1. Structure formation in dark energy cosmology La Magia, April 2005

2. outline Quintessence scheme Cosmological expansion rate Cosmological perturbations Cosmic microwave background Gravitational lensing Non-linear structure formation Quintessence, dark matter and gravity Conclusion

3. Quintessence scheme

4. The Quintessence: a minimal generalization of  setting up a phenomenology of the impact of vacuum energy in cosmology Predicting observable signatures if the acceleration is not due to a constant into the Einstein equations

5. Quintessence tracking solutions Classical trajectories for the Quintessence field converging to the present energy density from a large set of initial conditions The field may (Wetterich 1988) or may not (Ratra- Peebles 1998) scale as the dominant component Dark energy abundance today still severely tuned

6. Cosmological expansion

7. Cosmological expansion rate For a fixed value today, H -1 is larger if w > -1 in the past The comoving distance at a given redshift gets contracted The redshift dependence of w is washed out by two redshift integrals

8. Cosmological expansion rate For a fixed value today, H -1 is larger if w > -1 in the past The comoving distance at a given redshift gets contracted The redshift dependence of w is washed out by two redshift integrals

9. Cosmological perturbations

10. Effects on cosmological perturbations Modified geometry affects the growth of linear perturbations The dark energy possesses fluctuations which are dragged on large scales by the background evolution (Brax & Martin 2000)

11. Effects on cosmological perturbations Modified geometry affects the growth of linear perturbations The dark energy possesses fluctuations which are dragged on large scales by the background evolution (Brax & Martin 2000)

12. Effects from modified geometry For w greater than -1, the cosmological friction gets enhanced for a fixed H 0 This affects the linear density perturbations growth and the dynamics of the gravitational potentials on all scales in linear regime

13. Effects from quintessence perturbations A minimally coupled quintessence field is light, m  » (d 2 V/d  2 ) 1/2 » H -1 Fluctuations live on horizon and super-horizon scales Excess power visible on small wavenumbers in the density power spectrum (Ma et al. 1999)

14. Cosmic microwave background

15. Projection

16. Integrated sachs-wolfe

17. Effects at decoupling If the dark energy tracks the dominant component at a few percent level, the physics at decoupling is affected at a measurable level (early quintessence, see Caldwell et al. 2005 and references therein) The equivalence epoch is shifted The dark energy sound speed enters into the acoustic oscillations

18. Constraining dark energy with primary CMB anisotropies Main effect from the shift of acoustic peaks due to the variation of distances The constraining power is limited by the projection degeneracy

19. Constraining dark energy with primary CMB anisotropies Assume flatness, fix H, gravitational waves in single field inflation Fit with B98, COBE, MAXIMA, DASI, get some preference for a dynamical dark energy (Baccigalupi et al. 2002) Mind degeneracies Is WMAP  tot =1.02 § 0.02 a similar indication? Probably not…

20. Gravitational lensing

21. Weak lensing in dark energy cosmology Probing intermediate redshifts only Collecting effects from modified geometry and perturbations Details in Acquaviva et al. 2004

22. Breaking the projection degeneracy Dark energy records in lensed CMB, Acquaviva and Baccigalupi, 2005, in preparation

23. Breaking the projection degeneracy Dark energy records in lensed CMB, Acquaviva and Baccigalupi, 2005, in preparation

24. CMB three-point correlation function from lensing

25. CMB bispectrum l1l1 l2l2 l3l3

27. Lensing chronology Giovi et al. 2003, PhD thesis

28. CMB three-point statistics and dark energy Giovi et al. 2003, 2005, PhD thesis

29. CMB three-point statistics and dark energy Giovi et al. 2003, 2005, PhD thesis

30. Non-linear structure formation

31. Galaxy clusters

32. Matthias Bartelmann Massimo Meneghetti Klaus Dolag Carlo Baccigalupi Viviana Acquaviva Francesca Perrotta Lauro Moscardini

