1. Dark Energy Phenomenology  a new parametrization  Je-An Gu 顧哲安 臺灣大學梁次震宇宙學與粒子天文物理學研究中心 Leung Center for Cosmology and Particle Astrophysics (LeCosPA), NTU Collaborators : Yu-Hsun Lo 羅鈺勳 @ NTHU Qi-Shu Yan 晏啟樹 @ NTHU 2009/03/19 @ 清華大學

2. CONTENTS  Introduction (basics, SN, SNAP)  Supernova Data Analysis — Parametrization  Summary  A New (model-indep) Parametrization by Gu, Lo and Yan  Test and Results

3. Introduction (Basic Knowledge, SN, SNAP)

4. Accelerating Expansion (homogeneous & isotropic) Based on FLRW Cosmology Concordance:   = 0.73,  M = 0.27

5. from Supernova Cosmology Project: http://www-supernova.lbl.gov/ redshift z absolute magnitude M luminosity distance dLdL F: flux (energy/area  time) L: luminosity (energy/time) SN Ia Data: d L (z) [ i.e, d L,i (z i ) ] distance modulus

6. (can hardly distinguish different models) SCP (Perlmutter et. al.) Distance Modulus 1998

7. 2006 Riess et al., ApJ 659, 98 (2007) [astro-ph/0611572]

8. Supernova / Acceleration Probe (SNAP) z0~0.20.2~1.21.2~1.41.4~1.7 # of SN5018005015 observe ~2000 SNe in 2 years statistical uncertainty  mag = 0.15 mag  7% uncertainty in d L  sys = 0.02 mag at z =1.5  z = 0.002 mag (negligible) (2366 in our analysis)

10. (Non-FLRW) Models : Dark Geometry vs. Dark Energy Einstein Equations Geometry Matter/Energy Dark Geometry ↑ Dark Matter / Energy ↑ G μν ＝ 8πG N T μν Modification of Gravity Averaging Einstein Equations Extra Dimensions for an inhomogeneous universe  (from vacuum energy) Quintessence/Phantom (based on FLRW)

11. Supernova Data Analysis — Parametrization / Fitting Formula —

12. Observations Data Data Analysis Models Theories mapping out the evolution history (e.g. SNe Ia, BAO) M1M2M3:::M1M2M3::: (e.g.  2 fitting) Data vs. Models Quintessence a dynamical scalar field M 1 (tracker quint., exponential) M 2 (tracker quint., power-law)

13. M 1 (O) M 2 (O) M 3 (X) M 4 (X) M 5 (O) M 6 (O) : Observations Data Data Analysis Models Theories mapping out the evolution history (e.g. SNe Ia, BAO) (e.g.  2 fitting) Data :::::: Dark Energy info NOT clear. Reality : Many models survive Shortages: – Tedious. – Distinguish between models ?? – Reality: many models survive.

14. Reality : Many models survive  Instead of comparing models and data (thereby ruling out models), Extract information about dark energy directly from data by invoking model independent parametrizations.

15. Data Parametrization Fitting Formula Dark Energy Information Model-independent Analysis Constraints on Parameters analyzed by invoking in Example  Linder, PRL, 2003 w : equation of state, an important quantity characterizing the nature of an energy content. It corresponds to how fast the energy density changes along with the expansion. 0 1 w0w0 wawa Riess et al. ApJ, 2007 -1.5 -0.5 w DE (z) z [e.g. w DE (z),  DE (z)]  w1w1 w0w0 Wang & Mukherjee ApJ 650, 2006

16. Answering questions about Dark Energy  Instead of comparing models and data (thereby ruling out models), Extract information about dark energy directly from data by invoking model independent parametrizations, thereby answering essential questions about dark energy. Issue ? How to choose the parametrization ? “standard parametrization” ?

17. A New Parametrization (proposed by Gu, Lo, and Yan)

18. New Parametrization by Gu, Lo & Yan SN Ia Data: d L (z) [ i.e, d L,i (z i ) (and errors) ] Assume flat universe. ( H : Hubble expansion rate ) “m”: NR matter – DM & baryons “r”: radiation “x”: dark energy

19. New Parametrization by Gu, Lo & Yan The density fraction  (z) is the very quantity to parametrize. [ instead of  x (z) or w x (z) ]

20. New Parametrization by Gu, Lo & Yan General Features

21. New Parametrization by Gu, Lo & Yan The lowest-order nontrivial parametrization:

22. New Parametrization by Gu, Lo & Yan w 0 : present value of DE EoS A  “amplitude” of the correction  x (z) i.e., In our analysis, we set  2 parameters: w 0, A

23. New Parametrization by Gu, Lo & Yan For the present epoch, ignore  r (z). Linder

24. Test and Results

25. Background cosmology [pick a DE Model with w DE th (z)]  generate Data w.r.t. present or future observations (Monte Carlo simulation) Procedures of Testing Parametrizations employ a Fit to the d L (z) or w(z) reconstruct w DE exp’t (z)  compare w DE exp’t and w DE th

26. 192 SNe Ia : real data and simulated data A w0w0 Gu, Lo & Yan real 11 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue overlap  consistency no overlap  distinguishable from 192 SNe Ia

