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Dark Energy: current theoretical issues and progress toward future experiments A. Albrecht UC Davis KITPC Colloquium November 4 2009.

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Presentation on theme: "Dark Energy: current theoretical issues and progress toward future experiments A. Albrecht UC Davis KITPC Colloquium November 4 2009."— Presentation transcript:

1 Dark Energy: current theoretical issues and progress toward future experiments A. Albrecht UC Davis KITPC Colloquium November

2 Dark Energy (accelerating) Dark Matter (Gravitating) Ordinary Matter (observed in labs) 95% of the cosmic matter/energy is a mystery. It has never been observed even in our best laboratories

3 American Association for the Advancement of Science

4 …at the moment, the nature of dark energy is arguably the murkiest question in physics--and the one that, when answered, may shed the most light.

5

6 Oct

7 ?

8 Supernova Preferred by data c  Amount of gravitating matter   Amount of w=-1 matter (“Dark energy”)  “Ordinary” non accelerating matter Cosmic acceleration Accelerating matter is required to fit current data

9 Cosmic acceleration Accelerating matter is required to fit current data Supernova  Amount of w=-1 matter (“Dark energy”)  “Ordinary” non accelerating matter Preferred by data c BAO Kowalski, et al., Ap.J.. (2008)  Amount of gravitating matter 

10 Cosmic acceleration Accelerating matter is required to fit current data Supernova  Amount of w=-1 matter (“Dark energy”)  “Ordinary” non accelerating matter Preferred by data c BAO Kowalski, et al., Ap.J.. (2008) (Includes dark matter)  Amount of gravitating matter 

11 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) astro-ph/ *My emphasis

12 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) astro-ph/ *My emphasis DETF = a HEPAP/AAAC subpanel to guide planning of future dark energy experiments More info here

13 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: Part 2 Planning new experiments - DETF - Next questions

14 Some general issues: Properties: Solve GR for the scale factor a of the Universe (a=1 today): Positive acceleration clearly requires (unlike any known constituent of the Universe) or a non-zero cosmological constant or an alteration to General Relativity.

15 Some general issues: Properties: Solve GR for the scale factor a of the Universe (a=1 today): Positive acceleration clearly requires (unlike any known constituent of the Universe) or a non-zero cosmological constant or an alteration to General Relativity. See work by Pengjie Zhang (SHAO)

16 Today, Many field models require a particle mass of Some general issues: Numbers: from

17 Today, Many field models require a particle mass of Some general issues: Numbers: from Where do these come from and how are they protected from quantum corrections?

18 Some general issues: Properties: Solve GR for the scale factor a of the Universe (a=1 today): Positive acceleration clearly requires (unlike any known constituent of the Universe) or a non-zero cosmological constant or an alteration to General Relativity. Two “familiar” ways to achieve acceleration: 1) Einstein’s cosmological constant and relatives 2) Whatever drove inflation: Dynamical, Scalar field?

19 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)  =   0 ? Vacuum Fluctuations

20 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)

21 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” ?

22 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

23 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

24 “De Sitter Space: The ultimate equilibrium for the universe? Horizon Quantum effects: Hawking Temperature

25 “De Sitter Space: The ultimate equilibrium for the universe? Horizon Quantum effects: Hawking Temperature Does this imply (via “ “) a finite Hilbert space for physics? Banks, Fischler

26 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 Dyson, Kleban & Susskind; AA & Sorbo etc

27 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” ? Dyson, Kleban & Susskind; AA & Sorbo etc

28 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 Dyson, Kleban & Susskind; AA & Sorbo etc This picture is in deep conflict with observation

29 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 Dyson, Kleban & Susskind; AA & Sorbo etc This picture is in deep conflict with observation (resolved by landscape?)

30 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 Dyson, Kleban & Susskind; AA & Sorbo etc This picture forms a nice foundation for inflationary cosmology

31 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 Dyson, Kleban & Susskind; AA & Sorbo etc This picture forms a nice foundation for inflationary cosmology Contrast with eternal inflation!

32 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 Dyson, Kleban & Susskind; AA & Sorbo etc This picture forms a nice foundation for inflationary cosmology Contrast with eternal inflation! AA 2009

33 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 Dyson, Kleban & Susskind; AA & Sorbo etc Perhaps “saved” from this discussion by instability of De Sitter space (i.e. Woodard et al)

34 Specific ideas: i) A cosmological constant Nice “textbook” solutions BUT Deep problems/impacts re fundamental physics is not the “simple option”

35 Some general issues: Alternative Explanations?: Is there a less dramatic explanation of the data?

36 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.

