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An Approach to Testing Dark Energy by Observations

An Approach to Testing Dark Energy by Observations. 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 : Chien-Wen Chen 陳建文 @ Phys, NTU Pisin Chen 陳丕燊 @ LeCosPA, NTU. 2009/11/20 @ CosPA 2009, Melbourne.

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An Approach to Testing Dark Energy by Observations

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  1. An Approach to Testing Dark Energy by Observations 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 : Chien-Wen Chen 陳建文@ Phys, NTU Pisin Chen 陳丕燊@ LeCosPA, NTU 2009/11/20 @ CosPA 2009, Melbourne

  2. An Approach to Testing Dark Energy by Observations 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 : Chien-Wen Chen 陳建文@ Phys, NTU Pisin Chen 陳丕燊@ LeCosPA, NTU 2009/11/20 @ CosPA 2009, Melbourne

  3. References • Je-An Gu, Chien-Wen Chen, and Pisin Chen, “A new approach to testing dark energy models by observations,” New Journal of Physics11 (2009) 073029 [arXiv:0803.4504]. • Chien-Wen Chen, Je-An Gu, and Pisin Chen, “Consistency test of dark energy models,” Modern Physics LettersA 24 (2009) 1649 [arXiv:0903.2423].

  4. Observations (which are driving Modern Cosmology) Dark Energy Accelerating Expansion Based on FLRW Cosmology (homogeneous & isotropic) Concordance:  = 0.73 , M = 0.27

  5. 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)

  6. 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 : : :

  7. An Approach to Testing Dark Energy Models via CharacteristicQ(z) Gu, C.-W. Chen and P. Chen, New J. Phys. [arXiv:0803.4504] C.-W. Chen, Gu and P. Chen, Mod. Phys. Lett. A [arXiv:0903.2423]

  8. Gu, CW Chen & P Chen arXiv:0803.4504 Characteristic Q(z) Along a similar line of thought, focusing on CDM:  Sahni, Shafieloo and Starobinsky, PRD [0807.3548]: Zunckel and Clarkson 2008, PRL101 [0807.4304]: wDE(z) = w0 + waz/(1+z) E.g., CDM For each model, introduce a characteristic Q(z) with the following features: DE(z): energy density • Q(z) is time-varying (i.e. dependent on z) in general. • Q(z) is constant within the model M(under consideration). • Q(z) plays the role of a key parameter within Model M. • Q(z) is a functional of the parametrized physical quantityP(z). • Q(z) can be reconstructed from data via the constraint on P(z). • dQ(z)/dzcan also be reconstructed from data. • The (in)compatibility of • the observational constraint of M dQ(z)/dz • and the theoretical prediction of dQ(z)/dz: “0” • tells the (in)consistency between data and Model M.

  9. Test the Consistency between Models and Data Qi [P(z),z] Model Characteristic Q M1 M2 M3 : Mi : : : in Gu, CW Chen and P Chen, 2008 Q1(z) Q2(z) Q3(z) : Qi(z) : : : Constraints on Parameters Data P(z) (parametrization)

  10. Test the Consistency between Models and Data Model Q1(z) Q2(z) Q3(z) : Qi(z) : : : M1 M2 M3 : Mi : : : M1(z) M2(z) M3(z) : Mi(z) : : : reconstruct : : in : : : : : : consistent inconsistent   Gu, CW Chen and P Chen, 2008 Mi  dQi (z)/dz Measure of Consistency M Constraints on Parameters Data P(z) (parametrization) observational constraint theoretical prediction:0

  11. Test the Consistency between Models and Data Model Chevallier&Polarski, 2001 M1 M2 M3 : Mi : : : Linder, 2003 reconstruct : : in : : : : : : consistent inconsistent   Gu, CW Chen and P Chen, 2008 Mi  dQi (z)/dz parameters: {m,w0,wa} Measure of Consistency M Q1(z) Q2(z) Q3(z) : Qi(z) : : : M1(z) M2(z) M3(z) : Mi(z) : : : SN Ia (Constitution) CMB (WMAP 5) BAO (SDSS,2dFGRS) Constraints on Parameters Data P(z) (parametrization) observational constraint theoretical prediction:0

  12. Test the Consistency between Models and Data Chevallier&Polarski, 2001 Linder, 2003 in consistent inconsistent   CW Chen, Gu and P Chen, 2009 Mi  dQi (z)/dz parameters: {m,w0,wa} Measure of Consistency M Model  Qexp Qpower Qinv-exp Chaplygin : : : Q1(z) Q2(z) Q3(z) : Qi(z) : : : M1(z) M2(z) M3(z) M4(z) M5(z) : : : SN Ia (Constitution) CMB (WMAP 5) BAO (SDSS,2dFGRS) reconstruct Constraints on Parameters Data P(z) : : : : : : (parametrization) observational constraint theoretical prediction:0

  13. Characteristics Q(z) of 5 Models Gu, CW Chen and P Chen, 2008 CW Chen, Gu and P Chen, 2009  CDM :  = constant  Quintessence, exponential: V() = V1exp[/M1]  Quintessence, power-law: V() = m4nn  Quintessence, inverse-exponential: V() = V2exp[M2/]  generalized Chaplygin gas: pDE(z) = A/DE(z) , A>0,  1

