Slides of 5 lectures at XV Brazilian School on Cosmology and ...

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From smooth to lumpyUniverse was very smooth <strong>at</strong> time <strong>of</strong> last sc<strong>at</strong>tering;fluctu<strong>at</strong>ions in the fluid were tiny (δρ/ρ ∼ 10 −5 in photonsand baryons; ∼ 10 −4 ,10 −3 in non–baryonic dark m<strong>at</strong>ter).FLRW approxim<strong>at</strong>ion very good early on.Universe is very lumpy or inhomogeneous today.Recent surveys estim<strong>at</strong>e th<strong>at</strong> 40–50% <strong>of</strong> the volume <strong>of</strong>the universe is contained in voids <strong>of</strong> diameter 30h −1Mpc. [Hubble constant H 0= 100h km/s/Mpc] (Hoyle &Vogeley, ApJ 566 (2002) 641; 607 (2004) 751)Add some larger voids, and many smaller minivoids,and the universe is void–domin<strong>at</strong>ed <strong>at</strong> present epoch.Clusters <strong>of</strong> galaxies are strung in filaments and bubblesaround these voids.15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.6/143
Coarse-graining, averaging, backreactionCoarse-graining: Replace the the microphysics <strong>of</strong> agiven spacetime region by some collective degrees <strong>of</strong>freedom sufficient to describe physics on scales largerthan the coarse-graining scale. BOTTOM UP.Averaging: Consider overall macroscopic dynamics andevolution, without direct consider<strong>at</strong>ion <strong>of</strong> the details <strong>of</strong>the course-graining procedure. TOP DOWN.Often assumes the existence <strong>of</strong> a particular average,e.g., FLRW background, without showing th<strong>at</strong> suchan average exists.Backreaction: Consider the effects <strong>of</strong> departuresfrom the average, perturb<strong>at</strong>ive or nonperturb<strong>at</strong>ive, onthe average evolution.15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.7/143
Page 1 and 2: Cosmic structure, averaging anddark
Page 3 and 4: Lecture 1What is d
Page 5: 6df: voids & bubble walls (A. Faira
Page 9 and 10: Layers of coarse-g
Page 11 and 12: Coarse-graining: further steps(2)
Page 13 and 14: Dilemma of gravit<
Page 15 and 16: What is a cosmolog
Page 17 and 18: Largest typical structuresSurvey Vo
Page 19 and 20: Scale of st<strong
Page 21 and 22: I. Coarse-graining at</stro
Page 23 and 24: Korzyński’s covariant coarse-gra
Page 25 and 26: Averaging and backreactionAltern<st
Page 27 and 28: Approach 1: Weak backreactionMuch a
Page 29 and 30: Zalaletdinov’s macroscopic gravit
Page 31 and 32: Approach 3: Spatia
Page 33 and 34: The 3 + 1 decompositionn µN i dtdx
Page 35 and 36: Buchert-Ehlers-Carfora-Piotrkowska-
Page 37 and 38: III. Average spati
Page 39 and 40: Perturbative avera
Page 41 and 42: The Copernican principleRetain Cope
Page 43 and 44: What expands? Can
Page 45 and 46: Semi-tethered latt
Page 47 and 48: Thought experimentsaverage t = cons
Page 49 and 50: Finite infinityVirialized=0 θ>0Col
Page 51 and 52: Better formalism?CEP should be asso
Page 53 and 54: Two/three scale modelSplit sp<stron
Page 55 and 56: Other ingredients〈R〉 = k v /a v
Page 57 and 58:
Dust modelSpecialize to dust only;
Page 59 and 60:
Tracker solution limitParameters ǫ
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Physical interpretat</stron
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Physical interpretat</stron
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Dressed cosmological parametersH is
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Cosmic coincidence problem solvedSp
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Redshift, luminosity distancePerfor
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Void fraction, lapse functionThe vo
Page 73 and 74:
Age of universeThe
Page 75 and 76:
Magnitude of backr
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Test 1: SneIa luminosity distancesD
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Test 1: SneIa luminosity distancesT
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Smale + DLW, MNRAS 413 (2011) 367SA
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CMB anisotropiesPower in CMB temper
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Photon to baryon rat</stron
Page 87 and 88:
Li abundance anomalyBig-bangnucleos
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CMB - calibration
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Test 3: Baryon acoustic oscill<stro
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Dressed “comoving distance” D(z
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Equivalent “equat</strong
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Sahni, Shafieloo and Starobinsky Om
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Sahni, Shafieloo and Starobinsky Om
Page 101 and 102:
Baryon Acoustic Oscillat</s
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Gaztañaga, Cabre and Hui 0807.3551
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Redshift time drift (Sandage-Loeb t
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Clarkson, Bassett and Lu homogeneit
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Lecture 5Variance of</stron
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Result: arXiv:1201.5371v2CMB dipole
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Spherical averagesDetermine vari<st
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Analysis of COMPOS
Page 117 and 118:
Radial variance δH s = (H s − H
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But why try the LG frame?From viewp
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Angular varianceTwo approaches; fit
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Hubble variance: CMB frame15th <str
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Angular uncertainties LG frame15th
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Value of β in cz
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Dipole directionCMB frame: directio
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Correlation with r
Page 133 and 134:
Redshift-distance anisotropyAs long
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Why a strong CMB dipole?Ray tracing
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Towards a new formalismFor each she
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Large angle CMB anomalies?Anomalies
Page 141 and 142:
Comments on ISW amplitudeIntegr<str
Page 143:
ConclusionApparent cosmic acceler<s
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