37 Some general issues: Alternative Explanations?: Is there a less dramatic explanation of the data? Or perhaps Nonlocal gravity from loop corrections (Woodard & Deser) Misinterpretation of a genuinely inhomogeneous universe (ie. Kolb and collaborators)

38 Recycle inflation ideas (resurrect dream?) Serious unresolved problems  Explaining/ protecting  5 th force problem  Vacuum energy problem  What is the Q field? (inherited from inflation)  Why now? (Often not a separate problem) Specific ideas: ii) A scalar field (“Quintessence”)

39 Recycle inflation ideas (resurrect dream?) Serious unresolved problems  Explaining/ protecting  5 th force problem  Vacuum energy problem  What is the Q field? (inherited from inflation)  Why now? (Often not a separate problem) Specific ideas: ii) A scalar field (“Quintessence”) Inspired by

40 Recycle inflation ideas (resurrect dream?) Serious unresolved problems  Explaining/ protecting  5 th force problem  Vacuum energy problem  What is the Q field? (inherited from inflation)  Why now? (Often not a separate problem) Specific ideas: ii) A scalar field (“Quintessence”) Result?

41 V Learned from inflation: A slowly rolling (nearly) homogeneous scalar field can accelerate the universe

42 V Dynamical

43 V Learned from inflation: A slowly rolling (nearly) homogeneous scalar field can accelerate the universe Dynamical Rolling scalar field dark energy is called “quintessence”

44 Some quintessence potentials Exponential (Wetterich, Peebles & Ratra) PNGB aka Axion (Frieman et al) Exponential with prefactor (AA & Skordis) Inverse Power Law (Ratra & Peebles, Steinhardt et al)

45 Some quintessence potentials Exponential (Wetterich, Peebles & Ratra) PNGB aka Axion (Frieman et al) Exponential with prefactor (AA & Skordis) Inverse Power Law (Ratra & Peebles, Steinhardt et al)

46 Some quintessence potentials Exponential (Wetterich, Peebles & Ratra) PNGB aka Axion (Frieman et al) Exponential with prefactor (AA & Skordis) Inverse Power Law (Ratra & Peebles, Steinhardt et al)

47 Some quintessence potentials Exponential (Wetterich, Peebles & Ratra) PNGB aka Axion (Frieman et al) Exponential with prefactor (AA & Skordis) Inverse Power Law (Ratra & Peebles, Steinhardt et al)

48 Some quintessence potentials Exponential (Wetterich, Peebles & Ratra) PNGB aka Axion (Frieman et al) Exponential with prefactor (AA & Skordis) Inverse Power Law (Ratra & Peebles, Steinhardt et al)

49 Some quintessence potentials Exponential (Wetterich, Peebles & Ratra) PNGB aka Axion (Frieman et al) Exponential with prefactor (AA & Skordis) Inverse Power Law (Ratra & Peebles, Steinhardt et al)

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) Stronger than average motivations & interest

51 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) Stronger than average motivations & interest See important work on this topic by Mingzhi Li et al and Bo Feng et al

52 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) Stronger than average motivations & interest See important work on this topic by Mingzhi Li et al and Bo Feng et al

53 …they cover a variety of behavior. a = “cosmic scale factor” ≈ time

54 Dark energy and the ego test

55 Specific ideas: ii) A scalar field (“Quintessence”) Illustration: Exponential with prefactor (EwP) models:  All parameters O(1) in Planck units,  motivations/protections from extra dimensions & quantum gravity AA & Skordis 1999 Burgess & collaborators (e.g. )

56 Specific ideas: ii) A scalar field (“Quintessence”) Illustration: Exponential with prefactor (EwP) models:  All parameters O(1) in Planck units,  motivations/protections from extra dimensions & quantum gravity AA & Skordis 1999 Burgess & collaborators (e.g. ) AA & Skordis 1999

57 Specific ideas: ii) A scalar field (“Quintessence”) Illustration: Exponential with prefactor (EwP) models:  All parameters O(1) in Planck units,  motivations/protections from extra dimensions & quantum gravity AA & Skordis 1999 Burgess & collaborators (e.g. ) AA & Skordis 1999

58 Specific ideas: ii) A scalar field (“Quintessence”) Illustration: Exponential with prefactor (EwP) models: AA & Skordis 1999

