N-body Simulations and Gravitational Lensing with Dark Energy

Beyond Einstein Meeting, May 13, 2004

Outline• Why Structure Formation and Dark Energy? • Studying Dark Energy with Structure Formation:

achievements and plans• Dark Energy Models Considered: Minimally

Coupled (Quintessence), Degenerate Today, Different in the Past

• Cluster Concentrations (Dolag etal. 2003, A&A 416, 853)

• Lensing (Arc Statistics, Meneghetti etal. 2004, A&A submitted, astro-ph/0405070)

• Next Steps

Why studying Dark Energy with Structure Formation?

• Epochs of structure formation and cosmic acceleration overlap

Why studying Dark Energy with Structure Formation?

• Epochs of structure formation and cosmic acceleration overlap

• Looking for signatures of a possible link between the two processes

Why studying Dark Energy with Structure Formation?

• Epochs of structure formation and cosmic acceleration overlap

• Looking for signatures of a possible link between the two processes

• Essential complement to the CMB data to compare the early, well behaving universe and the present weird cosmology

Kuhlen etal. 2004, Dolag etal. 2004, Linder & Jenkins 2003, Klypin et al. 2003, …

The Corrupted Universe The Corrupted Universe z=1000, Flat, sCDMz=1000, Flat, sCDM

z=0, Accelerating, Large Scale Power Lackz=0, Accelerating, Large Scale Power Lack

Studying Dark Energy with Structure Formation: Achievements and Plans

Background and Linear Perturbations Input to The N-body Machinery (gadget)

Cluster Dependence on The Behavior of the Dark Energy Equation of State

Imprint on Lensing Arc Statistics

Large BoxesMergingWeak LensingCMB DistortionTime Variation of GDark Energy and GravityTwo Component Clustering

Dolag etal. A&A 416, 853, 2004, Meneghetti etal. A&A submitted, astro-ph/0405070,

Bartelmann etal. A&A 409, 449, 2003, A&A 400, 19, 2003, A&A 396, 21, 2002

DE, lin. Pert., Carlo Baccigalupi

DE theory & models, Francesca Perrotta

Trieste

DE, lin. Pert., Carlo Baccigalupi

DE theory & models, Francesca Perrotta

Lensing, Str.Form., Matthias Bartelmann

Lensing, Massimo MeneghettiHeidelberg

DE, lin. Pert., Carlo Baccigalupi

DE theory & models, Francesca Perrotta

Lensing, Str.Form., Matthias Bartelmann

Lensing, Massimo Meneghetti

Str. Form., Lauro Moscardini

N-body, Klaus Dolag

Str. Form., Giuseppe Tormen Bologna

Padua

DE, lin. Pert., Carlo Baccigalupi

DE theory & models, Francesca Perrotta

Lensing, Str.Form., Matthias Bartelmann

Lensing, Massimo Meneghetti

Str. Form., Lauro Moscardini

N-body, Klaus Dolag

Str. Form., Giuseppe Tormen

Dark Energy Models

• Cosmological Constant (LCDM), Constant w=-0.6 Effective Dark Energy (DECDM), RP and SUGRA Quintessence, Open Cold Dark Matter (OCDM)

• Criticalities: Equation of state behavior, Linear growth factor

Clusters

• Parent simulation: CDM, 5123 particles in 479 h-1 kpc, 17 clusters identified at z=0 with radius between 5 and 10 h-1 Mpc, mass exceeding 3£ 1014 Mo . Clusters re-sampled with 106 particles

• background evolution and initial conditions according to the underlying dark energy scenario

• Mass resolution: 109 h-1 Mo

Cluster Concentration

• Radial profile binning and concentration found from a NFW fit

• Comparison of the numerically determined concentrations with semi-analytical expectations

Cluster Concentration

Simulating Arcs

• 52 equidistant time snapshots between z=0 and 1

• Surface density map from the central cluster region (3 h-1 Mpc comoving)

• 2048£ 2048 light tracing grid in the central quarter of the lens plane

• Deflection angle computed summing all contributions from the surface density map

• Background galaxies at z=1• Lensed images built out of the

light rays lying within single sources

Simulating Arcs

Caustics, Critical Curves and Cross Sections

Optical Depth

Studying Dark Energy with Structure Formation: Achievements and Plans

Background and Linear Perturbations Input to The N-body Machinery (gadget)

Cluster Dependence on The Behavior of the Dark Energy Equation of State

Imprint on Lensing Arc Statistics

Large BoxesMergingWeak LensingCMB DistortionTime Variation of GDark Energy and GravityTwo Component Clustering

Studying Dark Energy with Structure Formation: Achievements and Plans

Background and Linear Perturbations Input to The N-body Machinery (gadget)

Cluster Dependence on The Behavior of the Dark Energy Equation of State

Imprint on Lensing Arc Statistics

Large BoxesMergingWeak LensingCMB DistortionTime Variation of GDark Energy and GravityTwo Component Clustering

CMB bispectrum CMB bispectrum

BBllm m

l`l`m`m`

l``l``m``m``=a=almlm a al`m`l`m` a al``m``l``m``

aalmlm==ss ( ( )Y )Ylmlm(( )d )d

BBl l`l``l l`l``==m m` m``m m` m`` ( (mmllm`m`

l`l`m``m``

l``l``) a) almlm a al`m`l`m` a al``m``l``m``

ll

l`l`l``l``

(( ) ) ´́ T(T( )/T )/T

CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation

< B< Bllm m

l`l`m`m`

l``l``m`` m`` >=0>=0

< B< Bllm m

l`l`m`m`

l``l``m`` m`` >> 0 0

CMB bispectrum line of sight chronology CMB bispectrum line of sight chronology

ll-1-1

horizon crossing, horizon crossing, decaying linearly, dQ/dz>0 decaying linearly, dQ/dz>0

zz!1!1 :super-horizon scales in a flat :super-horizon scales in a flat CDM universe, dPCDM universe, dP/d/d =0, dQ/dz =0, dQ/dz!! 0 0

zzrr

Non-linearity, Non-linearity, grows, dQ/dz<0 grows, dQ/dz<0

zz!! 0, 0, vanishes, dQ/dz vanishes, dQ/dz!! 0 0

onset of acceleration, change in cosmic onset of acceleration, change in cosmic equation of state, equation of state, decaying linearly, dQ/dz>0 decaying linearly, dQ/dz>0

CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy

Giovi, Baccigalupi, Perrotta PRD 2003, astro-ph/0308118 Giovi, Baccigalupi, Perrotta PRD 2003, astro-ph/0308118

Studying Dark Energy with Structure Formation: Achievements and Plans

Background and Linear Perturbations Input to The N-body Machinery (gadget)

Cluster Dependence on The Behavior of the Dark Energy Equation of State

Imprint on Lensing Arc Statistics

Large BoxesMergingWeak LensingCMB DistortionTime Variation of GDark Energy and GravityTwo Component Clustering