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Dark Energy Phenomenology  a new parametrization 

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. CONTENTS.

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Dark Energy Phenomenology  a new parametrization 

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  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 • A New (model-indep) Parametrization • by Gu, Lo and Yan • Test and Results • Summary

  3. Introduction (Basic Knowledge, SN, SNAP)

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

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

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

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

  8. Supernova / Acceleration Probe (SNAP) observe ~2000 SNe in 2 years statistical uncertainty mag = 0.15 mag  7% uncertainty in dL sys = 0.02 mag at z =1.5 z= 0.002 mag (negligible) (2366 in our analysis)

  9. Models: Dark Geometryvs. Dark Energy Geometry Matter/Energy ↑ ↑ Dark Geometry Dark Matter / Energy • (from vacuum energy) • Quintessence/Phantom (based on FLRW) Einstein Equations Gμν＝ 8πGNTμν • Modification of Gravity • Extra Dimensions • Averaging Einstein Equations for an inhomogeneous universe (Non-FLRW)

  10. Supernova Data Analysis — Parametrization / Fitting Formula —

  11. Data vs. Models Observations Data Models Theories Data Analysis mapping out the evolution history (e.g. SNe Ia , BAO) M1 M2 M3 : : : (e.g. 2 fitting) M1 (tracker quint., exponential) M2 (tracker quint., power-law) Quintessence a dynamical scalar field

  12. Reality : Many models survive Observations Data Models Theories Data Analysis mapping out the evolution history (e.g. SNe Ia , BAO) (e.g. 2 fitting) M1(O) M2(O) M3(X) M4(X) M5 (O) M6 (O) : : : Data : : : Shortages: – Tedious. – Distinguish between models ?? – Reality: many models survive. Dark Energy info NOT clear.

  13. Reality : Many models survive • Instead of comparing models and data (thereby ruling out models), Extract information about dark energydirectly from data by invoking model independentparametrizations.

  14. Model-independent Analysis wa wDE(z) 1 -0.5 z -1 0  Linder, PRL, 2003 Riess et al. ApJ, 2007 -1.5 -1 w0 w1  w0 Dark Energy Information Constraints on Parameters Data analyzed by invoking [e.g. wDE(z), DE(z)] Parametrization Fitting Formula in Example Wang & Mukherjee ApJ 650, 2006 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.

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

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

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

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

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

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

  21. New Parametrization In our analysis, we set by Gu, Lo & Yan i.e., w0 : present value of DE EoS A “amplitude” of the correction x(z)  2 parameters:w0, A

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

  23. Test and Results

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

  25. Gu, Lo & Yan 192 SNe Ia : real data and simulated data 1 overlap  consistency Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue no overlap  distinguishable real A from 192 SNe Ia w0

  26. Gu, Lo & Yan 192 SNe Ia : real data and simulated data 2 real A from 192 SNe Ia w0 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

  27. Gu, Lo & Yan 192 SNe Ia : real data and simulated data 3 real A from 192 SNe Ia w0 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

  28. Linder 192 SNe Ia : real data and simulated data 1 from 192 SNe Ia real wa w0 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

  29. Linder 192 SNe Ia : real data and simulated data 2 real from 192 SNe Ia wa w0 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

  30. Linder 192 SNe Ia : real data and simulated data real 3 from 192 SNe Ia wa w0 Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

  31. Gu, Lo & Yan Linder A wa w0 w0 From 192 SNe Ia 1 1 real real Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

  32. Gu, Lo & Yan Linder A wa w0 w0 From 192 SNe Ia 2 2 real real Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

  33. Gu, Lo & Yan Linder A wa w0 w0 From 192 SNe Ia 3 3 real real Info1 : Black vs. Blue(s) Info2 : Blue vs. Blue

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

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

  36. Gu, Lo & Yan 2366 simulated SNevs.192 real SNe 1 from 192 real SNe Ia from 2366 simulated SNe Ia A w0

  37. Linder 2366 simulated SNevs.192 real SNe 1 from 192 real SNe Ia from 2366 simulated SNe Ia wa w0

  38. Gu, Lo & Yan 2366 Simulated SN Ia Data 1 A from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  39. Gu, Lo & Yan 2366 Simulated SN Ia Data 2 A from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  40. Gu, Lo & Yan 2366 Simulated SN Ia Data 3 A from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  41. Gu, Lo & Yan 2366 Simulated SN Ia Data 4 A from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  42. Gu, Lo & Yan 2366 Simulated SN Ia Data 5 A from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  43. Linder 2366 Simulated SN Ia Data 1 wa from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  44. Linder 2366 Simulated SN Ia Data 2 wa from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  45. Linder 2366 Simulated SN Ia Data 3 wa from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  46. Linder 2366 Simulated SN Ia Data 4 wa from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  47. Linder 2366 Simulated SN Ia Data 5 wa from 2366 simulated SNe Ia w0 Info from comparing nearby contours

  48. Summary

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

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