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DARK MATTER
AND DARK ENERGY
AT HIGH REDSHIFT
MATTEO VIEL
INAF & INFN – Trieste
SISSA IDEALS WORKSHOP --- 11th November 2011
RATIONALE
HIGHLIGHT THE IMPORTANCE OF HIGH REDSHIFT (z>1) OBSERVABLESIN ORDER TO CONSTRAIN:
1) NEUTRINOS
2) COLDNESS OF COLD DARK MATTER
3) EARLY DARK ENERGY
4) BAOs
STATUS
THE MEASUREMENT OF MATTER POWER AT HIGH-z (COMBINED with the CMB) IS CURRENTLY PROVIDING THE TIGHTEST CONSTRAINTS on 1), 2) and 3) AND WILL PROVIDE THE TIGHTEST CONSTRAINTS on 4).
z=1100
WDM
NEUTRINOS
High-z BAO
NEUTRINOS
N-body + Hydro neutrino simulations – I: slices
Viel, Haehnelt & Springel 2010, JCAP, 06 ,15
TreeSPH code Gadget-IIIfollows DM, neutrinos, gas and starparticles in a cosmological volume
EVOLUTION of LSS –I : dynamics in the linear regime
Effects in terms of matter clustering,Hubble constant,Energy density
(see Lesgourgues & Pastor 2006)
Different evolution in terms of dynamicsand geometry as compared to masslessneutrino universes
CMB GALAXIES IGM (WL)
N-body simulations – II: effects in terms of non-linear power
Brandbyge et al 08
--
Hydro simulations – III: redshift/scale dependence of non-linear power
Viel, Haehnelt & Springel 2010, JCAP, 06 ,15
Full hydro simulations: gas physics does impact at the <10 % level at scales k < 10 h/Mpc
Hydro simulations – IV: redshift space distortions
Marulli, Carbone, MV, Moscardini e Cimatti 2011
Hydro simulations – V: the distribution of high-z voids
Navarro-Villaescusa, Vogelsberger, MV, Loeb 2011
N-body simulations – VI: very non-linear regime
Bird, MV, Haehnelt 2011
LINEAR
SIMULATIONS
HALOFIT
Neutrino constraints from SDSS flux power
Seljak, Slosar, McDonald, 2006, JCAP, 0610, 014
normal
inverted1
2
31,2
32σ limit DISFAVOURED
BY LYMAN-α
Lesgourgues, Bird, MV, Haehnelt 2012
Non-linear neutrinos VII: EUCLID forecasts
DARK MATTER’S COLDNESS
Warm Dark Matter and structure formation - I
ΛCDM
k FS ~ 5 Tv/Tx (m x/1keV) Mpc-1
See Bode, Ostriker, Turok 2001 Abazajian, Fuller, Patel 2001 Avila-Reese et al. 2001 Boyarsky et al. 2009 Colin et al. 2008 Wang & White 2007 Gao & Theuns 2007 Abazajian et al. 2007 Lovell et al. 2011
z=0
z=2
z=5
1 keV
MV, Markovic, Baldi & Weller 2011
Warm Dark Matter and non-linear power - II
Range of wavenumbers important for weak lensing tomography , IGMand small scale clustering of galaxies!
MV, Markovic, Baldi & Weller 2011
MV et al., Phys.Rev.Lett. 100 (2008) 041304
Tightest constraints on mass ofWDM particles to date:
m WDM > 4 keV (early decoupled thermal relics)
m sterile > 28 keV (standard Dodelson-Widrow mechanism)
SDSS + HIRES data
(SDSS still very constraining!)
