Fixes: Good convergence slide? Condense scalar field stuff Make nice condensed followup questions section. ego test synergy between JDEM and LST

Transcription

1 Fixes: Good convergence slide? Condense scalar field stuff Make nice condensed followup questions section. ego test synergy between JDEM and LST

2 Dark Energy: the problem, models and distinctions, and measurement of cosmological parameters A. Albrecht (UC Davis) ICFA SLAC October

3 95% of the cosmic matter/energy is a mystery. It has never been observed even in our best laboratories Ordinary Matter (observed in labs) Dark Energy (accelerating) Dark Matter (Gravitating)

4 American Association for the Advancement of Science

5 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. American Association for the Advancement of Science

6 Right now, not only for cosmology but for elementary particle theory, this is the bone in our throat. - Steven Weinberg This is the biggest embarrassment in theoretical physics - Michael Turner Basically, people don t have a clue as to how to solve this problem. - Jeff Harvey would be No. on my list of things to figure out. - Edward Witten Maybe the most fundamentally mysterious thing in basic science. - Frank Wilczek

7 QUANTUM UNIVERSE THE REVOLUTION IN 2 ST CENTURY PARTICLE PHYSICS

8 Questions that describe the current excitement and promise of particle physics. 2 HOW CAN WE SOLVE THE MYSTERY OF DARK ENERGY? QUANTUM UNIVERSE THE REVOLUTION IN 2 ST CENTURY PARTICLE PHYSICS

9 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. Dark Energy Task Force (DETF) astro-ph/060959

10 Of all the challenges in cosmology, the discovery of dark energy poses the greatest challenge for physics because there is no plausible or natural explanation ESA Peacock report

11 2008 P5 report Dark Energy

12 2008 P5 report Dark Energy

13 Dark Energy LSST JDEM 2008 P5 report

14 (EPP 200) ASPERA roadmap BPAC Q2C

15 (EPP 200) ASPERA roadmap BPAC Q2C

16 ?

17 Cosmic acceleration Accelerating matter is required to fit current data Ordinary non accelerating matter Amount of w=- matter ( Dark energy ) Amount Supernova of ordinary gravitating matter Preferred by data c. 2003

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

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

20 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

21 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 the dark subpanel to guide planning of energy properties as well as possible. future dark energy experiments From the Dark Energy Task Force report (2006) astro-ph/ More info here *My emphasis

22 This talk Part : Part 2 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: Planning new experiments - DETF - Next questions

23 Some general issues: Properties: Solve GR for the scale factor a of the Universe (a= today): a&& 4π G Λ = ( ρ + 3p) + a 3 3 Positive acceleration clearly requires w p/ ρ < /3 (unlike any known constituent of the Universe) or a non-zero cosmological constant or an alteration to General Relativity.

24 Some general issues: Numbers: Today, ρ DE 0 M 0 ( ev ) P Many field models require a particle mass of 3 mq 0 ev H0 from mm ρ 2 2 Q P DE

25 Some general issues: Numbers: Today, ρ DE 0 M 0 ( ev ) P Many field models require a particle mass of 3 mq 0 ev H0 from mm ρ 2 2 Q P DE Where do these come from and how are they protected from quantum corrections?

26 Some general issues: Two familiar ways to achieve acceleration: Properties: ) Einstein s cosmological constant Solve GR for the scale and factor relatives a of the ( w Universe = ) (a= today): a&& a 4π G Λ = ( ρ + 3p) ) Whatever drove inflation: Dynamical, Scalar field? Positive acceleration clearly requires w p / ρ < /3 (unlike any known constituent of the Universe) or a non-zero cosmological constant or an alteration to General Relativity.

27 Specific ideas: i) A cosmological constant Λ Nice textbook solutions BUT Deep problems/impacts re fundamental physics Vacuum energy problem (we ve gotten nowhere with this) Λ = 0 20 Λ 0? Vacuum Fluctuations

28 Specific ideas: i) A cosmological constant Λ 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)

29 Specific ideas: i) A cosmological constant Λ 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

30 Specific ideas: i) A cosmological constant Λ 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

31 Specific ideas: i) A cosmological constant Λ Nice textbook solutions BUT Deep problems/impacts re fundamental physics De Sitter limit: Horizon Finite Entropy Banks, Fischler, Susskind, AA & Sorbo etc

