# Mapping structure of the Universe. the very large scale. INAF IASF Milano

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1 Mapping the large scale structure of the Universe the very large scale structure Marco Scodeggio INAF IASF Milano

2 The large scale structure (100Mpc) Zero order approximation: the Universe is homegeneous and isotropic

3 How uniform is our Universe?

4 How uniform is our Universe? Counts cannot continue to rise indefinitely, otherwise we would violate the simplest astronomical observation of them all: the fact that the night sky is basically dark!! This is known as Olber's Paradox, although it was proposed to the astronomical community by Edmund Halley and perhaphs even before

5 The large scale structure (100 Mpc) First order approximation: there are density fluctuations, which were distributed originally in a Gaussian distribution We have 3 basic methods to study them: CMB fluctuations (corresponding to z~1000) Weak gravitational lensing The galaxy correlation function The final goal is always to derive the Power Spectrum of the density fluctuations

6 The Morphology-Density relation

7 The CMB map of density fluctuations CMB: T=2.73 K + dipole (mk) + fluctuations (μk) COBE data WMAP data

8 The CMB Power Spectrum

9 Mapping our Universe: the acceleration

10 The CMB view of Dark Energy

11 Cluster Cl

12 Strong gravitational lensing

13 Weak gravitational lensing

14 The weak lensing map of density fluctuations

15 Weak lensing map of the COSMOS field

16 The 2-points correlation functions Definition: excess probablility (with respect to a random distribution) of finding a pair of galaxies with a given spatial separation r (Pebbles, 1980). For a random distribution: δp = r02 δv1 δv2, for a clustered distribution: δp = r02 ξ[1+(r12)] δv1 δv2 From previous studies: (in the range 1-30 h-1 Mpc) it is well described by a single power law: ξ(r)=(r/r0)-γ 2 free parameters: r0 (correlation length) = indication of the strenght of correlation γ (slope of the correlation function) = indication of scale dependence small r0 Correlation lenght: Greater r0 means galaxies more clustered Smaller r0 means galaxies less clustered Slope: Greater γ means more marked difference between clustering at different scales Smaller γ means less marked difference between clustering at different scales large r0

17 Distorsions in redshift space Real space Redshift space Redshift distortions can be separated from true spatial correlation by computing ξ(r_p, π) along and transversally to the line of sight. This way, only one variable (π) is affected by redshift distortions. On small scale: elongation along the line of sight (Finger-of-God effect) = due to peculiar velocities of galaxies in clusters On large scale : flattening along the line of sight (Kaiser effect) = due to coherent motions of galaxies falling towards clusters ξ(r_p, π) for the mean of 10 mock catalogs (0.3<z<0.5) Colourcoded level describe the degree of correlation as a function of r_p and π. Actual measurements are replicated over 4 quadrants

18 Projected correlation function We can recover real-space correlation function by projecting ξ(r_p, π) along the line of sight. This way we integrate out the line-of-sight effects and we obtain a quantity wp(r_p) that is independent of redshift space distortions (Davis & Peebles, 1983). If we now assume the power-law model ξ(r)=(r/r0)-γ, the integral can be computed analytically, given as a results: where Γ in Euler's Gamma function.

19 Projected corr. function (F22-F14-F10) Secure redshift (confidence >75%) <z> r_ F22 <z> r_ F14 <z> F10 wp(rp) for real data in 4 z-bins with best fit parameters F22: green F14: red F10: magenta gamma chi^ r_ gamma chi^ gamma chi^

20 CF Parameters (F22-F14-F10) Findings Clustering evolution: no clear evolution hints of r_0 increase with z step in γ between z=0.2 and z=0.4 Cosmic variance: different correlation lenght in different fields (effect > 3σ) question: effects of cosmological parameters?

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24 The CMB Power Spectrum

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