1. Dark energy fluctuations and structure formation Rogério Rosenfeld Instituto de Física Teórica/UNESP I Workshop "Challenges of New Physics in Space" Campos do Jordão, Brazil 26/04/2009

2. Standard Model of Cosmology + homogeneity and isotropy FLRW model

3. Summary of observations Concordance model Tegmark 07 What´s going on? Cosmological constant Dynamical dark energy Modified gravity Inhomogeneities (Hubble bubble)

4. Standard Model of Cosmology Evolution of small perturbations: It is not possible to fully describe the non-linear regime in RG: large numerical simulations are necessary (Millenium, MareNostrum, etc…)

5. Semi-analytical methods to study structure formation (dark matter haloes) in the non-linear regime: Spherical collapse model (Gunn&Gott 1972) Spherical collapse model (Gunn&Gott 1972) Press-Schechter formalism (Press&Schechter 1974) Press-Schechter formalism (Press&Schechter 1974)

6. Homogeneous Dark Energy Let’s first consider  amartine  iberato and R. Rosenfe d, JCAP 2006

7. Spherical collapse model Consider a spherical region of radius r(t) with density  c (t) constant in space (“top-hat” profile) immersed in a homogeneous (FLRW) universe with density  (t) This region first expands with an expansion rate a bit smaller than the Hubble expansion. The density contrast increases and eventually this region detaches from the expansion of the universe and starts to contract (turn around).

8. Spherical collapse model

12. Modelo de colapso esférico

13. Growth of perturbations  in the spherical collapse model only Homogeneous dark energy affects only the expansion rate!

14. Linear growth of perturbation  in the spherical collapse model linearized equation (coincides with GR) dark matter dominated universe dark energy dominated universe Dark energy suppresses structure formation (Weinberg’s anthropic argument)

16. Parametrization of dark energy equation of state Completely characterizes homogeneous dark energy

17. Linear growth of dark matter perturbations in the presence of homogeneous dark energy  CDM dark matter only larger perturbations in DE models

18. Non-linear growth of dark matter perturbations in the presence of dark energy The overdense sphere shrinks and eventually collapes (perturbation diverges!) (we are not considering dissipative effects) Exemple  CDM with initial conditions chosen such as the perturbation diverges today. non-linear evolution linear evolution Important quantity  c (z) is defined as the linearly extrapolated perturbation such that the non-linear perturbation diverges at z.

19.  c (z col ) depends on the cosmological model. Einstein-de Sitter:

20. Press-Schechter formalism Estimate the number density of dark matter haloes with mass M at a redshift z. P&S hypothesis: fluctuations of linear density contrast  are gaussian. Structure form in regions where  c. Critical density is computed in the spherical approx. P&S mass function can be derived rigorously using excursion set theory This simple approximation captures main features of the cluster mass function

21. Number of dark matter haloes

22. Inhomogeneous Dark Energy If DE is not a cosmological constant, its density can (and should) also vary! We now consider the consequences of the existence of dark energy fluctuations . R. Abramo, R. C. Batista, .  iberato e R. Rosenfe d, JCAP 0711:012 (2007)

23. Parametrization of dark energy background equation of state Characterizes completely the dark energy background In order to characterize the pressure perturbations of dark energy in the context of a simplified assumption it is convenient to introduce: “effective” speed of sound (Hu 98)

24. Top-hat spherical collapse model Equation of state inside perturbed region can be different from the background: Let’s first consider the case where there is no change in w:

25. Non-linear equations for the evolution of perturbations in the 2 fluids (dark matter and dark energy): We showed that the same equations also arise from the so-called pseudo-newtonian formalism for general. We also compared their linearized form with linearized GR recently: L.R. Abramo, R.C. Carlotto, L. Liberato and RR L.R. Abramo, R.C. Carlotto, L. Liberato and RR arXiv 0806.3461, Phys.Rev.D79:023516,2009 arXiv 0806.3461, Phys.Rev.D79:023516,2009 Top-hat spherical collapse model

26. Growth of perturbations Non-phantom case: dark energy clusters and suppresses structure formation

27. Phantom case: dark energy becomes underdense and enhances structure formation Growth of perturbations

28. non-linear regime non-linear regime phantom non-phantom

29. Non-linear regime Non-linear regime  c (z) including dark energy perturbations. Large modifications in number counts. phantom case: enhances structure formation non-phantom case: suppresses structure formation

30. Number of dark haloes

31. Dark energy mutation Equation of state inside perturbed region can be different from the background: . R. Abramo, R. C. Batista, .  iberato e R. Rosenfe d, Phys.Rev.D77:067301,2008 small effect for  DE <<1

32. Dark energy mutation  w can be large in the non-linear regime,  DE ~1 Effect was already seen in Mota & van de Bruck (2004) in the context of a scalar field w = -0.8 w = -0.99

33. Conclusions and Challenges Dark energy has a large impact on the structure formation in the universe (used in the 1987 Weinberg’s anthropic argument) Effects of homogeneous dark energy is completely characterized by its equation of state Effects of inhomogenous dark energy needs at least one extra function: Dark energy cumpling can alter its equation of state (mutation) It can be possible to distinguish among different dark energy models using future cluster number counts data. Errors in parameter estimations using Fisher matrix and characteristics of a given experiment (SPT+DES, LSST, EUCLID,...). See Abramo’s talk! It would be important to have a more precise study of a scalar field in GR with spherical symmetry (LTB) to confirm (or not) the approximations. see Ronaldo’s talk! N-body simulations including DE fluctuations?

34. Adiabatical perturbations For a two fluid combination, the perturbations are adiabatic when: In the case of dark matter and dark energy:

35. M 8 is the mass cointained in a sphere of radius R 8 = 8 h -1 Mpc. Parametrize Viana e Liddle (1996)