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

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Notions <strong>of</strong> average sp<strong>at</strong>ial homogeneityHow do we define average sp<strong>at</strong>ial homogeneity?Assumption <strong>of</strong> FLRW average is restrictive, demanding3 separ<strong>at</strong>e notions:1. Average sp<strong>at</strong>ial homogeneity is described by class <strong>of</strong>ideal comoving observers with synchronized clocks.2. Average sp<strong>at</strong>ial homogeneity is described byaverage surfaces <strong>of</strong> constant sp<strong>at</strong>ial curv<strong>at</strong>ure.3. The expansion r<strong>at</strong>e <strong>at</strong> which the ideal comovingobservers separ<strong>at</strong>e within the hypersurfaces <strong>of</strong>average sp<strong>at</strong>ial homogeneity is uniform.No need to demand all <strong>of</strong> these notions must holdtogether15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.38/143
Perturb<strong>at</strong>ive average homogeneityBardeen (1980) described gauge invariant FLRWperturb<strong>at</strong>ions in different foli<strong>at</strong>ions which take one orother property as more fundamentalcomoving hypersurfaces (and rel<strong>at</strong>ed synchronousgauge) embody (1)minimal shear hypersurfaces (and rel<strong>at</strong>ed Newtoniangauge) are one type <strong>of</strong> foli<strong>at</strong>ion rel<strong>at</strong>ed to (2)uniform Hubble flow hypersurfaces embody (3)Bičak, K<strong>at</strong>z & Lynden-Bell (2007) consider Machianfoli<strong>at</strong>ions (LIF coords uniquely determined by δT µ ν):uniform 3 R hypersurfaces – embody (2)minimal shear hypersurfacesuniform Hubble flow hypersurfaces plus minimal shiftdistortion gauge condition <strong>of</strong> Smarr and York (1978)15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.39/143
Page 1 and 2: Cosmic structure, averaging anddark
Page 3 and 4: Lecture 1What is d
Page 5 and 6: 6df: voids & bubble walls (A. Faira
Page 7 and 8: Coarse-graining, averaging, backrea
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: III. Average spati
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
Page 61 and 62: Physical interpretat</stron
Page 63 and 64: Physical interpretat</stron
Page 65 and 66: Dressed cosmological parametersH is
Page 67 and 68: Cosmic coincidence problem solvedSp
Page 69 and 70: Redshift, luminosity distancePerfor
Page 71 and 72: Void fraction, lapse functionThe vo
Page 73 and 74: Age of universeThe
Page 75 and 76: Magnitude of backr
Page 77 and 78: Test 1: SneIa luminosity distancesD
Page 79 and 80: Test 1: SneIa luminosity distancesT
Page 81 and 82: Smale + DLW, MNRAS 413 (2011) 367SA
Page 83 and 84: CMB anisotropiesPower in CMB temper
Page 85 and 86: Photon to baryon rat</stron
Page 87 and 88: Li abundance anomalyBig-bangnucleos
Page 89 and 90:
CMB - calibration
Page 91 and 92:
Test 3: Baryon acoustic oscill<stro
Page 93 and 94:
Dressed “comoving distance” D(z
Page 95 and 96:
Equivalent “equat</strong
Page 97 and 98:
Sahni, Shafieloo and Starobinsky Om
Page 99 and 100:
Sahni, Shafieloo and Starobinsky Om
Page 101 and 102:
Baryon Acoustic Oscillat</s
Page 103 and 104:
Gaztañaga, Cabre and Hui 0807.3551
Page 105 and 106:
Redshift time drift (Sandage-Loeb t
Page 107 and 108:
Clarkson, Bassett and Lu homogeneit
Page 109 and 110:
Lecture 5Variance of</stron
Page 111 and 112:
Result: arXiv:1201.5371v2CMB dipole
Page 113 and 114:
Spherical averagesDetermine vari<st
Page 115 and 116:
Analysis of COMPOS
Page 117 and 118:
Radial variance δH s = (H s − H
Page 119 and 120:
But why try the LG frame?From viewp
Page 121 and 122:
Angular varianceTwo approaches; fit
Page 123 and 124:
Hubble variance: CMB frame15th <str
Page 125 and 126:
Angular uncertainties LG frame15th
Page 127 and 128:
Value of β in cz
Page 129 and 130:
Dipole directionCMB frame: directio
Page 131 and 132:
Correlation with r
Page 133 and 134:
Redshift-distance anisotropyAs long
Page 135 and 136:
Why a strong CMB dipole?Ray tracing
Page 137 and 138:
Towards a new formalismFor each she
Page 139 and 140:
Large angle CMB anomalies?Anomalies
Page 141 and 142:
Comments on ISW amplitudeIntegr<str
Page 143:
ConclusionApparent cosmic acceler<s
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