27. 192 SNe Ia : real data and simulated data A w0w0 Gu, Lo & Yan real 22 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue from 192 SNe Ia

28. 192 SNe Ia : real data and simulated data A w0w0 Gu, Lo & Yan real 33 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue from 192 SNe Ia

29. 192 SNe Ia : real data and simulated data wawa w0w0 11 Linder real Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue from 192 SNe Ia

30. 192 SNe Ia : real data and simulated data wawa w0w0 Linder real 22 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue from 192 SNe Ia

31. 192 SNe Ia : real data and simulated data wawa w0w0 Linder real 33 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue from 192 SNe Ia

32. A w0w0 wawa w0w0 11 Gu, Lo & YanLinder real 11 From 192 SNe Ia Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

33. A w0w0 wawa w0w0 Gu, Lo & YanLinder real 22 22 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue From 192 SNe Ia

34. A w0w0 wawa w0w0 Gu, Lo & YanLinder real 33 33 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue From 192 SNe Ia

35. real data 11 Info1 : Blue vs. White(s) overlap  consistency simulated data simulated real Gu, Lo & Yan from 192 SNe Ia

36. Linder 11 from 192 SNe Ia real data Info1 : Blue vs. White(s) overlap  consistency simulated data simulated real

37. A w0w0 11 from 2366 simulated SNe Ia from 192 real SNe Ia 2366 simulated SNe vs. 192 real SNe Gu, Lo & Yan

38. 2366 simulated SNe vs. 192 real SNe w0w0 wawa Linder from 192 real SNe Ia from 2366 simulated SNe Ia 11

39. A w0w0 2366 Simulated SN Ia Data 11 Gu, Lo & Yan Info from comparing nearby contours from 2366 simulated SNe Ia

40. 2366 Simulated SN Ia Data A w0w0 22 Gu, Lo & Yan Info from comparing nearby contours from 2366 simulated SNe Ia

41. 2366 Simulated SN Ia Data A w0w0 Gu, Lo & Yan 33 Info from comparing nearby contours from 2366 simulated SNe Ia

42. 2366 Simulated SN Ia Data A w0w0 Gu, Lo & Yan 44 Info from comparing nearby contours from 2366 simulated SNe Ia

43. 2366 Simulated SN Ia Data A w0w0 Gu, Lo & Yan 55 Info from comparing nearby contours from 2366 simulated SNe Ia

44. 2366 Simulated SN Ia Data Linder wawa w0w0 11 Info from comparing nearby contours from 2366 simulated SNe Ia

45. 2366 Simulated SN Ia Data Linder wawa w0w0 22 Info from comparing nearby contours from 2366 simulated SNe Ia

46. 2366 Simulated SN Ia Data Linder wawa w0w0 33 Info from comparing nearby contours from 2366 simulated SNe Ia

47. 2366 Simulated SN Ia Data Linder wawa w0w0 44 Info from comparing nearby contours from 2366 simulated SNe Ia

48. 2366 Simulated SN Ia Data Linder wawa w0w0 55 Info from comparing nearby contours from 2366 simulated SNe Ia

49. Summary

50.  A parametrization (by utilizing Fourier series) is proposed.  This parametrization is particularly reasonable and controllable.  The current SN Ia data, including 192 SNe, can distinguish between constant-w x models with  w x = 0.2 at 1  confidence level. Summary Via this parametrization:  The future SN Ia data, if including 2366 SNe, can distinguish between constant-w x models with  w x = 0.05 at 3  confidence level, and the models with  w x = 0.1 at 5  confidence level  It is systematical to include more terms and more parameters.

51. Thank you.

53. Supernova (SN) : mapping out the evolution herstory Type Ia Supernova (SN Ia) : (standard candle) – thermonulear explosion of carbon-oxide white dwarfs –  Correlation between the peak luminosity and the decline rate  absolute magnitude M  luminosity distance d L (distance precision:  mag = 0.15 mag   d L /d L ~ 7%)  Spectral information  redshift z SN Ia Data: d L (z) [ i.e, d L,i (z i ) ] [ ~ x(t) ~ position (time) ] F: flux (energy/area  time) L: luminosity (energy/time) Distance Modulus  (z) (z) history

54. Fig.4 in astro-ph/0402512 [Riess et al., ApJ 607 (2004) 665] Gold Sample (data set) [MLCS2k2 SN Ia Hubble diagram] - Diamonds: ground based discoveries - Filled symbols: HST-discovered SNe Ia - Dashed line: best fit for a flat cosmology:  M =0.29   = 0.71 2004

55. 2006 Riess et al., ApJ 659, 98 (2007) [astro-ph/0611572]

56. M 1 (X) M 2 (X) M 3 (O) M 4 (X) M 5 (X) M 6 (X) : Observations Data Data Analysis Models Theories mapping out the evolution history (e.g. SNe Ia, BAO) (e.g.  2 fitting) OK, if few models survive. Data :::::: Tedious work, worthwhile if few models survive, and accordingly clear Dark Energy info obtained.