent can these data sets deliver discriminating power
between specific DE models?
A:
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach (AA) 115
Summary
 In what ways might the choice of DE parameters have skewed
the DETF results?
A: Only by an overall (possibly important) rescaling
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
A: Very similar to DETF results in w0-wa space
To what extent can these data sets deliver discriminating power
between specific DE models?
A:
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach (AA) 116
Summary
 In what ways might the choice of DE parameters have skewed
the DETF results?
A: Only by an overall (possibly important) rescaling
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
A: Very similar to DETF results in w0-wa space
To what extent can these data sets deliver discriminating power
between specific DE models?
A:
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach (AA) 117
Summary
 In what ways might the choice of DE parameters have skewed
the DETF results?
A: Only by an overall (possibly important) rescaling
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
A: Very similar to DETF results in w0-wa space
To what extent can these data sets deliver discriminating power
between specific DE models?
A:
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach (AA) 118
Summary
 In what ways might the choice of DE parameters have skewed
the DETF results?
A: Only by an overall (possibly important) rescaling
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
A: Very similar to DETF results in w0-wa space
To what extent can these data sets deliver discriminating power
between specific DE models?
A:
• DETF Stage 3: Poor
• DETF Stage 4: Marginal… Excellent within reach (AA) 119
Summary
 In what ways might the choice of DE parameters have skewed
the DETF results?
A: Only by an overall (possibly important) rescaling
 What impact can these data sets have on specific DE models (vs
abstract parameters)?
A: Very similar to DETF results in w0-wa space
To what extent can these data sets deliver
discriminating
power
Interesting
contribution
between specific DE models?
A:
• DETF Stage 3: Poor
to discussion of Stage 4
(if you believe scalar
field modes)
• DETF Stage 4: Marginal… Excellent within reach (AA) 120
 How is the DoE/ESA/NASA Science Working Group looking at these
questions?
i) Using w(a) eigenmodes
ii) Revealing value of higher modes
121
DETF= Stage 4 Space Opt All
f k=6 = 1, Pr = 0
4
i
2
0
2
4
6
8
10
12
14
16
18
20
2
Mode 1
Mode 2
Principle Axes
0
-2
0
fi
0.2
0.5
1
z
2
2
4
0
-2
1
Mode 3
0.8
0.6
0.4
0.2
a
2
0
-2
0
0
Mode 4
0.2
0.5
1
z
2
4
122
END
123
Additional Slides
124
10
average projection
10
10
10
10
10
2
PNGB mean
Exp. mean
IT mean
AS mean
PNGB max
Exp. max
IT max
AS max
1
0
-1
-2
-3
0
2
4
6
mode
8
10
125
2
10
PNGB mean
Exp. mean
IT mean
AS mean
PNGB max
Exp. max
IT max
AS max
1
average projection
10
0
10
-1
10
-2
10
-3
10
0
5
mode
10
126
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 to which BAO is particularly sensitive. Why
does this not show up in the 9D analysis?
127
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 lst128
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
z-=4
0.3
0.4
z =1.5
0.5
0.6
a
0.7
0.8
z =0.25
0.9
1
z =0
129
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
z-=4
0.3
0.4
z =1.5
0.5
0.6
a
0.7
0.8
z =0.25
0.9
1
z =0
130
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
z-=4
0.3
0.4
z =1.5
0.5
0.6
a
0.7
0.8
z =0.25
0.9
1
z =0
131
SN
 2lin-a N
Stage 4 Space
SN
DETF
1 ,Opt;
Grid
= 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
z-=4
0.3
0.4
z =1.5
0.5
0.6
a
0.7
0.8
z =0.25
0.9
1
z =0
132
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
z-=4
0.3
0.4
0.5
0.6
a
0.7
0.8


1  2    i 
 1

0.4
z =1.5
0.5
0.6
a
9
0.7
2 /  De  3.5 
0.8
z =0.25
0.9
1
7
8
9
0.9
9D
1
z =0
133
134
135
136
137
138
139
140