1. N-body Simulations and Gravitational Lensing with Dark Energy Beyond Einstein Meeting, May 13, 2004

2. Outline Why Structure Formation and Dark Energy? Studying Dark Energy with Structure Formation: achievements and plans Dark Energy Models Considered: Minimally Coupled (Quintessence), Degenerate Today, Different in the Past Cluster Concentrations (Dolag etal. 2003, A&A 416, 853) Lensing (Arc Statistics, Meneghetti etal. 2004, A&A submitted, astro-ph/0405070) Next Steps

3. Why studying Dark Energy with Structure Formation? Epochs of structure formation and cosmic acceleration overlap

4. Why studying Dark Energy with Structure Formation? Epochs of structure formation and cosmic acceleration overlap Looking for signatures of a possible link between the two processes

5. Why studying Dark Energy with Structure Formation? Epochs of structure formation and cosmic acceleration overlap Looking for signatures of a possible link between the two processes Essential complement to the CMB data to compare the early, well behaving universe and the present weird cosmology Kuhlen etal. 2004, Dolag etal. 2004, Linder & Jenkins 2003, Klypin et al. 2003, …

6. The Corrupted Universe z=1000, Flat, sCDM z=0, Accelerating, Large Scale Power Lack

7. Studying Dark Energy with Structure Formation: Achievements and Plans Background and Linear Perturbations Input to The N-body Machinery (gadget) Cluster Dependence on The Behavior of the Dark Energy Equation of State Imprint on Lensing Arc Statistics Large Boxes Merging Weak Lensing CMB Distortion Time Variation of G Dark Energy and Gravity Two Component Clustering Dolag etal. A&A 416, 853, 2004, Meneghetti etal. A&A submitted, astro-ph/0405070, Bartelmann etal. A&A 409, 449, 2003, A&A 400, 19, 2003, A&A 396, 21, 2002

8. DE, lin. Pert., Carlo Baccigalupi DE theory & models, Francesca Perrotta Trieste

9. DE, lin. Pert., Carlo Baccigalupi DE theory & models, Francesca Perrotta Lensing, Str.Form., Matthias Bartelmann Lensing, Massimo Meneghetti Heidelberg

10. DE, lin. Pert., Carlo Baccigalupi DE theory & models, Francesca Perrotta Lensing, Str.Form., Matthias Bartelmann Lensing, Massimo Meneghetti Str. Form., Lauro Moscardini N-body, Klaus Dolag Str. Form., Giuseppe TormenBologna Padua

11. DE, lin. Pert., Carlo Baccigalupi DE theory & models, Francesca Perrotta Lensing, Str.Form., Matthias Bartelmann Lensing, Massimo Meneghetti Str. Form., Lauro Moscardini N-body, Klaus Dolag Str. Form., Giuseppe Tormen

12. Dark Energy Models Cosmological Constant (LCDM), Constant w=-0.6 Effective Dark Energy (DECDM), RP and SUGRA Quintessence, Open Cold Dark Matter (OCDM) Criticalities: Equation of state behavior, Linear growth factor

13. Clusters Parent simulation:  CDM, 512 3 particles in 479 h -1 kpc, 17 clusters identified at z=0 with radius between 5 and 10 h -1 Mpc, mass exceeding 3 £ 10 14 M o. Clusters re-sampled with 10 6 particles background evolution and initial conditions according to the underlying dark energy scenario Mass resolution: 10 9 h -1 M o

14. Cluster Concentration Radial profile binning and concentration found from a NFW fit Comparison of the numerically determined concentrations with semi-analytical expectations

15. Cluster Concentration

16. Simulating Arcs 52 equidistant time snapshots between z=0 and 1 Surface density map from the central cluster region (3 h -1 Mpc comoving) 2048 £ 2048 light tracing grid in the central quarter of the lens plane Deflection angle computed summing all contributions from the surface density map Background galaxies at z=1 Lensed images built out of the light rays lying within single sources

17. Simulating Arcs

18. Caustics, Critical Curves and Cross Sections

19. Optical Depth

20. Studying Dark Energy with Structure Formation: Achievements and Plans Background and Linear Perturbations Input to The N-body Machinery (gadget) Cluster Dependence on The Behavior of the Dark Energy Equation of State Imprint on Lensing Arc Statistics Large Boxes Merging Weak Lensing CMB Distortion Time Variation of G Dark Energy and Gravity Two Component Clustering

21. Studying Dark Energy with Structure Formation: Achievements and Plans Background and Linear Perturbations Input to The N-body Machinery (gadget) Cluster Dependence on The Behavior of the Dark Energy Equation of State Imprint on Lensing Arc Statistics Large Boxes Merging Weak Lensing CMB Distortion Time Variation of G Dark Energy and Gravity Two Component Clustering

22. CMB bispectrum B l m l` m` l`` m`` =a lm a l`m` a l``m`` a lm = s  (  )Y lm (  )d  B l l`l`` =  m m` m`` ( m l m` l` m`` l`` ) a lm a l`m` a l``m`` l l` l``  (  ) ´  T(  )/T

23. CMB bispectrum & Structure Formation =0 =0  0  0

24. CMB bispectrum line of sight chronology l -1 horizon crossing,  decaying linearly, dQ/dz>0 z !1 :super-horizon scales in a flat CDM universe, dP  /d  =0, dQ/dz ! 0 z r Non-linearity,  grows, dQ/dz<0 z ! 0, vanishes, dQ/dz ! 0 onset of acceleration, change in cosmic equation of state,  decaying linearly, dQ/dz>0

25. CMB bispectrum & Dark Energy Giovi, Baccigalupi, Perrotta PRD 2003, astro-ph/0308118

26. Studying Dark Energy with Structure Formation: Achievements and Plans Background and Linear Perturbations Input to The N-body Machinery (gadget) Cluster Dependence on The Behavior of the Dark Energy Equation of State Imprint on Lensing Arc Statistics Large Boxes Merging Weak Lensing CMB Distortion Time Variation of G Dark Energy and Gravity Two Component Clustering