1. Falsifying Paradigms for Cosmic Acceleration Michael Mortonson Kavli Institute for Cosmological Physics University of Chicago January 22, 2009

2. Outline Cosmic acceleration Observables and fiducial data for forecasts (SNAP, Planck) Dark energy models – principal components of w(z) Predictions for growth and expansion observables from distances January 22, 20092Michael Mortonson KICP/UChicago

3. Dark Energy Consistency Tests 1.Find the range of possible growth histories (and other observables) for a given set of distance measurements for all dark energy models in a particular class (e.g. quintessence) 2.Test the dark energy model class by measuring the growth history directly and comparing with the growth predicted from distances January 22, 20093Michael Mortonson KICP/UChicago

4. Cosmic Expansion and Acceleration Friedmann equation: Acceleration: January 22, 20094Michael Mortonson KICP/UChicago

5. Evidence for Acceleration Type Ia Supernovae “Union” compilation (Kowalski et al. 2008) January 22, 20095Michael Mortonson KICP/UChicago

6. Acceleration Paradigms Cosmological constant/vacuum energy (  ): Scalar field (quintessence): Dark energy beyond quintessence (e.g., non-canonical kinetic term) Modified gravity Violation of spatial homogeneity January 22, 20096Michael Mortonson KICP/UChicago

7. Dark Energy Phenomenology Time-varying w(z): Early dark energy (e.g. tracking models) CMB acoustic peaks: (Doran, Robbers, & Wetterich 2007) Big Bang nucleosynthesis: (Bean, Hansen, & Melchiorri 2001) January 22, 20097Michael Mortonson KICP/UChicago

8. Flat  CDM Observables  m =0.24,  K =0, h=0.73 Expansion rate: January 22, 20098Michael Mortonson KICP/UChicago

9. Distance:  m =0.24,  K =0, h=0.73 Flat  CDM Observables January 22, 20099Michael Mortonson KICP/UChicago

10.  m =0.24,  K =0, h=0.73 Growth: Flat  CDM Observables January 22, 200910Michael Mortonson KICP/UChicago

11. Dark Energy Consistency Tests 1.Find the range of possible growth histories (and other observables) for a given set of distance measurements for all dark energy models in a particular class (e.g. quintessence) 2.Test the dark energy model class by measuring the growth history directly and comparing with the growth predicted from distances January 22, 200911Michael Mortonson KICP/UChicago

12. Dark Energy Consistency Tests 1.Find the range of possible growth histories (and other observables) for a given set of distance measurements for all dark energy models in a particular class (e.g. quintessence) SNAP SNe, Planck CMB, priors based on current data Measure distances: Choose class of DE models: + priors on w(z) Find models that fit distances: MCMC Compute observables (e.g. growth) for models that fit distance data January 22, 200912Michael Mortonson KICP/UChicago

13. Planck SNAP SNe, Planck CMB, priors based on current data Measure distances: January 22, 200913Michael Mortonson KICP/UChicago

14. Planck SNAP SNe, Planck CMB, priors based on current data Measure distances: Priors BAO: D V (z=0.35) [SDSS] H 0 [HST Key Project] Early DE fraction [WMAP] January 22, 200914Michael Mortonson KICP/UChicago

15. Choose class of DE models: + priors on w(z) January 22, 200915Michael Mortonson KICP/UChicago

16.  or w(z)? Principal components of w(z) at z < 1.7 Choose class of DE models: + priors on w(z) January 22, 200916Michael Mortonson KICP/UChicago

17. Dark Energy Principal Components Eigenfunctions of SN+CMB Fisher matrix Principal components of w(z) PCs ordered by eigenvalues of F = (variance) -1 from distance data, so higher variance PCs affect observables less January 22, 200917Michael Mortonson KICP/UChicago

18. Dark Energy Principal Components January 22, 200918Michael Mortonson KICP/UChicago N ~ 10-15 PCs for completeness

19. Dark Energy Principal Components January 22, 200919Michael Mortonson KICP/UChicago Use PC basis functions to span the model space within a class of DE models These are not physically-motivated models, but any particular w(z) can be represented by PCs Reconstruction of w(z) is not the goal (PCs are complete in observables, not w)

20. Large fraction of DE at early times (EDE)? w(z > 1.7) = w ∞ Choose class of DE models: + priors on w(z) January 22, 200920Michael Mortonson KICP/UChicago

21. Flat, or nonzero spatial curvature? KK Choose class of DE models: + priors on w(z) January 22, 200921Michael Mortonson KICP/UChicago

22. January 22, 2009Michael Mortonson KICP/UChicago 22 Find models that fit distances: MCMC w(z), w ∞,  K H(z)H(z) D(z)D(z)G(z)G(z)

23. January 22, 2009Michael Mortonson KICP/UChicago 23 Find models that fit distances: MCMC w(z), w ∞,  K H(z)H(z) D(z)D(z)G(z)G(z) SN+CMB data Predictions

24. Compute observables (e.g. growth) for models that fit distance data January 22, 200924Michael Mortonson KICP/UChicago

25. Compute observables (e.g. growth) for models that fit distance data January 22, 200925Michael Mortonson KICP/UChicago

26. Compute observables (e.g. growth) for models that fit distance data January 22, 200926Michael Mortonson KICP/UChicago

27. Compute observables (e.g. growth) for models that fit distance data January 22, 200927Michael Mortonson KICP/UChicago

28. January 22, 200928Michael Mortonson KICP/UChicago  CDM

29. Michael Mortonson KICP/UChicago  CDM pivot H 2 ≈  m H 0 2 (1+z) 3 H ≈ H 0 January 22, 200929

30. Quintessence: -1<w<1 (flat, no early DE) January 22, 200930Michael Mortonson KICP/UChicago

31. Quintessence + early DE or curvature flat, early dark energy w < –1 January 22, 200931Michael Mortonson KICP/UChicago

32. Quintessence + early DE or curvature closed, no early dark energy w < –1 January 22, 200932Michael Mortonson KICP/UChicago

33. Quintessence + early DE or curvature January 22, 200933Michael Mortonson KICP/UChicago

34. Quintessence + early DE and curvature January 22, 200934Michael Mortonson KICP/UChicago

35. Smooth DE: -5<w<3 (flat, no early DE) January 22, 200935Michael Mortonson KICP/UChicago

36. January 22, 200936Michael Mortonson KICP/UChicago Smooth DE with early DE and curvature

37. January 22, 200937Michael Mortonson KICP/UChicago Smooth DE with early DE and curvature

38. Smooth DE with early DE and curvature January 22, 200938Michael Mortonson KICP/UChicago

39. Growth Index  Growth rate: Growth index: January 22, 200939Michael Mortonson KICP/UChicago

40. January 22, 200940Michael Mortonson KICP/UChicago Growth Index   CDM Quintessence Smooth dark energy

41. Summary Combinations of distance and growth observables can falsify classes of dark energy models With SNAP + Planck data,  CDM predictions for growth and expansion histories are very strong More general w(z) have strong distance-growth relations for flat geometry and small early DE fraction Allowing freedom in curvature and early DE, quintessence makes one-sided predictions, and more general w(z) can be tested by checking consistency of observations across multiple redshifts Mortonson, Hu, & Huterer (2009), PRD (in press) [arXiv:0810.1744] January 22, 200941Michael Mortonson KICP/UChicago