59 Specific ideas: iii) A mass varying neutrinos (“MaVaNs”) Exploit Issues  Origin of “acceleron” (varies neutrino mass, accelerates the universe)  gravitational collapse Faradon, Nelson & Weiner Afshordi et al 2005 Spitzer 2006

60 Specific ideas: iii) A mass varying neutrinos (“MaVaNs”) Exploit Issues  Origin of “acceleron” (varies neutrino mass, accelerates the universe)  gravitational collapse Faradon, Nelson & Weiner Afshordi et al 2005 Spitzer 2006 “ ”

61 Specific ideas: iii) A mass varying neutrinos (“MaVaNs”) Exploit Issues  Origin of “acceleron” (varies neutrino mass, accelerates the universe)  gravitational collapse Faradon, Nelson & Weiner Afshordi et al 2005 Spitzer 2006 “ ”

62 Specific ideas: iv) Modify Gravity Not something to be done lightly, but given our confusion about cosmic acceleration, very much worth considering. Many deep technical issues e.g. DGP (Dvali, Gabadadze and Porrati) Charmousis et al Ghosts

63 Specific ideas: iv) Modify Gravity Not something to be done lightly, but given our confusion about cosmic acceleration, very much worth considering. Many deep technical issues e.g. DGP (Dvali, Gabadadze and Porrati) Charmousis et al Ghosts Important work by Pengjie Zhang

64 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: Part 2 Planning new experiments - DETF - Next questions

65 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: Part 2 Planning new experiments - DETF - Next questions

66 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: Part 2 Planning new experiments - DETF - Next questions

67 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: Part 2 Planning new experiments - DETF - Next questions

68 Astronomy Primer for Dark Energy Solve GR for the scale factor a of the Universe (a=1 today): Positive acceleration clearly requires unlike any known constituent of the Universe, or a non-zero cosmological constant - or an alteration to General Relativity. The second basic equation is Today we have From DETF

69 Astronomy Primer for Dark Energy Solve GR for the scale factor a of the Universe (a=1 today): Positive acceleration clearly requires unlike any known constituent of the Universe, or a non-zero cosmological constant - or an alteration to General Relativity. The second basic equation is Today we have From DETF See also Frieman Huterer and Turner for a review

70 Hubble Parameter We can rewrite this as 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: Dark Energy curvature rel. matter non-rel. matter

71 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.

72 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.

73 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.

74 What are the observable quantities? Future dark-energy experiments will require percent-level precision on the primary observables D(z) and g(z).

75 Supernovae (exploding stars) can have well determined luminosities and can be (briefly) as bright as an entire galaxy. As very bright “standard candles” they can be used to probe great cosmic distances. Supernova

76 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  D 2. SNIa are not homogeneous events. Are all luminosity- affecting variables manifested in observed properties of the explosion (light curves, spectra)? Supernovae Detected in HST GOODS Survey (Riess et al)

77 Dark Energy with Type Ia Supernovae Example of SN data: HST GOODS Survey (Riess et al) Clear evidence of acceleration!

78 Riess et al astro-ph/

79 Dark Energy with Baryon Acoustic Oscillations Acoustic waves propagate in the baryon- photon plasma starting at end of inflation. When plasma combines to neutral hydrogen, sound propagation ends. Cosmic expansion sets up a predictable standing wave pattern on scales of the Hubble length. The Hubble length (~sound horizon r s) ~140 Mpc is imprinted on the matter density pattern. Identify the angular scale subtending r s then use  s =r s /D(z) WMAP/Planck determine r s and the distance to z=1088. Survey of galaxies (as signposts for dark matter) recover D(z), H(z) at 0

80 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 . Dark energy sensitivity: Mass function is very sensitive to M; very sensitive to g(z). Also very sensitive to mis- estimation of mass, which is not directly observed. Optical View (Lupton/SDSS) Cluster method probes both D(z) and g(z)

81 Dark Energy with Galaxy Clusters 30 GHz View (Carlstrom et al) Sunyaev-Zeldovich effect X-ray View (Chandra) Optical View (Lupton/SDSS)

82 Galaxy Clusters from ROSAT X-ray surveys ROSAT cluster surveys yielded ~few 100 clusters in controlled samples. Future X-ray, SZ, lensing surveys project few x 10,000 detections. From Rosati et al, 1999:

83 Gravitational Lensing

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85

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87 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 10 8 redshifts from optical spectroscopy is infeasible. “photometric” redshifts instead. Lensing method probes both D(z) and g(z)

88 Dark Energy with Weak Gravitational Lensing In weak lensing, shapes of galaxies are measured. Dominant noise source is the (random) intrinsic shape of galaxies. Large- N statistics extract lensing influence from intrinsic noise.