  14. Testing DE Models:Results

  15. Test the Consistency between Models and Data Linder, PRL, 2003 in consistent inconsistent   Gu, CW Chen and P Chen, 2008 CW Chen, Gu and P Chen, 2009 Mi  dQi (z)/dz parameters: {m,w0,wa} Measure of Consistency M Model  Qexp Qpower Qinv-exp Chaplygin : : : Q1(z) Q2(z) Q3(z) : Qi(z) : : : M1(z) M2(z) M3(z) M4(z) M5(z) : : : SN Ia (Constitution) CMB (WMAP 5) BAO (SDSS,2dFGRS) reconstruct Constraints on Parameters Data P(z) : : : : : : (parametrization) observational constraint theoretical prediction:0

  16. Test the Consistency between Models and Data Chevallier&Polarski, 2001 Linder, 2003 in consistent inconsistent   CW Chen, Gu and P Chen, 2009 Mi  dQi (z)/dz parameters: {m,w0,wa} Measure of Consistency M Model  Qexp Qpower Qinv-exp Chaplygin : : : Q1(z) Q2(z) Q3(z) : Qi(z) : : : M1(z) M2(z) M3(z) M4(z) M5(z) : : : SN Ia (Constitution) CMB (WMAP 5) BAO (SDSS,2dFGRS) reconstruct Constraints on Parameters Data P(z) : : : : : : (parametrization) observational constraint theoretical prediction:0

  17. CDM: measure of consistency M  dQ(z)/dz CW Chen, Gu and P Chen, 2009  CDM :  = constant 95.4% C.L. 68.3% C.L. consistent

  18. Quintessence: Exponential potential CW Chen, Gu and P Chen, 2009  Quintessence, exponential: V() = V1exp[/M1] 95.4% C.L. inconsistent 68.3% C.L.

  19. Quintessence: Power-law potential CW Chen, Gu and P Chen, 2009  Quintessence, power-law: V() = m4nn 68.3% C.L. consistent 95.4% C.L.

  20. Quintessence: Inverse-exponential potential CW Chen, Gu and P Chen, 2009  Quintessence, inverse-exponential: V() = V2exp[M2/] 95.4% C.L. consistent 68.3% C.L.

  21. Generalized Chaplygin Gas CW Chen, Gu and P Chen, 2009  generalized Chaplygin gas: pDE(z) = A/DE(z) , A>0,  1 95.4% C.L. 68.3% C.L. consistent

  22. Measure of Consistency for 5 DE Models CW Chen, Gu and P Chen, 2009

  23. Discriminative Power between Dark Energy Models

  24. Distinguish … M1 M2 M3 M4 M5 M6 M7 M8 Gu, CW Chen and P Chen, 2009  Quintessence, exponential: V() = V1exp[/M1]  Quintessence, power-law: V() = m4nn from (8 models)

  25. Procedures Fiducial Models Mi  dQi (z)/dz M1,…,M8 Measure of Consistency M Chevallier&Polarski, 2001 simulation Linder, 2003 in indistinguishable distinguishable observational constraint theoretical prediction:0   Gu, CW Chen and P Chen, 2009 parameters: {m,w0,wa} Model  Qexp Qpower M1(z) M2(z) M3(z) 2023 SNe (SNAP quality) CMB (WMAP5 quality) BAO (current quality) reconstruct Constraints on Parameters Data P(z) (parametrization)

  26. Distinguish from 8 models (M1–M8) O O O O X X O O more slowly evolving wDE(z) faster evolving wDE(z) O O O O X X O O Exp. potential Power-law … Gu, CW Chen and P Chen, 2009 exp. power- law exp. power- law

  27. Summary

  28. Summary and Discussions • We proposed an approach to the testing of dark energymodels by observational results via a characteristic Q(z) for each model. • We performed the consistency test of 5 dark energy models: CDM, generalized Chaplygin gas, and 3 quintessence with exponential, power-law, and inverse-exponential potentials. • The exponential potential is ruled out at 95.4% C.L. while the other 4models are consistent with current data. • With the future observations and via our approach: – Exponential potential: distinguishable from the 8 models (under consideration). – Power-law potential: distinguishable from the models with faster evolving w(z)[M3,M4,M7,M8]; but NOT from those with more slowly evolving w(z)[M1,M2,M5,M6].

  29. Summary and Discussions (cont.) • The consistency test is to examine whether the condition necessary for a model is excluded by observations. • Our approach to the consistency test is simple and efficient because: For all models, Q(z) and dQ/dz are reconstructed from data via the observational constraints on a single parameter space that by choice can be easily accessed.  By our design of Q(z), the consistency test can be performed without the knowledge of the other parameters of the models. • Generally speaking, an approach invoking parametrization may be accompanied by a bias against certain models. This issue requires further investigation.

  30. Summary and Discussions (cont.) • This approach can be applied to other DE models and other explanations of the cosmic acceleration. • The general principle of this approach may be applied to other cosmological models and even those in other fields beyond the scope of cosmology.

  31. Thank you.

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