1. Impact of Early Dark Energy on non-linear structure formation Margherita Grossi MPA, Garching Volker Springel Advisor : Volker Springel 3rd Biennial Leopoldina Conference on Dark Energy LMU Munich, 10 October 2008

2. Early dark energy models Parametrization in terms of three parameters (Wetterich 2004) :  Flat universe :  Fitting formula :  Effective contribution during structure formation : (see Bartelmann’s Talk)

3. Current predictions for EDE Bartelmann, Doran, Wetterich (2006) Bartelmann, Doran, Wetterich (2006)   Geometry of the universe: distance, time reduced redshift z Cosmic time relative to LCDM

4. Current predictions for EDE Bartelmann, Doran, Wetterich (2006) Bartelmann, Doran, Wetterich (2006)   Geometry of the universe: distance, time reduced   Spherical collapse model: virial overdensity moderately changed, linear overdensity significantly reduced The ‘Top Hat Model’ : uniform, spherical perturbation The ‘Top Hat Model’ : uniform, spherical perturbation  i oOverdensity within virialized halos oOverdensity linearly extrapolated to collapse density collapse density collapse redshift z c

5. Current predictions for EDE Bartelmann, Doran, Wetterich (2006) Bartelmann, Doran, Wetterich (2006)   Geometry of the universe: distance, time reduced   Mass function: increase in the abundance of dark matter halos at high-z   Spherical collapse model: virial overdensity moderately changed, linear overdensity significantly reduced dn/dM (M, z) At any given redshift, we can compute the probability of living in a place with (PS)

6. Current predictions for EDE Bartelmann, Doran, Wetterich (2006) Bartelmann, Doran, Wetterich (2006)   Geometry of the universe: distance, time reduced   Mass function: increase in the abundance of dark matter halos at high-z   Halo properties: concentration increased   Spherical collapse model: virial overdensity moderately changed, linear overdensity significantly reduced Concentration parameter : Halos density profile have roughly self similar form (NFW)

7. Current predictions for EDE Bartelmann, Doran, Wetterich (2006) Bartelmann, Doran, Wetterich (2006) Simulations are necessary to interpret observational results and compare them with theoretical models   Geometry of the universe: distance, time reduced   Mass function: increase in the abundance of dark matter halos at high-z   Halo properties: concentration increased   Spherical collapse model: virial overdensity moderately changed, linear overdensity significantly reduced

8. N-Body Simulations ΛCDM DECDM EDE1 EDE2 Models : 512 3 particles, m p  5 *10 9 solar masses L=100 3 (Mpc/h) 3, softening length of 4.2 kpc/h Resolution requirements: N-GenIC (IC) + P-Gadget3 (simulation) ( C + MPI) at RZG (Garching) 128 processors on OPA at RZG (Garching) Computation requests : Codes:

9. From the Friedmann equations: Expansion function Growth factor Structures need to grow earlier in EDE models in order to reach the same level today

10. The mass function of DM haloes FoF b=0.2 b=0.2

11. The mass function of DM haloes Constant initial density contrast z = 0.

12. The mass function of DM haloes z = 0.25

13. The mass function of DM haloes z = 0.5

14. z = 0.75 The mass function of DM haloes

15. z = 1. The mass function of DM haloes

16. z = 1.5

17. z = 2. The mass function of DM haloes

18. z = 3. The mass function of DM haloes Theoretical MFs ~ 5-15% errors (0<z<5)

19. Do we need a modified virial overdensity for EDE ? Introduction of the linear density contrast predicted by BDW for EDE models worsens the fit! % Spherical overdensity (SO) The virial mass is : Friends-of-friends (FOF) b=0.2

20. The concentration-mass relation Halo selections: >3000 particles Substructure mass fraction Substructure mass fraction Centre of mass displacement Centre of mass displacement Virial ratio Virial ratio EDE halos always more concentrated EDE halos always more concentrated Profile fitting Uniform radial range for density profile Uniform radial range for density profile More robust fit from maximum in the profile More robust fit from maximum in the profile Eke et al. (2001) works for EDE without modifications

21.  DM 2 [km/sec] 2 Substructures in CDM haloes Cumulative velocity dispersion function from sub-halos dynamics Robust quantity against richness threshold. Robust quantity against richness threshold. N(>  DM 2 ) [h -1 Mpc] 3

22. Conclusions  Higher cluster populations at high z for EDE models: linear growth behaviour and power spectrum analysis  Halo-formation time: trend in concentration for EDE halos  Possibility of putting cosmological constraints on equation of state parameter: cumulative velocity distribution function  Connection between mass and galaxy velocity dispersion: virial relation for massive dark matter halos  Constant density contrast (spherical collapse theory for EDE models): mass function Probing Dark Energy is one of the major challenge for the computational cosmology