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