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) OBSERVABLES IN 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).
NEUTRINOS High-z BAO WDM z=1100
NEUTRINOS
N-body + Hydro neutrino simulations I: slices TreeSPH code Gadget-III follows DM, neutrinos, gas and star particles in a cosmological volume Viel, Haehnelt & Springel 2010, JCAP, 06,15
EVOLUTION of LSS I : dynamics in the linear regime CMB GALAXIES IGM (WL) Effects in terms of matter clustering, Hubble constant, Energy density (see Lesgourgues & Pastor 2006) Different evolution in terms of dynamics and geometry as compared to massless neutrino universes
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 Full hydro simulations: gas physics does impact at the <10 % level at scales k < 10 h/mpc Viel, Haehnelt & Springel 2010, JCAP, 06,15
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 LINEAR SIMULATIONS HALOFIT Bird, MV, Haehnelt 2011
Neutrino constraints from SDSS flux power 3 normal 1,2 2 inverted 3 1 2σ limit Seljak, Slosar, McDonald, 2006, JCAP, 0610, 014 DISFAVOURED BY LYMAN-α
Non-linear neutrinos VII: EUCLID forecasts Lesgourgues, Bird, MV, Haehnelt 2012
DARK MATTER S COLDNESS
Warm Dark Matter and structure formation - I k FS ~ 5 Tv/Tx (m x/1kev) Mpc-1 ΛCDM 1 kev MV, Markovic, Baldi & Weller 2011 z=0 z=2 z=5 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
Warm Dark Matter and non-linear power - II MV, Markovic, Baldi & Weller 2011 Range of wavenumbers important for weak lensing tomography, IGM and small scale clustering of galaxies!
Lyman-α and Warm Dark Matter - III MV et al., Phys.Rev.Lett. 100 (2008) 041304 SDSS + HIRES data (SDSS still very constraining!) Tightest constraints on mass of WDM particles to date: m WDM > 4 kev (early decoupled thermal relics) m sterile > 28 kev (standard DodelsonWidrow mechanism) SDSS range Completely new small scale regime
WDM and non-linear power - IV: weak lensing with EUCLID MV, Markovic, Baldi & Weller 2011
Lyman-α and Cold+Warm Dark Matter Boyarsky et al. 09 SDSS+WMAP5 SDSS + VHS
HIGH-Z DARK ENERGY
Early Dark Energy from the CMB Calabrese et al. 2011 Reichardt et al. 2011
Early Dark Energy in the Dark Ages Xia & Viel 2009
Coupled dark energy and the IGM Baldi & MV 10
BAOs
SDSS from low to high redshift Slosar et al. 2011 (BOSS collaboration)
Future perspectives: BAOs about 20 QSOs per square degree with BOSS McDonald & Eisenstein 2007 BOSS-like simulated flux power
Future perspectives-ii: BAOs McDonald & Eisenstein 2007
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 era Close to BAO detection at z=3 via Lyman-α
Outline - What data we got The data sets - How we used them Theoretical framework - What we achieved Results
The data sets SDSS vs LUQAS McDonald et al. 2005 Kim, MV et al. 2004 SDSS 3035 LOW RESOLUTION LOW S/N LUQAS vs 30 HIGH RESOLUTION HIGH S/N
The interpretation: full grid of sims - I 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) + 132 data points z=4.2 z=2.2 Cosmological parameters + e.g. bias IGM physics + Parameters describing
The interpretation: full grid of sims - II McDonald et al. 05 Tens of thousands of models Monte Carlo Markov Chains - Cosmology - Cosmology - Mean flux - T=T0 (1+δ )γ -1 - Reionization - Metals - Noise - Resolution - Damped Systems - Physics - UV background - Small scales
The interpretation: flux derivatives - III Independent analysis of SDSS power The flux power spectrum is a smooth function of k and z Both methods have drawbacks and advantages: 1- McDonald et al. 05 better sample the parameter space 2- Viel & Haehnelt 06 rely on hydro simulations, but probably error bars are underestimated Flux power P F (k, z; p) = P F (k, z; p0) + Σ i=1,n Best fit P F (k, z; pi) pi p = p0 (pi - pi0) p: astrophysical and cosmological parameters but even resolution and/or box size effects if you want to save CPU time
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% uncertainty Croft et al. 02 28% uncertainty Viel et al. 04 29% uncertainty McDonald et al. 05 14% uncertainty AMPLITUDE χ2 likelihood code distributed with COSMOMC SLOPE Redshift z=3 and k=0.009 s/km corresponding to 7 comoving Mpc/h
Results Lyman-α only with flux derivatives: correlations Fitting SDSS data with GADGET-2 this is SDSS Ly-α only!! FLUX DERIVATIVES SDSS data only σ8 = 0.91 ± 0.07 n = 0.97 ± 0.04
Lyman-α forest + Weak Lensing + WMAP 3yrs AMPLITUDE 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 VHS+WMAP1 MATTER DENSITY Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11 SPECTRAL INDEX