32 De Sitter Space: The ultimate equilibrium for the universe? Horizon 2 S A= H =Λ Quantum effects: Hawking Temperature T = H = 8π G ε 3 DE

33 De Sitter Space: The ultimate equilibrium for the universe? Horizon 2 S A= H =Λ Quantum effects: Hawking Temperature T = H = Does this imply (via ) a finite Hilbert space for physics? S = ln N 8π G ε 3 DE Banks, Fischler

34 Specific ideas: i) A cosmological constant Λ 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

35 Specific ideas: i) A cosmological constant Λ 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 Boltzmann s Brain?

36 Specific ideas: i) A cosmological constant Λ 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

37 Specific ideas: i) A cosmological constant Λ 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?)

38 Specific ideas: i) A cosmological constant Λ Nice textbook solutions BUT Deep problems/impacts re fundamental physics De Sitter limit: Horizon Finite Entropy Equilibrium Cosmology Dyson, Kleban & Susskind; AA & Sorbo etc Rare Fluctuation This picture forms a nice foundation for inflationary cosmology

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

40 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)

41 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.

42 Specific ideas: ii) A scalar field ( Quintessence ) Recycle inflation ideas (resurrect dream?) Serious unresolved problems Explaining/ protecting 5 th force problem Λ=0 3 mq 0 ev H0 Vacuum energy problem What is the Q field? (inherited from inflation) Why now? (Often not a separate problem)

43 Specific ideas: ii) A scalar field ( Quintessence ) Inspired Recycle by inflation ideas (resurrect dream?) Serious unresolved problems Explaining/ protecting 5 th force problem Λ=0 3 mq 0 ev H0 Vacuum energy problem What is the Q field? (inherited from inflation) Why now? (Often not a separate problem)

44 Specific ideas: ii) A scalar field ( Quintessence ) Recycle inflation ideas (resurrect Λ= 0 dream?) Result? Serious unresolved problems Explaining/ protecting 5 th force problem 3 mq 0 ev H0 Vacuum energy problem What is the Q field? (inherited from inflation) Why now? (Often not a separate problem)

45 Learned from inflation: A slowly rolling (nearly) homogeneous scalar field can accelerate the universe && φ + 3H & φ = V w 2 p φ + & ρ V V ϕ

46 Learned from inflation: A slowly rolling (nearly) homogeneous scalar field can accelerate the universe && φ + 3H & φ = V Dynamical w 2 p φ + & ρ V 0 V ϕ

47 Learned from inflation: A slowly rolling (nearly) homogeneous scalar field can accelerate the universe && φ + 3H & φ = V Dynamical w 2 p φ + & ρ V 0 V ϕ Rolling scalar field dark energy is called quintessence

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) V( ϕ) = V e λϕ PNGB aka Axion (Frieman et al) V( ϕ) = V (cos( ϕ/ λ) + ) 0 Exponential with prefactor (AA & Skordis) 0 0 ( 2 ( ) ) V( ϕ) = V χ ϕ β + δ e λϕ Inverse Power Law (Ratra & Peebles, Steinhardt et al) V( ϕ) V m ϕ = 0 α

50 The potentials Exponential (Wetterich, Peebles & Ratra) V( ϕ) = V e λϕ PNGB aka Axion (Frieman et al) V( ϕ) = V (cos( ϕ/ λ) + ) 0 Exponential with prefactor (AA & Skordis) 0 0 ( 2 ( ) ) V( ϕ) = V χ ϕ β + δ e λϕ Stronger than average motivations & interest Inverse Power Law (Ratra & Peebles, Steinhardt et al) V( ϕ) V m ϕ = 0 α

51 they cover a variety of behavior. PNGB EXP IT AS w(a) a a = cosmic scale factor time

52 Specific ideas: iii) A mass varying neutrinos ( MaVaNs ) Exploit Δm ρ 0 ν /4 3 DE ev Issues Origin of acceleron (varies neutrino mass, accelerates the universe) Faradon, Nelson & Weiner gravitational collapse Afshordi et al 2005 Spitzer 2006

53 Specific ideas: iii) A mass varying neutrinos ( MaVaNs ) Exploit Δm ρ 0 ν /4 3 DE ev Issues Origin of acceleron (varies neutrino mass, accelerates the universe) Faradon, Nelson & Weiner gravitational collapse Afshordi et al 2005 Spitzer 2006