89 Choose your background photon source: Faint background galaxies: Use visible/NIR imaging to determine shapes. Photometric redshifts. Photons from the CMB: Use mm-wave high- resolution imaging of CMB. All sources at z= cm photons: Use the proposed Square Kilometer Array (SKA). Sources are neutral H in regular galaxies at z 6. (lensing not yet detected) Hoekstra et al 2006:

90 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? One Answer: ( DETF, Joint Dark Energy Mission Science Definition Team JDEM STD ) Model dark energy as homogeneous fluid  all information contained in Model possible breakdown of GR by inconsistent determination of w(a) by different methods.

91 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? One Answer: ( DETF, Joint Dark Energy Mission Science Definition Team JDEM STD ) Model dark energy as homogeneous fluid  all information contained in Model possible breakdown of GR by inconsistent determination of w(a) by different methods. Also: Std cosmological parameters including curvature

92 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? One Answer: ( DETF, Joint Dark Energy Mission Science Definition Team JDEM STD ) Model dark energy as homogeneous fluid  all information contained in Model possible breakdown of GR by inconsistent determination of w(a) by different methods. Also: Std cosmological parameters including curvature  We know very little now

93 Some general issues: Properties: Solve GR for the scale factor a of the Universe (a=1 today): Positive acceleration clearly requires (unlike any known constituent of the Universe) or a non-zero cosmological constant or an alteration to General Relativity. Two “familiar” ways to achieve acceleration: 1) Einstein’s cosmological constant and relatives 2) Whatever drove inflation: Dynamical, Scalar field? Recall:

94 ww wawa   DETF figure of merit:  Area 95% CL contour (DETF parameterization… Linder)

95 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

96 DETF Projections Stage 3 Figure of merit Improvement over Stage 2 

97 DETF Projections Ground Figure of merit Improvement over Stage 2 

98 DETF Projections Space Figure of merit Improvement over Stage 2 

99 DETF Projections Ground + Space Figure of merit Improvement over Stage 2 

100 A technical point: The role of correlations

101 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.

102 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

103 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? 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

104

105 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? NB: To make concrete comparisons this work ignores various possible improvements to the DETF data models. (see for example J Newman, H Zhan et al & Schneider et al, H Zhan et al to appear, NIR synergies) ALSO Ground/Space synergies DETF

106 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? NB: To make concrete comparisons this work ignores various possible improvements to the DETF data models. (see for example J Newman, H Zhan et al & Schneider et al, H Zhan et al to appear, NIR synergies i.e Dome A & LSST synergies ) ALSO Ground/Space synergies DETF

107 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?

108 A: DETF Stage 3: Poor DETF Stage 4: Marginal… Excellent within reach (AA)  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 Summary To what extent can these data sets deliver discriminating power between specific DE models?

109 w0-wa can only do these DE models can do this (and much more) w z How good is the w(a) ansatz?

110 w0-wa can only do these DE models can do this (and much more) w z How good is the w(a) ansatz? NB: Better than & flat

111 Try N-D stepwise constant w(a) AA & G Bernstein 2006 (astro-ph/ ). More detailed info can be found at N parameters are coefficients of the “top hat functions”

112 Try N-D stepwise constant w(a) AA & G Bernstein 2006 (astro-ph/ ). More detailed info can be found at N parameters are coefficients of the “top hat functions” Used by Huterer & Turner; Huterer & Starkman; Knox et al; Crittenden & Pogosian Linder; Reiss et al; Krauss et al de Putter & Linder; Sullivan et al

113 Try N-D stepwise constant w(a) AA & G Bernstein 2006 N parameters are coefficients of the “top hat functions”  Allows greater variety of w(a) behavior  Allows each experiment to “put its best foot forward”  Any signal rejects Λ

114 Try N-D stepwise constant w(a) AA & G Bernstein 2006 N parameters are coefficients of the “top hat functions”  Allows greater variety of w(a) behavior  Allows each experiment to “put its best foot forward”  Any signal rejects Λ “Convergence”

115 115 Illustration of stepwise parameterization of w(a) Each bin height is a free parameter Z=4 Z=0

116 116 Each bin height is a free parameter Refine bins as much as needed Illustration of stepwise parameterization of w(a) Z=4 Z=0

