BAO AS COSMOLOGICAL PROBE- I

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1 BAO AS COSMOLOGICAL PROBE- I Introduction Enrique Gaztañaga, ICE (IEEC/CSIC) Barcelona PhD Studenships (on simulations & galaxy surveys) Postdoctoral oportunities: (or AAS Job: #26205/26206) Outline Intro Distance Scales Inflation & Horizons Spectrum of Fluctuations the need of CDM BAO physics: sound horizon 1 1

2 Baryon wiggles Angular Spectrum For single redshift slice: z = Turnover Of MICE Simulation 2

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.

3 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 dχ -> 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 3

4 Using galaxies to trace structure Observables (null) Light-like radial (dω=0) events cdt = adr => cdz = Hπ π dr Light-like angular (dr=0) events cdt = a rθ Comoving transverse separation σ = d A θ Comoving radial separation π = cdz/h Observer dz= z 2 - z 1 - θ d A z 2 r 2 = σ 2 + π 2 π σ z 1 Comoving Radial distance (Angular) Comoving distance π = c H(z) dz S z cdzʹ ʹ k (χ) 1 d A (z) = = (1+ z)d 0 A (z) H(zʹ ) H(z) = cδz BAO π BAO Observed Known d A (z) = σ BAO Δθ BAO Luminosity distance M = m log(d L / 10pc) d L = d A (1+z)= D A (1+z) 2 Comoving Horizon scale = conformal time η χ H = t cdt = 0 a a 0 cda a 2 H t = Age 0 a cda ah Alcock-Paczynski (1979) test 4 4

Where does Structure in the Universe come

Physical scales Stage-II: baryon radiative

halos Collapsed region = DM hierarchical

5 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 seed background Physical scales Stage-II: baryon radiative cooling into gas and stars DM remains In halos Collapsed region = DM hierarchical halos dust STARS H2 Disk formation: colapse is faster in direction parallel to spin axis 5

6 VIRGO simulations N-body 6

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Inflation ->Why is the universe so uniform on the largest scales?[!] ->Why causally disconnected regions are alike?

larger than fundamental scale of gravity, the Planck length? ->What produced the initial density fluctuations?

) of the Inflation Theory: Universe is flat, (almost) scaleinvariant & gaussian (no self-coupling) Lenght λ

8 Inflation ->Why is the universe so uniform on the largest scales?[!] ->Why causally disconnected regions are alike? ->Flatness problem: small deviations from W=1 are not stable ->Why is the physical scale of the universe so much larger than fundamental scale of gravity, the Planck length? ->What produced the initial density fluctuations? the Predictions (?) of the Inflation Theory: Universe is flat, (almost) scaleinvariant & gaussian (no self-coupling) Lenght λ logscale inflation Lenght λ d h ~log(a) H = a / a = Λ => a ~ e Λt non causal d h ~ a 2 HOT d h ~ a 3/2 COLD a_enter a_equal a_decoupling z~1100 a = scale factor = t α Hubble radius: d h ~ t proper lenght: λ ~ a transparent a_now 8

9 Gravitational Instability: growth of fluctuations δ ρ/ <ρ> 1 Lenght λ inflation non causal Hubble radius: d h ~ t d h ~ a 3/2 d h ~ a 2 proper lenght: λ ~ a Amplitude δ d h ~log(a) δ δ~a 2 HOT δ~log(a) COLD a_de δ~a c transparent a_inflate a_enter a_equal a_decoupling a = scale factor = t α a_now δ'' + α Η δ ' - ( µη 2 k 2 v 2 /a 2 ) δ = 0 harmonic osc. for δ(k), k=2π/λ HOT Damped oscilations: a 2 µh 2 < k 2 v 2 COLD Growing fluctuations 9

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11 The need of CDM: 1. Explains collisionless DM halos 2. No radiative cooling: halos & RD 3. Explains origin of structure 4. Fills up DM budget 11

12 500 Myr (d=ct) correspond to horizon (~ct/a) at t=0.4 Myr)º This movie shows the evolution of a initial point-like density fluctuation. The density of four species is shown: dark matter (black), gas (blue), microwave background photons (red), and neutrinos (green). We have plotted the comoving fractional density of each species, holding the normalization consistent between the time slices. In other words, if two curves are the same height, then the fractional perturbation is the same in the two species. However, the absolute densities would be different: the dark matter would be 5 times denser than the baryons, which the photons and neutrinos would be changing relative to the gas and dark matter. All time slices are on the same scale, i.e. you can compare the fractional densities between epochs. comoving Remember that all of these perturbations are small, typically only a part in a thousand at high redshift. Also, the actual density field in the universe is composed of many such perturbations, both positive and negative, arising from all points in space. So we don't get to see this nice spherical shell pattern, but only the imprint of it in the statistical correlations. Note: - All fluctuations (but CDM) washed away fast: this is because of cosmic expansion and thermal (acoustic) pressure. - CDM grow thanks to gravity: has no pressure (no BAO) - After 0.4Myr the sound wave has traveled 500 comoving Mlyr! (physical 500Mlyr/1100~0.45Mlyr, at speed c/ 3 but in an expanding background). - At decoupling (z~1100), the rms amplitude is