54 Specific ideas: iii) A mass varying neutrinos ( MaVaNs ) Exploit Δm ρ 0 ν /4 3 DE ev Issues Origin of acceleron (varies neutrino mass, accelerates the universe) Faradon, Nelson & Weiner gravitational collapse Afshordi et al 2005 Spitzer 2006

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

56 Specific ideas: iv) Modify Gravity Not something to be done lightly, but given our confusion about cosmic acceleration, well worth considering. Many deep technical issues e.g. DGP (Dvali, Gabadadze and Porrati) Ghosts Charmousis et al See Origins of Dark Energy meeting May 07 for numerous talks

57 This talk Part : Part 2 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: Planning new experiments - DETF - Next questions

58 This talk Part : Part 2 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: Planning new experiments - DETF - Next questions

59 This talk Part : Part 2 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: Planning new experiments - DETF - Next questions

60 This talk Part : Part 2 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: Planning new experiments -DETF - Next questions

61 Recall: Some general issues: Two familiar ways to achieve acceleration: Properties: ) Einstein s cosmological constant Solve GR for the scale and factor relatives a of the ( w Universe = ) (a= today): a&& a 4π G Λ = ( ρ + 3p) ) Whatever drove inflation: Dynamical, Scalar field? Positive acceleration clearly requires w p / ρ < /3 (unlike any known constituent of the Universe) or a non-zero cosmological constant or an alteration to General Relativity.

62 w a 95% CL contour ( ) wa ( ) = w + w a 0 a (DETF parameterization Linder) 0 DETF figure of merit: = / Area w 0

63 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

64 DETF Projections Stage 3 Figure of merit Improvement over Stage 2

65 Ground DETF Projections Figure of merit Improvement over Stage 2

66 Space DETF Projections Figure of merit Improvement over Stage 2

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

68 A technical point: The role of correlations Combination Technique #2 Technique #

69 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.

70 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 w w a 0 a

71 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?

72 The Dark Energy Task Force (DETF) NB: To make concrete comparisons this work ignores various possible improvements to the DETF data models. 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 (see for example J Newman, H Zhan et al & Schneider et al) Followup questions: ALSO In what ways might the choice of DE Ground/Space parameters synergies biased the DETF results? What impact can these data sets have on specific DE models (vs abstract parameters)? DETF 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?

73 The Dark Energy Task Force (DETF) NB: To make concrete comparisons this work ignores various possible improvements to the DETF data models. 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 (see for example J Newman, H Zhan et al & Schneider et al) Followup questions: ALSO In what ways might the choice of DE Ground/Space parameters synergies biased the DETF results? What impact can these data sets have on specific DE models (vs abstract parameters)? DETF 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?

74 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?

75 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?

76 How good is the w(a) ansatz? w 0-2 Sample w(z) curves in w 0 -w a space Sample w(z) curves for the PNGB models wa ( ) = w + w a 0 w0-wa can only do these a ( ) w w w Sample w(z) curves for the EwP models z z DE models can do this (and much more)

77 How good is the w(a) ansatz? w w w w 0-2 Sample w(z) curves in w 0 -w a space Sample w(z) curves for the PNGB models Sample w(z) curves for the EwP models z z NB: Better than wa ( ) = w + w a 0 ( ) w0-wa can only do these wa ( ) = & flat DE models can do this (and much more) a w 0

78 Δw( a) Try N-D stepwise constant w(a) ( ) ( ) wa ( ) = +Δ w a = + ΔwT i ai, a i + N i= z N parameters are coefficients of the top hat functions T ai, a i + ( ) AA & G Bernstein 2006 (astro-ph/ ). More detailed info can be found at

79 Δw( a) Try N-D stepwise constant w(a) ( ) ( ) wa ( ) = +Δ w a = + ΔwT i ai, a i + i= N parameters are coefficients of the top hat functions N AA & G Bernstein 2006 (astro-ph/ ). More detailed info can be found at z T ai, a i + ( ) Used by Huterer & Turner; Huterer & Starkman; Knox et al; Crittenden & Pogosian Linder; Reiss et al; Krauss et al de Putter & Linder; Sullivan et al