117 117 Each bin height is a free parameter Refine bins as much as needed Z=4 Z=0 Illustration of stepwise parameterization of w(a)

118 118 Each bin height is a free parameter Refine bins as much as needed Illustration of stepwise parameterization of w(a) Z=4 Z=0

119 119 Each bin height is a free parameter Refine bins as much as needed FOMSWG settled on 36 bins Illustration of stepwise parameterization of w(a) Z=4 Z=0

120 2D illustration: Axis 1 Axis 2 Q: How do you describe error ellipsis in N D space? A: In terms of N principle axes and corresponding N errors :

121 Q: How do you describe error ellipsis in N D space? A: In terms of N principle axes and corresponding N errors : 2D illustration: Axis 1 Axis 2 Principle component analysis

122 2D illustration: Axis 1 Axis 2 NB: in general the s form a complete basis: The are independently measured qualities with errors Q: How do you describe error ellipsis in N D space? A: In terms of N principle axes and corresponding N errors :

123 2D illustration: Axis 1 Axis 2 NB: in general the s form a complete basis: The are independently measured qualities with errors Q: How do you describe error ellipsis in N D space? A: In terms of N principle axes and corresponding N errors :

124 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors DETF stage 2 z-=4z =1.5z =0.25z =0

125 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors WL Stage 4 Opt z-=4z =1.5z =0.25z =0

126 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors WL Stage 4 Opt “Convergence” z-=4z =1.5z =0.25z =0

127 DETF(-CL) 9D (-CL)

128 DETF(-CL) 9D (-CL) Stage 2  Stage 4 = 3 orders of magnitude (vs 1 for DETF) Stage 2  Stage 3 = 1 order of magnitude (vs 0.5 for DETF)

129 Upshot of N-D 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). Inverts cost/FoM Estimates S3 vs S4

130 A: DETF Stage 3: Poor DETF Stage 4: Marginal… Excellent within reach (AA)  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 Summary To what extent can these data sets deliver discriminating power between specific DE models?

131 A: DETF Stage 3: Poor DETF Stage 4: Marginal… Excellent within reach (AA)  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 Summary To what extent can these data sets deliver discriminating power between specific DE models?

132 DETF stage 2 DETF stage 3 DETF stage 4 [ Abrahamse, AA, Barnard, Bozek & Yashar PRD 2008]

133 A: DETF Stage 3: Poor DETF Stage 4: Marginal… Excellent within reach (AA)  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 Summary To what extent can these data sets deliver discriminating power between specific DE models?

134 A: DETF Stage 3: Poor DETF Stage 4: Marginal… Excellent within reach (AA)  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 Summary To what extent can these data sets deliver discriminating power between specific DE models?

135 A: DETF Stage 3: Poor DETF Stage 4: Marginal… Excellent within reach (AA)  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 Summary To what extent can these data sets deliver discriminating power between specific DE models?

136 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors WL Stage 4 Opt z-=4z =1.5z =0.25z =0 Express models & data in space of coefficients of w(a) modes.

137 DETF Stage 4 ground [Opt]

138

139 The different kinds of curves correspond to different “trajectories” in mode space (similar to FT’s)

140 DETF Stage 4 ground  Data that reveals a universe with dark energy given by “ “ will have finite minimum “distances” to other quintessence models  powerful discrimination is possible.

141 A: DETF Stage 3: Poor DETF Stage 4: Marginal… Excellent within reach (AA)  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 Summary To what extent can these data sets deliver discriminating power between specific DE models?

142 A: DETF Stage 3: Poor DETF Stage 4: Marginal… Excellent within reach (AA)  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 Summary To what extent can these data sets deliver discriminating power between specific DE models? Interesting contribution to discussion of Stage 4

143  How is the DoE/ESA/NASA Science Working Group looking at these questions? i)Using w(a) eigenmodes ii)Revealing value of higher modes

144 DoE/ESA/NASA JDEM Science Working Group  Update agencies on figures of merit issues  formed Summer 08  finished Dec 08 (report on arxiv Jan 09, moved on to SCG)  Use w-eigenmodes to get more complete picture  also quantify deviations from Einstein gravity

145  How is the DoE/ESA/NASA Science Working Group looking at these questions? i)Using w(a) eigenmodes ii)Revealing value of higher modes

146 146 Principle Axes

147 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: Part 2 Planning new experiments - DETF - Next questions

148 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: Part 2 Planning new experiments - DETF - Next questions Deeply exciting physics