33. Matthias Bartelmann Massimo Meneghetti Klaus Dolag Carlo Baccigalupi Viviana Acquaviva Francesca Perrotta Lauro Moscardini Heidelberg

34. Matthias Bartelmann Massimo Meneghetti Klaus Dolag Carlo Baccigalupi Viviana Acquaviva Francesca Perrotta Lauro Moscardini MPA, Garching

35. Matthias Bartelmann Massimo Meneghetti Klaus Dolag Carlo Baccigalupi Viviana Acquaviva Francesca Perrotta Lauro Moscardini SISSA, Trieste

36. Matthias Bartelmann Massimo Meneghetti Klaus Dolag Carlo Baccigalupi Viviana Acquaviva Francesca Perrotta Lauro Moscardini Bologna

37. Dark energy records in galaxy cluster concentrations Klypin et al. 2003, Maccio et al. 2003, Dolag et al. 2004, …

38. Strong lensing arc statistics Numerical ray tracing machines integrate null geodesics across structures out of N- body codes Internal parameters of structures may be constrained through the lensing pattern Maccio 2004, Meneghetti et al. 2004

39. Strong lensing arc statistics A w > -1 dynamics in the dark energy makes the linear growth rate of perturbations behaving in the middle between an open and a  CDM universe The number of giant arcs is a cosmological probe, which favours an open universe (Bartelmann 1999) Meneghetti et al. 2004

40. Quintessence, dark matter and gravity

41. Coupled quintessence Coupling with baryons severely constrained by standard model physics Dark matter coupling realized with exchange in the energy density (Amendola 2000), variable masses for dark matter particles (Matarrese et al. 2003)

42. Extended quintessence Relating gravity and dark energy through an explicit coupling with the Ricci scalar Severely constrained on solar system scales Cosmological bounds improving with incoming data

43. Why weird cosmologies for the dark energy? Is it a new component or the signature of a modification in known physics? Coincidence unsolved The couplings with dark matter or gravity may induce new attractor mechanism driving the dark energy density to the present abundance from a large set of initial conditions (Bartolo and Pietroni 2000, Tocchini-Valentini and Amendola 2000, Matarrese et al. 2004)

44. Weird dark energy dynamics

47. Saving the Quintessence from fine-tuning…again Early universe attractors even for a cosmological constant behavior today (Matarrese et al. 2004) Examples: attraction to general relativity (Bartolo and Pietroni 1999), the R- boost (Baccigalupi et al. 2000, Pettorino et al. 2005) Consequences for the dark matter relic abundance (Catena et al. 2005)

48. Perturbation behavior in weird cosmologies Affecting geometry and perturbation growth rate The mutual interaction between dark energy and other components may drastically change the behavior of dark energy evolution and perturbations Spacetime variation of the gravitational constant, variable dark matter masses, scalar fields in galaxies, … Perrotta and Baccigalupi 2002, Wetterich 2002, Maccio et al. 2003, Perrotta et al. 2004, Amendola 2004, …

49. Gravitational dragging Power injection on the dark energy density from other components Dark energy density fluctuations may be dragged to non-linearity by structure formation itself (Perrotta and Baccigalupi 2002) Non-linear structure formation in these scenarios largely unknown T[  ]  ; =Q ,  T[  ]  ; =  Q 

50. Conclusion: minimally coupled Quintessence Linear perturbation behavior rather well understood Non-linear perturbation behavior still poorly known (only clusters, nothing on larger scales, mergers, …)

51. Conclusion: non-minimally coupled Quintessence Linear perturbation behavior still unclear (spacetime variations of constants, …) Possibility of gravitational dragging, dark energy density perturbations still present on sub-horizon scales Dark energy in dark haloes, major modification to N-body codes

52. Conclusion Constraints from observables including the present are polluted by the present, cosmological constant like behavior Need to isolate observables which cut out the present in order to study the onset of cosmic acceleration The promise of lensing