80 Δw( a) Try N-D stepwise constant w(a) ( ) ( ) wa ( ) = +Δ w a = + ΔwT i ai, a i + i= N parameters are coefficients of the top hat functions AA & G Bernstein 2006 N z T ai, a i + ( ) Allows greater variety of w(a) behavior Allows each experiment to put its best foot forward Any signal rejects Λ

81 Δw( a) Try N-D stepwise constant w(a) ( ) ( ) wa ( ) = +Δ w a = + ΔwT i ai, a i + i= N parameters are coefficients of the top hat functions N z T ai, a i + ( ) Any signal Convergence rejects Λ AA & G Bernstein 2006 Allows greater variety of w(a) behavior Allows each experiment to put its best foot forward

82 Q: How do you describe error ellipsis in ND space? A: In terms of N principle axes f r i and corresponding N errors : σ i 2D illustration: r f = Axis σ r f 2 = Axis 2 σ 2

83 Q: How do you describe error ellipsis in ND space? A: In terms of N principle axes f r i and corresponding N errors σ i : Principle component analysis 2D illustration: r f = Axis σ r f 2 = Axis 2 σ 2

84 Q: How do you describe error ellipsis in ND space? A: In terms of N principle axes f r i and corresponding N errors : σ i 2D illustration: NB: in general the f r is form a complete basis: r Δ w c f = r i i i r f = Axis r f 2 = Axis 2 σ σ 2 c i The are independently measured qualities with errors σ i

85 Q: How do you describe error ellipsis in ND space? A: In terms of N principle axes f r i and corresponding N errors : σ i 2D illustration: NB: in general the f r is form a complete basis: r Δ w c f = r i i i r f = Axis r f 2 = Axis 2 σ σ 2 c i The are independently measured qualities with errors σ i

86 DETF stage 2 2 Characterizing 9D ellipses by principle axes and Stage 2 ; lin-a corresponding N Grid = 9, z max = 4, Tag = errors σ i σ i Principle Axes f's f r f's a i a i f's a a z-=4 z =.5 z =0.25 z =0

87 WL Stage 4 Opt 2 Characterizing 9D ellipses by principle axes and Stage 4 Space WL corresponding Opt; lin-a N Grid = 9, z max = 4, Tag errors = σ i σ i Principle Axes f's f r f's a i a i f's a a z-=4 z =.5 z =0.25 z =0

88 WL Stage 4 Opt 2 Characterizing 9D ellipses by principle axes and Stage 4 Space WL corresponding Opt; lin-a N Grid = 6, z max = 4, errors Tag = σ i σ i Principle Axes f's f r f's i a a i f's a a Convergence z-=4 z =.5 z =0.25 z =

89 DETF(-CL) 9D (-CL) e4 e F DETF/9D Grid Linear in a zmax = 4 scale: 0 Stage 3 Stage 4 Ground e4 e BAOp BAOs SNp SNs WLp ALLp Bska Blst Slst Wska Wlst Aska Alst Stage 4 Space Stage 4 Ground+Space e4 e4 e3 00 e BAO SN WL S+W S+W+B [S S B lst W lst ] [B S S lst W lst ] All lst [S S W S B IIIs ] S s W lst

90 DETF(-CL) 9D (-CL) e4 e F DETF/9D Grid Linear in a zmax = 4 scale: 0 Stage 3 Stage 4 Ground e4 e BAOp BAOs SNp SNs WLp ALLp Bska Blst Slst Wska Wlst Aska Alst Stage 2 Stage 3 = order of magnitude (vs 0.5 for DETF) Stage 4 Space Stage 4 Ground+Space e4 e e4 e BAO SN WL S+W S+W+B [S S B lst W lst ] [B S S lst W lst ] All lst [S S W S B IIIs ] S s W lst Stage 2 Stage 4 = 3 orders of magnitude (vs for DETF)

91 Upshot of N-D FoM: ) 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).

92 Upshot of N-D FoM: ) 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).

93 Upshot of N-D FoM: ) 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).

94 Upshot of N-D FoM: ) 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).

95 Upshot of N-D FoM: ) 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 in Estimates terms of a simple rescaling (related to higher S3 vs S4 dimensional parameter space). 4) DETF FoM is fine for most purposes (ranking, value of combinations etc).

96 Upshot of N-D FoM: ) 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)

97 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?

98 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

99 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?