149 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: Part 2 Planning new experiments - DETF - Next questions  Rigorous quantitative case for “Stage 4” (i.e. LSST, JDEM, Euclid)  Advances in combining techniques  Insights into ground & space synergies

150 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: Part 2 Planning new experiments - DETF - Next questions  Rigorous quantitative case for “Stage 4” (i.e. LSST, JDEM, Euclid)  Advances in combining techniques  Insights into ground & space synergies

151 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: Part 2 Planning new experiments - DETF - Next questions  Rigorous quantitative case for “Stage 4” (i.e. LSST, JDEM, Euclid)  Advances in combining techniques  Insights into NIR synergies w Photo z-s

152 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: Part 2 Planning new experiments - DETF - Next questions  Rigorous quantitative case for “Stage 4” (i.e. LSST, JDEM, Euclid)  Advances in combining techniques Insights into  NIR synergies w Photo z-s (i.e Dome A & LSST synergies) Deeply exciting physics

153 END

154 Kowalski, et al., Ap.J.. (2008) [SCP] (Flat universe assumed)

155 Kowalski, et al., Ap.J.. (2008) [SCP] (Flat universe assumed)

156 Additional Slides

157 157 Focus on

158 158 Focus on Cosmic scale factor = “time”

159 159 Focus on Cosmic scale factor = “time” DETF:

160 160 Focus on Cosmic scale factor = “time” DETF: (Free parameters = ∞)

161 161 Focus on Cosmic scale factor = “time” DETF: (Free parameters = ∞) (Free parameters = 2)

162 162 Illustration of FOMSWG parameterization of w(a) Z=4 Z=0

163 163 Illustration of FOMSWG parameterization of w(a) Measure Z=4 Z=0

164 164 Illustration of FOMSWG parameterization of w(a) Each bin height is a free parameter

165 165 Illustration of FOMSWG parameterization of w(a) Each bin height is a free parameter Refine bins as much as needed

166 166 Illustration of FOMSWG parameterization of w(a) Each bin height is a free parameter Refine bins as much as needed Z=4 Z=0

167 167 Illustration of FOMSWG parameterization of w(a) Each bin height is a free parameter Refine bins as much as needed

168 168 Illustration of FOMSWG parameterization of w(a) Each bin height is a free parameter Refine bins as much as needed FOMSWG settled on 36 bins

169 N-D stepwise w(a) AA & G Bernstein 2006 (astro-ph/ ). More detailed info can be found at N parameters are coefficients of the “top hat functions”

170 AA & G Bernstein 2006 (astro-ph/ ). More detailed info can be found at N parameters are coefficients of the “top hat functions” Used by Huterer & Turner; Huterer & Starkman; Knox et al; Crittenden & Pogosian Linder; Reiss et al; Krauss et al de Putter & Linder; Sullivan et al N-D stepwise w(a)

171 N parameters are coefficients of the “top hat functions”  Allows greater variety of w(a) behavior  Allows each experiment to “put its best foot forward”  Any signal rejects Λ N-D stepwise w(a)

172 AA & G Bernstein 2006 N parameters are coefficients of the “top hat functions”  Allows greater variety of w(a) behavior  Allows each experiment to “put its best foot forward”  Any signal rejects Λ N-D stepwise w(a) “Convergence”

173 AA & G Bernstein 2006 N parameters are coefficients of the “top hat functions”  Allows greater variety of w(a) behavior  Allows each experiment to “put its best foot forward”  Any signal rejects Λ N-D stepwise w(a) “Convergence”

174 174 DETF FoM Marginalize over all other parameters and find uncertainties in w  and w a ww wawa   DETF FoM  (area of ellipse)   CDM value errors in w  and w a are correlated

175 From DETF: The figure of merit is a quantitative guide; since the nature of dark energy is poorly understood, no single figure of merit is appropriate for every eventuality. 175 FOMSWG emphasis

176 w0-wa can only do these DE models can do this (and much more) w z How good is the w(a) ansatz?

