Impact of Early Dark Energy on non-linear structure formation Margherita Grossi MPA, Garching Volker...

Impact of Early Dark Impact of Early Dark Energy on non-linear Energy on non-linear structure formation structure formation

Margherita GrossiMargherita GrossiMPA, Garching

Advisor : Volker SpringelVolker Springel

3rd Biennial Leopoldina Conference on Dark Energy

LMU Munich, 10 October 2008

Early darkEarly dark energy models energy models

Parametrization in terms of three Parametrization in terms of three parameters parameters (Wetterich 2004)(Wetterich 2004) : :

Flat universe :Flat universe :

Fitting formula :Fitting formula :

Effective contribution during structure Effective contribution during structure formation :formation :

(see Bartelmann’s Talk)(see Bartelmann’s Talk)

Current predictions for EDE Current predictions for EDE

Bartelmann, Doran, Wetterich (2006)Bartelmann, Doran, Wetterich (2006)

Geometry of the universe: distance, time reduced

)(

1

0 aaE

da

Ht

)(2 aEa

daDcom

redshift zredshift zCos

mic

tim

e re

lati

ve t

o L

CD

MC

osm

ic t

ime

rela

tive

to

LC

DM




Spherical collapse model: virial overdensity moderately changed, linear overdensity significantly reduced

The ‘Top Hat Model’ : The ‘Top Hat Model’ : uniform, spherical perturbationuniform, spherical perturbation i

oOverdensity within virialized halos Overdensity within virialized halos

oOverdensity linearly extrapolated Overdensity linearly extrapolated toto

collapse densitycollapse density

vir

inic zD )(

collapsecollapse redshift zredshift zcc

vir




Mass function: increase in the abundance of dark matter halos at high-z


dn/dM (M, z)

At any given redshift, we can compute the probability of living in a place with (PS)

2

2

2exp

2),(

ccPSf





Halo properties: concentration increased


Concentration parameter :Concentration parameter :

s

virvir R

Rc

Halos density profile have roughly self similar form Halos density profile have roughly self similar form

2)/1)(/(

)(

ss

c

crit RrRr

r

(NFW)(NFW)



Simulations are necessary to interpret Simulations are necessary to interpret observational results and compare them with observational results and compare them with

theoretical modelstheoretical models



Halo properties: concentration increased


N-Body SimulationsN-Body Simulations

• ΛCDM

• DECDM

• EDE1

• EDE2

Models :Models :

• 5123 particles, mp 5 *10 9 solar masses

• L=1003 (Mpc/h)3 , softening length of 4.2 kpc/h

Resolution requirements:Resolution requirements:

• N-GenIC (IC) + P-Gadget3 (simulation) ( C + MPI)

• 128 processors on OPA at at RZGRZG (Garching) (Garching) Computation requests :Computation requests :

Codes:Codes:

From the Friedmann equations:From the Friedmann equations:

Expansion function Expansion function

Growth factorGrowth factor

Structures need to grow Structures need to grow earlier in EDE models in earlier in EDE models in order to reach the same order to reach the same

level todaylevel today

The mass function of DM haloes The mass function of DM haloes

FoF FoF

b=0.2b=0.2


Constant initial Constant initial density contrastdensity contrast

z = 0.z = 0.


z = 0.25z = 0.25


z = 0.5z = 0.5

z = 0.75z = 0.75


z = 1.z = 1.



z = 1.5z = 1.5

z = 2.z = 2.


z = 3.z = 3.


Theoretical MFs Theoretical MFs ~ ~ 5-15% errors 5-15% errors

(0<z<5)(0<z<5)

Do we need a modified virial Do we need a modified virial overdensity for EDE ?overdensity for EDE ?

Introduction of the linear density contrast predicted by BDW Introduction of the linear density contrast predicted by BDW for EDE models worsens the fit!for EDE models worsens the fit!

%%

Spherical overdensity (SO)

The virial mass is :

3lim3

4rM critvir

Friends-of-friends (FOF) b=0.2

The concentration-mass relationThe concentration-mass relationHalo selections: >3000 particles Halo selections: >3000 particles • Substructure mass fraction Substructure mass fraction

• Centre of mass displacementCentre of mass displacement

• Virial ratioVirial ratio

1.0subf

07.0/ vircmc rrrs

35.1/2 UT

EDE halos always more EDE halos always more concentratedconcentrated

Profile fittingProfile fitting• Uniform radial range for density Uniform radial range for density profile profile

• More robust fit from maximum in More robust fit from maximum in the profilethe profile2r

5.2)/(log0 10 virrr

Eke et al. (2001) works Eke et al. (2001) works for EDE without for EDE without

modificationsmodifications

DM2[km/sec]2

Substructures in CDM haloes Substructures in CDM haloes

Cumulative velocity Cumulative velocity dispersion function dispersion function

from sub-halos from sub-halos dynamicsdynamics

Robust quantity against Robust quantity against richness threshold.richness threshold.

N(>

DM

2 ) [

h-1M

pc]3

sec/300kmSH

ConclusionsConclusions Higher cluster populations at high z for EDE models: Higher cluster populations at high z for EDE models:

linear growth behaviourlinear growth behaviour and power spectrum analysis and power spectrum analysis Halo-formation time: trend in Halo-formation time: trend in concentrationconcentration for EDE halos for EDE halos Possibility of putting cosmological constraints on equation Possibility of putting cosmological constraints on equation

of state parameter: of state parameter: cumulative velocity distribution cumulative velocity distribution functionfunction

Connection between mass and galaxy velocity Connection between mass and galaxy velocity dispersion: dispersion: virial relationvirial relation for massive dark matter halos for massive dark matter halos

Constant density contrast (spherical collapse theory for Constant density contrast (spherical collapse theory for EDE models): EDE models): mass functionmass function

Probing Dark Energy is one of the major Probing Dark Energy is one of the major challenge for the computational cosmologychallenge for the computational cosmology

Impact of Early Dark Energy on non-linear structure formation Margherita Grossi MPA, Garching Volker...

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