100 .2 DETF stage 2 [ Abrahamse, AA, Barnard, Bozek & Yashar PRD 2008] β β V 0 V 0 V DETF stage DETF stage β

101 .2 DETF stage 2 [ Abrahamse, AA, Barnard, Bozek & Yashar 2008] V 0 V β (S2/3) DETF stage Upshot: 0.6 Story in scalar field parameter space very similar to DETF story in w0-wa space β.2 V DETF stage 4 (S2/0) β

102 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?

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: Very similar to DETF results in w0-wa space

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?

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? Michael Barnard et al arxiv:

106 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.

107 WL Stage 4 Opt 2 Characterizing 9D ellipses by principle axes and Stage 4 Space WL corresponding Opt; lin-a N Grid = 9, z max = 4, Tag errors = σ i σ i Principle Axes f's f r f's f's a r 4 i σ Δ w= c 0 i f r i Axis a 0 r f = a a v r f 2 = Axis 2 σ 2 z-=4 z =.5 z =0.25 z =0 i i

108 Y 2 Concept: Uncorrelated data points (expressed in w(a) space) Data Theory Theory X

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

110 r Δ w = c f r i i i DETF Stage 3 photo [Opt] c / σ 2 2 c / σ

111 r Δ w = c f r i i i DETF Stage 3 photo [Opt] c / σ 2 2 c / σ

112 DETF Stage 3 photo [Opt] Distinct model locations mode amplitude/σ i physical Modes (and σ i s) reflect specific expts. c / σ 2 2 c / σ

113 r Δ w = c f r i i i DETF Stage 3 photo [Opt] c / σ 2 2 c / σ

114 r Δ w = c f r i i i DETF Stage 3 photo [Opt] c / σ 4 4 c / σ 3 3

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

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

117 r Δ w = c f r i i i DETF Stage 4 ground [Opt] c / σ 2 2 c / σ

118 r Δ w = c f r i i i DETF Stage 4 ground [Opt] c / σ 4 4 c / σ 3 3

119 r Δ w = c f r i i i DETF Stage 4 space [Opt] c / σ 2 2 c / σ

120 r Δ w = c f r i i i DETF Stage 4 space [Opt] c / σ 4 4 c / σ 3 3

121 The different kinds of curves correspond to different trajectories in mode space (similar to FT s) PNGB EXP IT AS w(a) a

122 DETF Stage 4 ground Data that reveals a universe with dark energy given by will have finite minimum 2 distances χ to other quintessence models powerful discrimination is possible.

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

124 r Δ w = c f r i i i DETF Stage 3 photo [Opt] c / σ 2 2 c / σ

125 r Δ w = c f r i i i DETF Stage 3 photo [Opt] c / σ 4 4 c / σ 3 3

126 r Δ w = c f r i i i DETF Stage 4 ground [Opt] c / σ 2 2 c / σ

127 r Δ w = c f r i i i DETF Stage 4 ground [Opt] c / σ 4 4 c / σ 3 3

128 r Δ w = c f r i i i DETF Stage 4 space [Opt] c / σ 2 2 c / σ

129 r Δ w = c f r i i i DETF Stage 4 space [Opt] c / σ 4 4 c / σ 3 3

130 Quantify discriminating power:

131 Stage 4 space Test Points Characterize each model distribution by four test points

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

133 Stage 4 space Test Points

134 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.

135 Model Separation in Mode Space 99% confidence at.36 Test point 2 χ Fraction of compared model within given χ 2 of test model s test point 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. 2 χ Test point 4

136 Model Separation in Mode Space Test point 99% confidence at.36 Fraction of compared model within given χ 2 of test model s test point This gap 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. is this gap 2 χ Test point 4

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

138 Comparison Model DETF Stage 3 photo Test Point Model

139 Comparison Model DETF Stage 4 ground Test Point Model

140 Comparison Model DETF Stage 4 space Test Point Model

141 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 =.36. Light orange > 95% rejection Dark orange > 99% rejection Blue: Ignore these because PNGB & Exp hopelessly similar, plus self-comparisons PNGB PNGB Exp IT AS Point Point Point Point Exp Point Point Point Point IT Point Point Point Point AS Point Point Point Point

142 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 =.36. Light orange > 95% rejection Dark orange > 99% rejection Blue: Ignore these because PNGB & Exp hopelessly similar, plus self-comparisons PNGB PNGB Exp IT AS Point Point Point Point Exp Point Point Point Point IT Point Point Point Point AS Point Point Point Point

143 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 =.36. Light orange > 95% rejection Dark orange > 99% rejection Blue: Ignore these because PNGB & Exp hopelessly similar, plus self-comparisons PNGB PNGB Exp IT AS Point Point Point Point Exp Point Point Point Point IT Point Point Point Point AS Point Point Point Point

144 DETF Stage 4 space 2/3 Error/mode 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 =.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 Point Point Point Exp Point Point Point Point IT Point Point Point Point AS Point Point Point Point

145 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.