177 w0-wa can only do these DE models can do this (and much more) w z How good is the w(a) ansatz? NB: Better than & flat

178 Try N-D stepwise constant w(a) AA & G Bernstein 2006 (astro-ph/ ). More detailed info can be found at N parameters are coefficients of the “top hat functions”

179 Try N-D stepwise constant w(a) AA & G Bernstein 2006 (astro-ph/ ). More detailed info can be found at N parameters are coefficients of the “top hat functions” Used by Huterer & Turner; Huterer & Starkman; Knox et al; Crittenden & Pogosian Linder; Reiss et al; Krauss et al de Putter & Linder; Sullivan et al

180 Try N-D stepwise constant w(a) AA & G Bernstein 2006 N parameters are coefficients of the “top hat functions”  Allows greater variety of w(a) behavior  Allows each experiment to “put its best foot forward”  Any signal rejects Λ

181 Try N-D stepwise constant w(a) AA & G Bernstein 2006 N parameters are coefficients of the “top hat functions”  Allows greater variety of w(a) behavior  Allows each experiment to “put its best foot forward”  Any signal rejects Λ “Convergence”

182 2D illustration: Axis 1 Axis 2 Q: How do you describe error ellipsis in N D space? A: In terms of N principle axes and corresponding N errors :

183 Q: How do you describe error ellipsis in N D space? A: In terms of N principle axes and corresponding N errors : 2D illustration: Axis 1 Axis 2 Principle component analysis

184 2D illustration: Axis 1 Axis 2 NB: in general the s form a complete basis: The are independently measured qualities with errors Q: How do you describe error ellipsis in N D space? A: In terms of N principle axes and corresponding N errors :

185 2D illustration: Axis 1 Axis 2 NB: in general the s form a complete basis: The are independently measured qualities with errors Q: How do you describe error ellipsis in N D space? A: In terms of N principle axes and corresponding N errors :

186 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors DETF stage 2 z-=4z =1.5z =0.25z =0

187 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors WL Stage 4 Opt z-=4z =1.5z =0.25z =0

188 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors WL Stage 4 Opt “Convergence” z-=4z =1.5z =0.25z =0

189 DETF(-CL) 9D (-CL)

190 DETF(-CL) 9D (-CL) Stage 2  Stage 4 = 3 orders of magnitude (vs 1 for DETF) Stage 2  Stage 3 = 1 order of magnitude (vs 0.5 for DETF)

191 Upshot of N-D 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).

192 Upshot of N-D 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).

193 Upshot of N-D 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).

194 Upshot of N-D 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).

195 Upshot of N-D 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). Inverts cost/FoM Estimates S3 vs S4

196 Upshot of N-D 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).  A nice way to gain insights into data (real or imagined)

197 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?

198 A: Only by an overall (possibly important) rescaling 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?

199 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?

200 DETF stage 2 DETF stage 3 DETF stage 4 [ Abrahamse, AA, Barnard, Bozek & Yashar PRD 2008]

201 DETF stage 2 DETF stage 3 DETF stage 4 (S2/3) (S2/10) Upshot: Story in scalar field parameter space very similar to DETF story in w0-wa space. [ Abrahamse, AA, Barnard, Bozek & Yashar 2008]

202 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?

203 A: Very similar to DETF results in w0-wa space 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?

204 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?

205 Michael Barnard et al arXiv: 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?

206 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.

207 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors WL Stage 4 Opt z-=4z =1.5z =0.25z =0 Axis 1 Axis 2

208 ●●●● ● ■ ■ ■ ■ ■ ■■■■■ ● Data ■ Theory 1 ■ Theory 2 Concept: Uncorrelated data points (expressed in w(a) space) X Y

209 Starting point: MCMC chains giving distributions for each model at Stage 2.

210 DETF Stage 3 photo [Opt]

211

212  Distinct model locations  mode amplitude/σ i “physical”  Modes (and σ i ’s) reflect specific expts.

213 DETF Stage 3 photo [Opt]

214

215 Eigenmodes: Stage 3 Stage 4 g Stage 4 s z=4z=2z=1z=0.5z=0

216 Eigenmodes: Stage 3 Stage 4 g Stage 4 s z=4z=2z=1z=0.5z=0 N.B. σ i change too

217 DETF Stage 4 ground [Opt]

218

219 DETF Stage 4 space [Opt]

220

221 The different kinds of curves correspond to different “trajectories” in mode space (similar to FT’s)

222 DETF Stage 4 ground  Data that reveals a universe with dark energy given by “ “ will have finite minimum “distances” to other quintessence models  powerful discrimination is possible.

223 Consider discriminating power of each experiment (  look at units on axes)

224 DETF Stage 3 photo [Opt]

225

226 DETF Stage 4 ground [Opt]

227

228 DETF Stage 4 space [Opt]

229

230 Quantify discriminating power:

231 Stage 4 space Test Points Characterize each model distribution by four “test points”

232 Stage 4 space Test Points Characterize each model distribution by four “test points” (Priors: Type 1 optimized for conservative results re discriminating power.)

