1 / 33

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.

mai
Download Presentation

An Approach to Testing Dark Energy by Observations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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.

More Related