SDSS range Completely new small scale regime
Lyman-α and Warm Dark Matter - III
WDM and non-linear power - IV: weak lensing with EUCLID
MV, Markovic, Baldi & Weller 2011
Lyman-α and Cold+Warm Dark Matter
SDSS+WMAP5 SDSS + VHS
Boyarsky et al. 09
HIGH-Z DARK ENERGY
Early Dark Energy from the CMB
Calabrese et al. 2011
Reichardt et al. 2011
Xia & Viel 2009
Early Dark Energy in the “Dark Ages”
Coupled dark energy and the IGM
Baldi & MV 10
BAOs
Slosar et al. 2011 (BOSS collaboration)
SDSS from low to high redshift
about 20 QSOs per square degree with BOSS
Future perspectives: BAOs
McDonald & Eisenstein 2007
BOSS-like simulatedflux power
McDonald & Eisenstein 2007
Future perspectives-II: BAOs
BAOs in the Lyman-α forest: probing the transverse direction
Transverse direction: MV et al 2002; White 2003; McDonald & Eisenstein 2007; Slosar et al. 2009, 2010
3D Correlations in BOSS 1yr data!
Slosar et al. 2011
Estimates of b and β performed
SUMMARY
Bridging the gap between z=1100 and z=0 via LSS probes:
Lyman-α
Weak Lensing
Clustering of galaxies
is important and is providing and will provide tight constraints on the small scale properties of the matter distribution and the cosmological model
Mν < 0.17 eV (0.3 eV) MWDM > 4 keV (2 keV) Ω EDE < 0.02 in the structure formation eraClose to BAO detection at z=3 via Lyman-α
Outline
- What data we got
- How we used them
- What we achieved
The data sets
Theoretical framework
Results
3035 LOW RESOLUTION LOW S/N vs 30 HIGH RESOLUTION HIGH S/NSDSS
LUQAS
SDSS vs LUQAS
McDonald et al. 2005 Kim, MV et al. 2004
The data sets
SDSS power analysed by forward modelling motivated by the huge amount of data with small statistical errors
+ +
CMB: Spergel et al. (05) Galaxy P(k): Sanchez & Cole (07) Flux Power: McDonald (05)
Cosmological parameters + e.g. bias + Parameters describing IGM physics
132 data points
The interpretation: full grid of sims - I
z=4.2
z=2.2
- Cosmology
- Cosmology
- Mean flux
- T=T0 (1+δ )γ -1
- Reionization
- Metals
- Noise- Resolution
- Damped Systems
- Physics- UV background
- Small scales
Tens of thousands of modelsMonte Carlo Markov Chains
McDonald et al. 05The interpretation: full grid of sims - II
Both methods have drawbacks and advantages:
1- McDonald et al. 05 better sample the parameter space2- Viel & Haehnelt 06 rely on hydro simulations, but probably error bars are underestimated
P F (k, z; p) = P F (k, z; p0) + Σ i=1,N P F (k, z; pi) (pi - pi0) ∂ pi p = p0
Best fit
Flux power
p: astrophysical and cosmological parameters
but even resolution and/or box size effects if you want to save CPU time
The interpretation: flux derivatives - III
Independent analysis of SDSS power
The flux power spectrum is a smooth function of k and z
RESULTS
Summary (highlights) of results
1. Competitive constraints in terms of cosmological parameters (in particular shape and
curvature of the power spectrum)
Lesgourgues, MV, Haehnelt, Massey (2007) JCAP 11 008
2. Tightest constraints to date on neutrino masses and running of the spectral index Seljak, Slosar, McDonald JCAP (2006) 10 014
3. Tightest constraints to date on the coldness of cold dark matter
MV et al., Phys.Rev.Lett. 100 (2008) 041304
Results Lyman-α only with full grid: amplitude and slope
McDonald et al. 05
Croft et al. 98,02 40% uncertaintyCroft et al. 02 28% uncertaintyViel et al. 04 29% uncertaintyMcDonald et al. 05 14% uncertainty
χ2 likelihood code distributed with COSMOMC
AM
PLI
TU
DE
SLOPE
Redshift z=3 and k=0.009 s/km corresponding to 7 comoving Mpc/h
SDSS data only
σ8 = 0.91 ± 0.07n = 0.97 ± 0.04
Fitting SDSS data with GADGET-2 this is SDSS Ly-α only !!
