DARK ENERGY PROBES Phenomenology Enrique Gaztañaga, ICE (IEEC/CSIC) Barcelona Outline Intro Cosmic history& Growth history DE vs Modify Gravity DE Probes DE with Simulations Marenostrum & MICE Lightcone & onion shells Applications: BAO, Clusters & WL Redshift space distortions The PAU Survey Onion models have been used for centuries to indicate hierarchical spheres of influence. Alexandre Koyré’s wonderful From the Closed World to the Infinite Universe (Koyré 1957) uses the beautiful 11- layered onion diagram of Peter Apian’s 1539 Cosmographia , a pre- Copernican model of the universe, on its cover. 1
HOW DID WE GET HERE? Two driving questions in Cosmology: Background: Evolution of scale a(t) + Symmetries + Einstein’s Eq. (Gravity?) + matter-energy content ? -> Friedman Eq.: H 2 (z) = H 2 0 [ Ω M (1+z) 3 + Ω R (1+z) 4 + Ω K (1+z) 2 + Ω DE (1+z) 3(1+w) ] c dt = a d χ -> χ = c ∫ dz/H(z) Dark Matter and Dark Energy! Structure Formation: + origin of structure (Initial Conditions) + gravitational instability (Gravity?) + matter-energy content ? δ L ’’ + H δ L ’ - 3/2 W m H 2 δ L = 0 + galaxy/star formation (SFR): bias
Using galaxies to trace structure z 2 Observables Comoving transverse separation σ = d A θ σ Comoving radial separation π = cdz /H π (null) Light-like radial (d Ω =0) events d A dz= z 2 - z 1 - cdt = adr => cdz = H π z 1 π ≡ dr r 2 = σ 2 + π 2 θ Observer Light-like angular (dr=0) events cdt = a r θ Comoving Radial distance (Angular) Comoving distance c cdz ′′ z H ( z ) dz S k ( χ ) − 1 ≡ d A ( z ) = ∫ = (1 + z ) D A ( z ) π = H ( z ′ ) 0 H ( z ) = c Δ z BAO d A ( z ) = σ BAO Observed π BAO Known Δ θ BAO Comoving Horizon scale Luminosity distance Age = conformal time M = m + 2.5 log(d L / 10pc) cda cdt cda a t a ∫ t = ∫ ∫ η ≡ χ H = = aH a 2 H 0 d L = d A (1+z)= D A (1+z) 2 a 0 0 Alcock-Paczynski (1979) test 3
Where does Structure in the Universe come From? How did galaxies/star/molecular clouds form? Stage-I: gravitational collapse from some initial seeds Overdensed region time Initial overdensed Physical scales seed background Collapsed region = DM hierarchical halos Stage-II: baryon radiative cooling into gas and stars DM remains In halos dust H2 STARS Disk formation: colapse is faster in direction parallel to spin axis
VIRGO N-body simulations
Mass conservation Euler Eq. d τ =a dt
Jeans Instability ( linear regime ) EdS Open δ L ( x , τ ) = D ( τ ) δ 0 ( x ) Λ Another handle on DE: z = 9 z = 0 (now) - Where Friedman Eq. (Expansion history) may not EdS separate modified gravity from DE: Growth of sctructure could: models with equal expansion history yield difference D(z) (EG & Lobo 2001), astro-ph/0303526 & 0307034) a = 1/(1+z) Velocity growth factor: tell us if gravity is really r responsible for structure! r • θ = − f( Ω ) δ = D v • ∇ Could also tell us about a ≡ − H θ δ D δ = − cosmological parameters
MODE COUPLING Coupling functions: • adimensional • geometrical • Non-linear • Gravitational instability Linear Theory: modes are independent 2 k 12 3 k 2 µ= cos θ k 1 1 Weakly non-linear Perturbation Theory 2nd order containts mode couplings EdS
Observations require an statistical approach: Evolution of (rms) variance ξ 2 = < δ 2 > instead of δ Or power spectrum P(k)= < δ 2 (k)> => ξ 2 = ∫ dk P(k) k 2 W(k) dk IC problem: Linear Theory δ = D δ 0 ξ 2 = < δ 2 > = D 2 < δ 0 2 > Normalization σ 8 2 ≡ < δ 2 (R=8)> To find D(z) -> Compare < δ 2 > at two times or find evolution invariants Problem: statistical bias: δ gal = b δ dm => < δ 2 gal > = b 2 < δ 2 dm > So linear measurements constrain degenerate product: D(z)*b(z) ; b* σ 8 θ = − f( Ω ) δ = − f( Ω )/b δ gal β Initial Gaussian distribution of density fluctuations: ξ p (V) = < δ P > c = 0 for all p ≠ 2 Perturbations due to gravity generate non-zero ξ p − > ξ 3 = S 3 ξ 2 2 with S 3 (m)= 34/7 (time invariant)
Bias: lets take a very simple model. rare peaks in a Gaussian field (Kaiser 1984, BBKS) Linear bias “b”: δ (peak) = b δ (mass) with b= ν / σ ( SC: ν = δ c / σ ) − > ξ 2 (peak) = b 2 ξ 2 (m) Threshold ν 11
Local bias δ h = F[ δ m ] = b δ m + b 2 δ m 2 c 2 ≡ b 2 / b
Does light traces mass?
