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Dark Energy Theory Andreas Albrecht (UC Davis) PASCOS OSU Sep 10 2006

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Cosmic acceleration Accelerating matter is required to fit current data Supernova Preferred by modern data Amount of “ordinary” gravitating matter Amount of w=-1 matter “Ordinary” non accelerating matter

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Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation. The acceleration of the Universe is, along with dark matter, the observed phenomenon which most directly demonstrates that our fundamental theories of particles and gravity are either incorrect or incomplete. Most experts believe that nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration. For these reasons, the nature of dark energy ranks among the very most compelling of all outstanding problems in physical science. These circumstances demand an ambitious observational program to determine the dark energy properties as well as possible. From the Dark Energy Task Force report (2006) www.nsf.gov/mps/ast/detf.jsp & to appear on the arXiv.

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This talk Part 1: A few attempts to explain dark energy - Motivations, Problems and other comments Theme: We may not know where this revolution is taking us, but it is already underway: (see e.g. Copeland et al 2006 review) Part 2 Modeling dark energy to make forecasts for new experiments (see e.g. DETF report and AA & Bernstein 2006)

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This talk Part 1: A few attempts to explain dark energy - Motivations, Problems and other comments Theme: We may not know where this revolution is taking us, but it is already underway: (see e.g. Copeland et al 2006 review) Part 2 Modeling dark energy to make forecasts for new experiments (see e.g. DETF report and AA & Bernstein 2006)

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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.

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

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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?

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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) = 10 120 0 ? Vacuum Fluctuations

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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)

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Specific ideas: i) A cosmological constant Nice “textbook” solutions BUT Deep problems/impacts re fundamental physics The string theory landscape (a radically different idea of what we mean by a fundamental theory) Not exactly a cosmological constant KKLT etc

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Specific ideas: i) A cosmological constant Nice “textbook” solutions BUT Deep problems/impacts re fundamental physics De Sitter limit: Horizon Finite Entropy Equilibrium Cosmology Rare Fluctuation Banks, Fischler, Susskind, AA Sorbo etc

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

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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”)

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today (t=14.5 Gyr). (not some other time) Why now? (Often not a separate problem)

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Specific ideas: ii) A scalar field (“Quintessence”) Illustration: Pseudo Nambu Goldstone Boson (PNGB) models With f 10 18 GeV, M 10 -3 eV PNGB: Frieman, Hill, Stebbins, & Waga 1995 PNGB mechanism protects M and 5 th force issues

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Specific ideas: ii) A scalar field (“Quintessence”) Illustration: Pseudo Nambu Goldstone Boson (PNGB) models Hall et al 05

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Dark energy and the ego test

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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

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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

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

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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

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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 “ ” Copeland et al

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Specific ideas: iv) Modify Gravity Not something to be done lightly, but given our confusion about cosmic acceleration, well worth considering. See previous talk Many deep technical issues

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This talk Part 1: A few attempts to explain dark energy - Motivations, Problems and other comments Theme: We may not know where this revolution is taking us, but it is already underway: (see e.g. Copeland et al 2006 review) Part 2 Modeling dark energy to make forecasts for new experiments (see e.g. DETF report and AA & Bernstein 2006)

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This talk Part 1: A few attempts to explain dark energy - Motivations, Problems and other comments Theme: We may not know where this revolution is taking us, but it is already underway: (see e.g. Copeland et al 2006 review) Part 2 Modeling dark energy to make forecasts for new experiments (see e.g. DETF report and AA & Bernstein 2006)

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Q: Given that we know so little about the cosmic acceleration, how do we represent source of this acceleration when we forecast the impact of future experiments? Consensus Answer: ( DETF, Joint Dark Energy Mission Science Definition Team JDEM STD ) Model dark energy as homogeneous fluid all information contained in Model possible breakdown of GR by inconsistent determination of w(a) by different methods.

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ww wawa w ( a ) w + w a ( a ) DETF figure of merit: Area 95% CL contour (DETF parameterization… Linder)

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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)

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DETF Projections Stage 3 Figure of merit Improvement over Stage 2

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DETF Projections Ground Figure of merit Improvement over Stage 2

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DETF Projections Space Figure of merit Improvement over Stage 2

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

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

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

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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

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Try 9D stepwise constant w(a) AA & G Bernstein 2006 9 parameters are coefficients of the “top hat functions” 0 -2

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Try 9D stepwise constant w(a) AA & G Bernstein 2006 9 parameters are coefficients of the “top hat functions” Allows greater variety of w(a) behavior Allows each experiment to “put its best foot forward” 0 -2

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Q: How do you describe error ellipsis in 9D space? A: In terms of 9 principle axes and corresponding 9 errors : 2D illustration: Axis 1 Axis 2

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Q: How do you describe error ellipsis in 9D space? A: In terms of 9 principle axes and corresponding 9 errors : 2D illustration: Axis 1 Axis 2 Assuming Gaussian distributions for this discussion

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Q: How do you describe error ellipsis in 9D space? A: In terms of 9 principle axes and corresponding 9 errors : 2D illustration: Axis 1 Axis 2 NB: in general the s form a complete basis: The are independently measured qualities with errors

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Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors DETF stage 2

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Principle Axes Characterizing 9D ellipses by principle axes and corresponding errors DETF stage 4 WL Opt.

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DETF Figure of Merit: 9D Figure of Merit: If we set

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DETF(-CL) 9D (-CL)

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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)

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Define the “scale to 2D” function The idea: Construct an effective 2D FoM by assuming two dimensions with “average” errors (~geometric mean of 9D errors) Purpose: Separate out the impact of higher dimensions on comparisons with DETF, vs other information from the D9 space (such relative comparisons of data model).

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DETF(-CL) 9D (-CL)-Scaled to 2D D e = 4 for Stage 4 Pes, ; De= 4.5 for Stage 4 Pes, D e =4.5 for Stage 3D e =4 for Stage 2.5

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Discussion of cost/benefit analysis should take place in higher dimensions (vs current standards) “form” Frieman’s talk Axis 1 Axis 2 DETF

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An example of the power of the principle component analysis: Q: I’ve heard the claim that the DETF FoM is unfair to BAO, because w0-wa does not describe the high-z behavior which to which BAO is particularly sensitive. Why does this not show up in the 9D analysis?

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

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BAO

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SN

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w0-wa analysis shows two parameters measured on average as well as 3.5 of these

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Upshot of 9D FoM: 1)DETF underestimates impact of expts 2)DETF underestimates relative value of Stage 4 vs Stage 3 3)The above can be understood approximately in terms of a simple rescaling 4)DETF FoM is fine for most purposes (ranking, value of combinations etc).

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Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation. The acceleration of the Universe is, along with dark matter, the observed phenomenon which most directly demonstrates that our fundamental theories of particles and gravity are either incorrect or incomplete. Most experts believe that nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration. For these reasons, the nature of dark energy ranks among the very most compelling of all outstanding problems in physical science. These circumstances demand an ambitious observational program to determine the dark energy properties as well as possible. From the Dark Energy Task Force report (2006) www.nsf.gov/mps/ast/detf.jsp & to appear on the arXiv.

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END

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Extra material

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Markers label different scalar field models Coordinates are first three in

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Markers label different scalar field models Coordinates are first three in Implication: New experiments will have very significant discriminating power among actual scalar field models. (See Augusta Abrahamse, Michael Barnard, Brandon Bozek & AA, to appear soon)

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