233 Stage 4 space Test Points

234 Measured the χ 2 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 χ 2 ‘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.

235 Model Separation in Mode Space Fraction of compared model within given χ 2 of test model’s test point Test point 4 Test point 1 Where the curve meets the axis, the compared model is ruled out by that χ 2 by an observation of the test point. This is the separation seen in the mode plots. 99% confidence at 11.36

236 Model Separation in Mode Space Fraction of compared model within given χ 2 of test model’s test point Test point 4 Test point 1 Where the curve meets the axis, the compared model is ruled out by that χ 2 by an observation of the test point. This is the separation seen in the mode plots. 99% confidence at …is this gap This gap…

237 DETF Stage 3 photo Test Point Model Comparison Model [4 models] X [4 models] X [4 test points]

238 DETF Stage 3 photo Test Point Model Comparison Model

239 DETF Stage 4 ground Test Point Model Comparison Model

240 DETF Stage 4 space Test Point Model Comparison Model

241 PNGB ExpITAS Point Point Point Point Exp Point Point Point Point IT Point Point Point Point AS Point Point Point Point DETF Stage 3 photo A tabulation of χ 2 for each graph where the curve crosses the x-axis (= gap) For the three parameters used here, 95% confidence  χ 2 = 7.82, 99%  χ 2 = Light orange > 95% rejection Dark orange > 99% rejection Blue: Ignore these because PNGB & Exp hopelessly similar, plus self-comparisons

242 PNGB ExpITAS Point Point Point Point Exp Point Point Point Point IT Point Point Point Point AS Point Point Point Point DETF Stage 4 ground A tabulation of χ 2 for each graph where the curve crosses the x-axis (= gap). For the three parameters used here, 95% confidence  χ 2 = 7.82, 99%  χ 2 = Light orange > 95% rejection Dark orange > 99% rejection Blue: Ignore these because PNGB & Exp hopelessly similar, plus self-comparisons

243 PNGB ExpITAS Point Point Point Point Exp Point Point Point Point IT Point Point Point Point AS Point Point Point Point DETF Stage 4 space A tabulation of χ 2 for each graph where the curve crosses the x-axis (= gap) For the three parameters used here, 95% confidence  χ 2 = 7.82, 99%  χ 2 = Light orange > 95% rejection Dark orange > 99% rejection Blue: Ignore these because PNGB & Exp hopelessly similar, plus self-comparisons

244 PNGB ExpITAS Point Point Point Point Exp Point Point Point Point IT Point Point Point Point AS Point Point Point Point DETF Stage 4 space 2/3 Error/mode Many believe it is realistic for Stage 4 ground and/or space to do this well or even considerably better. (see slide 5) A tabulation of χ 2 for each graph where the curve crosses the x-axis (= gap). For the three parameters used here, 95% confidence  χ 2 = 7.82, 99%  χ 2 = Light orange > 95% rejection Dark orange > 99% rejection

245 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.

246 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.

247 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.

248 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

249 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 Structure in mode space

250 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

251 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?

252 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 tomorrow: Something new we learned about (normalizing) modes

253 NB: in general the s form a complete basis: The are independently measured qualities with errors Define which obey continuum normalization: then where

254 Define which obey continuum normalization: then where Q: Why? A: For lower modes, has typical grid independent “height” O(1), so one can more directly relate values of to one’s thinking (priors) on

255 Principle Axes (w(z)) DETF Stage 4

256 Principle Axes (w(z)) DETF Stage 4

257 Upshot: More modes are interesting (“well measured” in a grid invariant sense) than previously thought.

258

259 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?

260 DETF(-CL) 9D (-CL) Specific Case:

261 Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors WL Stage 4 Opt z-=4z =1.5z =0.25z =0

262 BAO z-=4z =1.5z =0.25z =0

263 SN z-=4z =1.5z =0.25z =0

264 BAO DETF z-=4z =1.5z =0.25z =0

265 SN DETF z-=4z =1.5z =0.25z =0

266 z-=4z =1.5z =0.25z =0 SN w0-wa analysis shows two parameters measured on average as well as 3.5 of these DETF 9D

267 Stage 2

268

269

270

271

272

273

274 Detail: Model discriminating power

275 DETF Stage 4 ground [Opt] Axes: 1 st and 2 nd best measured w(z) modes

276 DETF Stage 4 ground [Opt] Axes: 3 rd and 4 th best measured w(z) modes


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