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

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

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

4. Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation. The acceleration of the Universe is, along with dark matter, the observed phenomenon which most directly demonstrates that our fundamental theories of particles and gravity are either incorrect or incomplete. Most experts believe that nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration. For these reasons, the nature of dark energy ranks among the very most compelling of all outstanding problems in physical science. These circumstances 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.

5. 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)

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

7. 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.

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

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

10. Specific ideas: i) A cosmological constant • Nice “textbook” solutions BUT • Deep problems/impacts re fundamental physics • Vacuum energy problem (we’ve gotten nowhere with this)  = 10120 Vacuum Fluctuations   0 ?

11. 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)

12. 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

13. 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

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

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

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

17. Specific ideas: ii) A scalar field (“Quintessence”) • Illustration: Pseudo Nambu Goldstone Boson (PNGB) models PNGB: Frieman, Hill, Stebbins, & Waga 1995 With f  1018GeV, M  10-3eV PNGB mechanism protects M and 5th force issues

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

19. Dark energy and the ego test

20. 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

21. 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 AA & Skordis 1999

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

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

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

25. 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

26. 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)

27. 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)

28. 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.

29. wa 95% CL contour w(a)=w0 + wa(1-a) (DETF parameterization… Linder) 0 DETF figure of merit: =Area w0 -1

30. 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)

31. DETF Projections Stage 3 Figure of merit Improvement over Stage 2 

32. DETF Projections Ground Figure of merit Improvement over Stage 2 

33. DETF Projections Space Figure of merit Improvement over Stage 2 

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

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

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

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

38. Try 9D stepwise constant w(a) 0 -1 -2 9 parameters are coefficients of the “top hat functions” AA & G Bernstein 2006

39. Try 9D stepwise constant w(a) 0 -1 -2 • Allows greater variety of w(a) behavior • Allows each experiment to “put its best foot forward” 9 parameters are coefficients of the “top hat functions” AA & G Bernstein 2006

40. 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

41. 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 Assuming Gaussian distributions for this discussion Axis 2

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

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

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

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

46. DETF(-CL) 9D (-CL)

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

48. 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).

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

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