Impact of Early Dark Energy on nonlinear structure formation

1
Impact of Early Dark Energy on non-linear
structure formation

• Margherita Grossi
• MPA, Garching
• Advisor Volker Springel

3rd Biennial Leopoldina Conference on Dark Energy
LMU Munich, 10 October 2008
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Early dark energy models
Parametrization in terms of three parameters
(Wetterich 2004)

• Flat universe
• Fitting formula
• Effective contribution during structure
  formation

(see Bartelmanns Talk)
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Current predictions for EDE

• Bartelmann, Doran, Wetterich (2006)

• Geometry of the universe distance, time reduced

Cosmic time relative to LCDM
redshift z
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Current predictions for EDE

• 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 di

• Overdensity within virialized halos
• Overdensity linearly extrapolated to
• collapse density

collapse redshift zc
5
Current predictions for EDE

• Bartelmann, Doran, Wetterich (2006)

• Geometry of the universe distance, time reduced

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

• 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)
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Current predictions for EDE

• Bartelmann, Doran, Wetterich (2006)

• Geometry of the universe distance, time reduced

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

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

• Halo properties concentration increased

Concentration parameter
Halos density profile have roughly self similar
form
(NFW)
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Current predictions for EDE

• Bartelmann, Doran, Wetterich (2006)

• Geometry of the universe distance, time reduced

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

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

• Halo properties concentration increased

Simulations are necessary to interpret
observational results and compare them with
theoretical models
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N-Body Simulations
Models

• ?CDM
• DECDM
• EDE1
• EDE2

• 5123 particles, mp ? 5 10 9 solar masses
• L1003 (Mpc/h)3 , softening length of 4.2 kpc/h

Resolution requirements

Codes

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

Computation requests

• 128 processors on OPA at RZG (Garching)

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Expansion function
From the Friedmann equations
Growth factor
Structures need to grow earlier in EDE models in
order to reach the same level today
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The mass function of DM haloes
FoF b0.2
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The mass function of DM haloes
Constant initial density contrast
z 0.
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The mass function of DM haloes
z 0.25
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The mass function of DM haloes
z 0.5
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The mass function of DM haloes
z 0.75
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The mass function of DM haloes
z 1.
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The mass function of DM haloes
z 1.5
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The mass function of DM haloes
z 2.
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The mass function of DM haloes
Theoretical MFs 5-15 errors (0ltzlt5)
z 3.
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Do we need a modified virial overdensity for EDE ?
Friends-of-friends (FOF) b0.2
Spherical overdensity (SO) The virial mass is

Introduction of the linear density contrast
predicted by BDW for EDE models worsens the fit!
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The concentration-mass relation

• Halo selections gt3000 particles
• Substructure mass fraction
• Centre of mass displacement
• Virial ratio

• Profile fitting
• Uniform radial range for density
  profile
• More robust fit from maximum in the
  profile

Eke et al. (2001) works for EDE without
modifications
EDE halos always more concentrated
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Substructures in CDM haloes
Cumulative velocity dispersion function from
sub-halos dynamics
N(gt?DM2) h-1Mpc3
?DM2km/sec2
Robust quantity against richness
threshold.
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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