FLUX DERIVATIVES
Results Lyman-α only with flux derivatives: correlations
Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11
VHS-LUQAS: high res Ly-a from (Viel, Haehnelt, Springel 2004)SDSS-d: re-analysis of low res data SDSS (Viel & Haehnelt 2006)WL: COSMOS-3D survey Weak Lensing (Massey et al. 2007) 1.64 sq degree public available weak lensing COSMOMC module
Lyman-α forest + Weak Lensing + WMAP 3yrs
VHS+WMAP1
AM
PL
ITU
DE
SPECTRAL INDEXMATTER DENSITY
Lesgourgues & Pastor Phys.Rept. 2006, 429, 307
Lyman-α forest
Σ m ν = 0.138 eV
Σ m ν = 1.38 eV
Active neutrinos - I
Active neutrinos - IISeljak, Slosar, McDonald, 2006, JCAP, 0610, 014
Σmν (eV) < 0.17 (95 %C.L.), < 0.19 eV (Fogli et al. 08) r < 0.22 (95 % C.L.)
running = -0.015 ± 0.012 Neff = 5.2 (3.2 without Ly α) CMB + SN + SDSS gal+ SDSS Ly-α
normal
inverted
1
2
31,2
3
Goobar et al. 06 get upper limits 2-3 times larger…… for forecasting see Gratton, Lewis, Efstathiou 2007
Tight constraints because dataare marginally compatible
2σ limit DISFAVOUREDBY LYMAN-α
Lyman-α and Warm Dark Matter - II
ΛCDM
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534
[P (k) WDM/P (k) CDM ]1/2
T x 10.75 =T ν g (T D)
1/3
1/3
Light gravitino contributing to a fraction of dark matter
10 eV
100 eV
m gravitino < 16 eV (2 σ C.L.)(or any particle with g(TD)~90-100)From high res. Lyman-a data
If the gravitino is the LSP then the susy breaking scale is limited from above
Λ susy < 260 TeV
WDM GRAVITINO
PRIMORDIAL Non Gaussianities in the IGM
Mathis et al. 04Kang et al. 07Grossi et al. 07,09Hikage et al. 08Desjacques et al. 08
N-body simulation in NG scenario: the mass distribution
Viel, Branchini, Dolag, Grossi, Matarrese, Moscardini 2009, MNRAS, 393, 774
First hydrodynamical simulation in NG scenario
f nl = - 200 f nl = + 200
SYSTEMATICS
Fitting the flux probability distribution function
Bolton, MV, Kim, Haehnelt, Carswell (08), MV et al. 2009, Puchwein et al. 2011
T=T0(1+δ ) γ -1
Flux probabilitydistributionfunction
Invertedequation of state γ <1 means voids arehotter than mean density regions
Systematics: Thermal state
T = T0 ( 1 + δ ) γ -1
Statistical SDSS errors on flux power
Thermal histories Flux power fractional differences
UV fluctuations from Lyman Break Galaxies Metal contribution
Systematics: UV fluctuations and Metals
McDonald, Seljak, Cen, Ostriker 2004 Kim, MV, Haehnelt, Carswell, Cristiani (2004)Croft 2006Lidz et al. 2007
Ratio of Flux power Ratio of Flux power
GALAXY-IGM
BOSS (or SUPERBOSS) – SDSS III150,000 (1,000,000) QSO spectra tailored for BAO and P(k) studies
X-Shooter (taking data now) spectrographMedium resolution between SDSS and high res at least 100 QSO spectraneeded to improve constraints
Independent analysis of thermal state using different statistics andconstraints both on astrophysics and cosmological at both HIGH and low redshift
E-ELT era: measuring the cosmic expansion
Future perspectives
BAOs
Slosar et al. 2011 (BOSS collaboration)
Importance of transverse direction: MV et al 2002; White 2003; McDonald & Eisenstein 2007; Slosar et al. 2009
about 20 QSOs per square degree with BOSS
Future perspectives : BAO
McDonald & Eisenstein 2007
BOSS-like simulatedflux power
BAOs in the Lyman-a forest: probing the transverse direction
Importance of transverse direction: MV et al 2002; White 2003; McDonald & Eisenstein 2007; Slosar et al. 2010
about 20 QSOs per square degree with BOSS
3D Correlations in BOSS 1yr data!