13 r BAO Sound horizon distance Calculation Amplitude of effect depends on baryon franction but position is fixed by sound horizon z at decoupling Sound speed (dependent on baryon/photon ratio) is only weakly dependent on epoch, and can be approximated by Gives the comoving sound horizon ~110h -1 Mpc, and BAO wavelength 0.06hMpc -1 Baryon oscillations (BAO) in the large-scale matter power spectrum 13 13

14 BAO AS COSMOLOGICAL PROBE- II CMB Enrique Gaztañaga, ICE (IEEC/CSIC) Barcelona PhD Studenships (on simulations & galaxy surveys) Postdoctoral oportunities: (or AAS Job: #26205/26206) Outline DE and BAO CMB measurements Harmonic space Sachs-Wolfe (COBE-1992) BAO detected: WMAP-2003 Parameter fitting 14 14

Dark energy and BAO After 0.4Myr the sound wave has traveled 500 (comoving) Myr! Physical distance is 500Mlyr/1100~0.45Mlyr which is coincidentaly close to 0.

15 Dark energy and BAO After 0.4Myr the sound wave has traveled 500 (comoving) Myr! Physical distance is 500Mlyr/1100~0.45Mlyr which is coincidentaly close to 0.4 (sound speed is c/ 3 but in an expanding background). CDM feel the baryons and radiation through gravity BAO gives us a standard distance with a co-moving value r BAO ~ 100 Mpc/h (r BAO = 146.8±1.8 Mpc) can be measured in z and/or in angles. Can be used to constrain: - distance to ruler H(z) : - or parameters in ruler (Omega_M) dr(z) = radial angular c H(z) dz d (z) = cdz z A 0 H(z) cδz BAO = r BAO H(z) Δθ BAO = r BAO d A (z) Amplitude depends on baryon fraction but position is fixed by sound horizon 15

energy to prevent nucleus to capture electrons: 1st atoms!

16 Cosmic Background Radiation The Big Bang The universe cools down to 3000K (few ev) when photons do not have enough energy to prevent nucleus to capture electrons: 1st atoms! Matter and radiation decoupled (the universe becomes transparent). 16

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the measured flux F(f) as a function of frequency f to a number of

19 COBE Text Text P-W Black-Body Spectrum, measured to very high accuracy COMPONENT SEPARATIO: At each point in CMB map we can fit the measured flux F(f) as a function of frequency f to a number of components (A,B,C) with know spectrum: F(f)=A(f)+B(f)+C(f) Transparent 19

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22 BOOMERANG 2x BBN!? MAXIMA-1 22

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24 Δφ is time (and scale!) invariant even when density fluctuations grow! Perturbation theory: ρ = ρ b ( 1 + δ) => Δρ = (ρ - ρ b ) = ρ b δ ρ b = Μ / V => ΔΜ /M = δ With : δ + H δ - 3/2 Ω m H 2 δ = 0 in EdS linear theory: δ = a δ 0 Gravitation potential: Φ = - G M /R => ΔΦ = G ΔM / R = GM/R δ in EdS linear theory: δ = a δ 0 => ΔΦ = GM (δ/ R) = GM (δ 0 / R 0 )!! 24

25 PRIMARY CMB ANISOTROPIES Sachs-Wolfe (ApJ, 1967) ΔT/T(n) = [Φ (n) ] i f Temp. F. = diff in N.Potential (SW) Φ i ΔT/T=(SW)= ΔΦ /c 2 ΔΦ = GM (δ/ R) /c 2 Φ f ΔT/T= G ρ m 4/3 π (R/c) 2 δ ΔT/T = Ω m /2 (Η 0 R/c) 2 δ Ω m /2 (R/3000Mpc) 2 δ <ΔT/T> rms 10 5 σ 8 for (R~8 Mpc, <δ> 1) 25

26 PRIMARY & SECONDARY ANISOTROPIES Sachs-Wolfe (ApJ, 1967) & Rees-Sciama (Nature, 1968) non-linear ΔT/T(n) = [ 1/4 δγ (n) + v.n + Φ (n) ] i f + 2 i f dτ dφ/dτ (n) Temp. F. = Rad-baryon fluid + Doppler + N.Potential (SW) + Integrated Sachs-Wolfe (ISW) Φ i Φ f A geometrical test for space: Measure the angular scale that Corresponds to the sound horizon 26

27 Dipole l=1 Statistics: Spherical- Harmonics Quadrupole l =2 Octopole l=

28 Hu, Sugiyama, Silk (Nature, 1995) 28

29 WMAP1 29

30 Constraints from CMB Komatsu etal Acustic scale θ A π /l A = r s /d A z * =1090 is z at decoupling Shift parameter R = d A Η(z * ) /c 30

CMB Anisotropies: The Acoustic Peaks. Boom98 CBI Maxima-1 DASI. l (multipole) Astro 280, Spring 2002 Wayne Hu

CMB Anisotropies: The Acoustic Peaks 80 T (µk) 60 40 20 Boom98 CBI Maxima-1 DASI 500 1000 1500 l (multipole) Astro 280, Spring 2002 Wayne Hu Physical Landscape 100 IAB Sask 80 Viper BAM TOCO Sound Waves