What is Dark Energy? 1 Whatever Energy-Momemtum Tensor is needed in Einstein Field Eq. (assumes GR) 2 Whatever causes cosmic acceleration includes Modified Gravity(MG) MG is degenerate with DE if we only use Cosmic history: need Growth history: Lue, Scoccimarro & Starkman astro-ph/0307034 working examples: Brans-Dicke, f(R), DGP ds 2 = - [1+ 2 Ψ (t,x) ] dt 2 + a 2 [1-2 ϕ (t,x)] dr 2 -k 2 ϕ (a,k) = 4 π a 2 G g(k) ρ δ η ≡ Curvature ϕ /Newtonian Ψ effective G g(k) Mukhanov, Feldman & Branderberger (1992) Guzik, Jain & Takada 2009 arXiv:0906.2221 14
a(t) = scale factor =1/(1+z) (a_0 = 1 ) General Relativity vs Brans-DicKe Einstein's Field Eq. R = curvature/metric T = matter content Hubble Cte (Friedman Eq) ω > 2500 (solar system) T. Damour & K. Nortdvedt, Phys. Rev. D 48, 3436 (1993) B.~Boisseau, G.~Esposito-Far\`ese, D.~Polarski, and A.A.~Starobinsky, Phys. Rev. D, 59, 123502, 1999 S.~Sen and A.A.~Sen,Phys. Rev. D in press 2001 (gr-qc/0010092) Flux= L/4 π D L 2 δ = δ 0 a (1+ ω )/(2 + ω ) EG & A.Lobo astro-ph/0003129, ApJ, v548, 47-59, 2001
DES= Dark Energy Survey • Study Dark Energy using 4 complementary* techniques: I. Cluster Counts II. Weak Lensing III. Baryon Acoustic Oscillations IV. Supernovae • Two multiband surveys: 5000 deg 2 g, r, i, Z,Y to i~24 9 deg 2 repeat (SNe) • Build new 3 deg 2 camera and Data management system Survey 30% of 5 years Response to NOAO AO *in systematics & in cosmological parameter degeneracies *geometric+structure growth: test Dark Energy vs. Gravity DES Forecast: FoM =4.6x
Photometric Redshifts Elliptical galaxy spectrum • Measure relative flux in multiple filters: track the 4000 A break • Estimate individual galaxy redshifts with accuracy σ (z) < 0.1 (~0.02 for clusters) • Precision is sufficient for Dark Energy probes, provided error distributions well measured. • Good detector response in z band filter needed to reach z>1
I. Clusters and Dark Energy Number of Clusters vs. Redshift •Requirements 1.Understand formation of dark w = − 1 matter halos 2.Cleanly select massive dark matter halos (galaxy clusters) over a range of redshifts w = − 1 3.Redshift estimates for each cluster 4.Observable proxy that can be used as cluster mass estimate: dN ( z ) dV g(O|M,z) ( ) dz d Ω n z dzd Ω = Primary systematics: Uncertainty in g (bias & scatter) Uncertainty in O selection fn.
II. Weak Lensing: Cosmic Shear Background Statistical measure of shear pattern, ~1% distortion Radial distances depend on geometry of Universe sources Foreground mass distribution depends on growth of structure Dark matter halos Observer • Cosmic Shear Angular Power Spectrum in Photo-z Slices • Shapes of ~300 million well-resolved galaxies, 〈 z 〉 = 0.7 • Primary Systematics: photo-z’s, PSF anisotropy, shear calibration • Extra info in bispectrum & galaxy-shear: robust
III. Baryon Acoustic Oscillations Acoustic series in P(k) becomes a CMB single peak in ξ (r) Angular Power Spectrum SDSS galaxy correlation function Eisenstein etal Bennett, etal
IV. Supernovae • Geometric Probe of Dark Energy • Baseline: repeat observations of 9 deg 2 using 10% of survey time: 5 visits per lunation in riz • ~1100-1400 well-measured SN Ia lightcurves to z~1 • Larger sample, improved z -band response (fully depleted CCDs) compared to ESSENCE, SNLS: reduce dependence on rest-frame u -band and Malmquist bias • Spectroscopic follow-up of large SN subsample+host galaxies (LBT, Magellan, SDSS Gemini, Keck, VLT,…) e.g., focus on ellipticals (low dust extinction)
DES Forecasts: Power of Multiple Techniques w ( z ) =w 0 +w a (1 –a ) 68% CL Assumptions: Clusters: σ 8 =0.75, z max =1.5, WL mass calibration (no clustering) DETF Figure of BAO: l max =300 Merit: inverse area of ellipse WL: l max =1000 (no bispectrum) geometric+ Statistical+photo-z growth systematic errors only Spatial curvature, galaxy bias Stage II not marginalized, included here geometric Planck CMB prior Factor 4.6 improvement over Stage II
PRIMARY & SECONDARY CMB ANISOTROPIES Sachs-Wolfe (ApJ, 1967) Δ T/T(n) = [ 1/4 δγ (n) + v.n + Φ (n) ] i f Temp. F. = Photon-baryon fluid AP + Doppler + N.Potential (SW) Φ i Φ f + Integrated Sachs-Wolfe (ISW) & Rees-Sciama (Nature, 1968) non-linear 2 ∫ if d τ d Φ / d τ (n) In EdS: D(z) = a, so that Φ ~ δ M / R~ D / a~cte and therefore Δ T/T = d Φ / d τ = 0 In DE universe => < Δ T/T δ G > ≠ 0 EG, Manera, Multamaki (astro-ph/ 0407022)
DARK ENERGY PROBES Spectroscopic Spectroscopic Photometric Y = OPTIONAL CMB PROBE Survey Survey (z<1) Follow-up X = REQUIRED SNe-Ia X X BAO Y Y X WL X X z-distortions clusters X Y X Y ISW X X Padmanabhan
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