Slosar et al. 2011
Estimates of b and β performed
COSMICEXPANSION
Measuring the cosmic expansion?
This is a fundamental quantity not related at all to the FRW equations….
COsmicDynamicEXperiment CODEX-I
REDSHIFT
Dz/Dt(10-10 yr-1)
Ultra-stable spectrograph
Liske et al. 2008, MNRAS, 386, 1192
COsmicDynamicEXperiment CODEX - II
‘ISOLATED’ CLOUDS
NETWORK OF FILAMENTS
PROBES OF THE JEANS SCALE
COSMOLOGICAL PROBES
BRIEF HISTORICAL OVERVIEW of the Lyman-α forest
Dark matter evolution: linear theory of density perturbation + Jeans length LJ ~ sqrt(T/ρ) + mildly non linear evolution
Hydrodynamical processes: mainly gas cooling cooling by adiabatic expansion of the universe heating of gaseous structures (reionization)
- photoionization by a uniform Ultraviolet Background - Hydrostatic equilibrium of gas clouds dynamical time = 1/sqrt(G ρ) ~ sound crossing time= size /gas sound speed
In practice, since the process is mildly non linear you need numerical simulationsTo get convergence of the simulated flux at the percent level (observed)
Size of the cloud: > 100 kpcTemperature: ~ 104 KMass in the cloud: ~ 109 M sunNeutral hydrogen fraction: 10 -5
Modelling the IGM
Bi & Davidsen 1997, ApJ, 479, 523
Modelling the IGM –II
M (> ρ)
V (> ρ)
N-body simulations – II: neutrino velocities matter
Brandbyge et al 08
Draw velocity from Fermi-Diracdistribution
N-body simulations – VII: halo density profile
Brandbyge, HannestadHaugbolle, Wong 2010
CDM q/T total q/T=1 q/T=2
q/T=3 q/T=4 q/T=5 q/T=6
N-body simulations – IV: mesh method
Computing the neutrino gravitational potential on the PM grid and summing upits contribution to the total matter gravitational potential – this is much faster!
COMPARISON GRID VS PARTICLES
M ν =0.6 eV M ν = 1.2 eV
Brandbyge et al 08b
N-body simulations – V: a hybrid approach
After neutrino decoupling CBE
Brandbyge & Hannestad 09
Expansion of ψ in Legendre series
N-body simulations – VI: comparison
PARTICLES: accurate non-linear sampling but prone to shot-noise errors GRID: fast and accurate but no phase mixing (i.e. non-linear regime suppression maybe it is less than it should be)
HYBRID: ideal for non-linear objects but memory demanding and prone to convergence issues
NEUTRINOS in the IGM – IV: impact on neutrino power spectrum
Increasing neutrino mass
INTRO
DATA: high resolution spectrum
SIMULATING NEUTRINOS at high-redshift – II: methods
Matter power @ z = 3
1) Significant non linearevolution at the smallest scales
2) Percent level discrepanciesbetween particle and grid methods
3) Poissonian contribution affectssmall scales
Methods differ
Hydro simulations – VI: matter and halo clustering
Marulli, Carbone, MV, Moscardini e Cimatti 2011
80 % of the baryons at z=3 are in the Lyman-α forest
baryons as tracer of the dark matter density field δ IGM ~ δ DM at scales larger than the Jeans length ~ 1 com Mpc
flux = exp(-τ) ~ exp(-(δ IGM )1.6 T -0.7 )
THEORY: GAS in a LCDM universe
Bi & Davidsen (1997), Rauch (1998)
COLD (a bit) WARM sterile 10 keV
Little room for standard warm dark matter scenarios…… … the cosmic web is likely to be quite “cold”
Hydro simulations – IV: halo mass functions
Marulli, Carbone, MV, Moscardini e Cimatti 2011