146 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.

147 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.

148 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

149 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 Structure in mode space DETF Stage 4: Marginal Excellent within reach

150 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

151 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?

152 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 new we learned about (normalizing) modes

153 NB: in general the f r is form a complete basis: r Δ w c f c i The are independently measured qualities with errors σ i = r i i i Define r r D f f / Δa i then r Δ w= c f r i i which obey continuum normalization: f k f k Δ a= δ ( ) D( ) D i j ij D i D i where D c c Δa i i

154 Q: Why? D f j A: For lower modes, has typical grid independent height O(), so one can more directly relate values D of σi σi Δa to one s thinking (priors) on Δw r r r r Δ w= c f = c f i D D i i i i i Define r r D f f / Δa i then r Δ w= c f r i i which obey continuum normalization: f k f k Δ a= δ ( ) D( ) D i j ij D i D i where D c c Δa i i

155 Principle Axes (w(z)) σ i f r i DETF= Stage 4 Space 4 Opt All f k=6 =, Pr = z a Mode Mode 2 Mode 3 0 Mode z 2 4

156 DETF= Stage 44Space Opt All f k=6 =, Pr = Mode z 2 4 Principle Axes (w(z)) f r i a z Mode 6 Mode 7 0 Mode z 2 4

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

158 This talk Part : Part 2 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: Planning new experiments - DETF - Next questions

159 This talk Part : Part 2 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: Planning new experiments - DETF - Next questions Deeply exciting physics

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

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

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

163 This talk Part : Part 2 Deeply exciting physics 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: Rigorous quantitative case for Planning new Stage experiments 4 (i.e. LSST, JDEM, Euclid) - DETF Advances in combining techniques - Next questions Insights into ground & space synergies

164 END

165 Additional Slides

166 average projection PNGB mean Exp. mean IT mean AS mean PNGB max Exp. max IT max AS max mode

167 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?

168 DETF(-CL) 9D (-CL) e4 e F DETF/9D Grid Linear in a zmax = 4 scale: 0 Stage 3 Stage 4 Ground e4 e BAOp BAOs SNp SNs WLp ALLp Bska Blst Slst Wska Wlst Aska Alst Stage 4 Space Stage 4 Ground+Space e4 Specific e3 Case: 00 0 e4 e BAO SN WL S+W S+W+B [S S B lst W lst ] [B S S lst W lst ] All lst [S S W S B IIIs ] S s W lst

169 BAO Stage 4 Space BAO Opt; lin-a N Grid = 9, z max = 4, Tag = σ i f's f's a a f's a z-=4 z =.5 z =0.25 z =0

170 SN Stage 4 Space SN Opt; lin-a N Grid = 9, z max = 4, Tag = σ i f's f's a a f's a z-=4 z =.5 z =0.25 z =0

171 BAO 2 DETF σ, σ 2 Stage 4 Space BAO Opt; lin-a N Grid = 9, z max = 4, Tag = σ i f's f's a a f's a z-=4 z =.5 z =0.25 z =0

172 SN 2 DETF σ, σ 2 Stage 4 Space SN Opt; lin-a N Grid = 9, z max = 4, Tag = σ i f's f's a a f's a z-=4 z =.5 z =0.25 z =0

173 SN σ i 2 w0-wa analysis shows two parameters measured on average as well as 3.5 of these Stage 4 Space SN Opt; lin-a N Grid = 9, z max = 4, Tag = f's f's f's a a 0 DETF σ σ σ 2 i 2/( = 3.5) a z-=4 z =.5 z =0.25 z =0 9 D e 9D

174 Stage 2

175 Stage 2

176 Stage 2

177 Stage 2

178 Stage 2

179 Stage 2

180 Stage 2

181 Detail: Model discriminating power

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

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