Active neutrinos - I Lesgourgues & Pastor Phys.Rept. 2006, 429, 307 Σ m ν = 0.138 ev Lyman-α forest Σ m ν = 1.38 ev
Active neutrinos - II Seljak, Slosar, McDonald, 2006, JCAP, 0610, 014 3 1,2 normal 2 inverted 3 1 2σ limit DISFAVOURED BY LYMAN-α Tight constraints because data are marginally compatible mν (ev) < 0.17 (95 %C.L.), < Σ 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 Goobar et al. 06 get upper limits 2-3 times larger for forecasting see Gratton, Lewis, Efstathiou 2007
Lyman-α and Warm Dark Matter - II ΛCDM 10 ev [P (k) WDM/P (k) CDM ]1/2 Light gravitino contributing to a fraction of dark matter 100 ev 1/3 Tx Tν 10.75 = g (T D) WDM 1/3 m gravitino < 16 ev (2 σ C.L.) (or any particle with g(td)~90-100) From high res. Lyman-a data GRAVITINO If the gravitino is the LSP then the susy breaking scale is limited from above Λ susy < 260 TeV MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534
PRIMORDIAL Non Gaussianities in the IGM
N-body simulation in NG scenario: the mass distribution Mathis et al. 04 Kang et al. 07 Grossi et al. 07,09 Hikage et al. 08 Desjacques et al. 08
First hydrodynamical simulation in NG scenario f nl = - 200 f nl = + 200 Viel, Branchini, Dolag, Grossi, Matarrese, Moscardini 2009, MNRAS, 393, 774
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 Inverted equation of state γ <1 means voids are hotter than mean density regions Flux probability distribution function
Systematics: Thermal state T = T0 ( 1 + δ ) γ -1 Thermal histories Flux power fractional differences Statistical SDSS errors on flux power
Systematics: UV fluctuations and Metals UV fluctuations from Lyman Break Galaxies Ratio of Flux power McDonald, Seljak, Cen, Ostriker 2004 Croft 2006 Lidz et al. 2007 Metal contribution Ratio of Flux power Kim, MV, Haehnelt, Carswell, Cristiani (2004)
GALAXY-IGM
Future perspectives BOSS (or SUPERBOSS) SDSS III 150,000 (1,000,000) QSO spectra tailored for BAO and P(k) studies X-Shooter (taking data now) spectrograph Medium resolution between SDSS and high res at least 100 QSO spectra needed to improve constraints Independent analysis of thermal state using different statistics and constraints both on astrophysics and cosmological at both HIGH and low redshift E-ELT era: measuring the cosmic expansion
BAOs
Slosar et al. 2011 (BOSS collaboration)
Future perspectives : BAO 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 McDonald & Eisenstein 2007 BOSS-like simulated flux 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
COSMIC EXPANSION
Measuring the cosmic expansion? This is a fundamental quantity not related at all to the FRW equations.
COsmicDynamicEXperiment CODEX-I Ultra-stable spectrograph Dz/Dt (10-10 yr-1) REDSHIFT
COsmicDynamicEXperiment Liske et al. 2008, MNRAS, 386, 1192 CODEX - II
BRIEF HISTORICAL OVERVIEW of the Lyman-α forest ISOLATED CLOUDS NETWORK OF FILAMENTS PROBES OF THE JEANS SCALE COSMOLOGICAL PROBES
Modelling the IGM 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 Size of the cloud: > 100 kpc Temperature: ~ 104 K Mass in the cloud: ~ 109 M sun Neutral hydrogen fraction: 10-5 In practice, since the process is mildly non linear you need numerical simulations To get convergence of the simulated flux at the percent level (observed)
Modelling the IGM II M (> ρ) V (> ρ) Bi & Davidsen 1997, ApJ, 479, 523
N-body simulations II: neutrino velocities matter Draw velocity from Fermi-Dirac distribution Brandbyge et al 08
N-body simulations VII: halo density profile CDM q/t=3 q/t total q/t=4 q/t=1 q/t=5 q/t=2 q/t=6 Brandbyge, Hannestad Haugbolle, Wong 2010
N-body simulations IV: mesh method Computing the neutrino gravitational potential on the PM grid and summing up its 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 Expansion of ψ in Legendre series Brandbyge & Hannestad 09
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 Methods differ Matter power @ z = 3 1) Significant non linear evolution at the smallest scales 2) Percent level discrepancies between particle and grid methods 3) Poissonian contribution affects small scales
Hydro simulations VI: matter and halo clustering Marulli, Carbone, MV, Moscardini e Cimatti 2011
THEORY: GAS in a LCDM universe 80 % of the baryons at z=3 are in the Lyman-α forest Bi & Davidsen (1997), Rauch (1998) baryons as tracer of the dark matter density field δ IGM ~ δ DM at scales larger than the Jeans length ~ 1 com Mpc
Little room for standard warm dark matter scenarios the cosmic web is likely to be quite cold COLD (a bit) WARM sterile 10 kev
Hydro simulations IV: halo mass functions Marulli, Carbone, MV, Moscardini e Cimatti 2011