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

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Coarse-graining: first steps(1) → (2) (fluid → universe, star etc): Realm <strong>of</strong> EFEs“m<strong>at</strong>ter tells space how to curve” – well-established forearly universe; vacuum geometries; starting point fordefining neutron stars etc(2) → (3) (isol<strong>at</strong>ed Schwarzschild, Kerr geometry →particle in fluid):Replace Weyl curv<strong>at</strong>ure → Ricci curv<strong>at</strong>ureNo formal coarse-graining solution; but reasonableto assume possible in terms <strong>of</strong> ADM-like mass (see,e.g., Korzyński 2010)Even for 2 particles, gravit<strong>at</strong>ional energy (bindingenergy etc) necessarily involvedNeglect inter-particle interactions → dustapproxim<strong>at</strong>ion15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.10/143
Coarse-graining: further steps(2) → (3) (stars, gas → galaxies):Newtonian gravity usually assumedCooperstock and Tieu (2006,2007): claimednon-Newtonian properties possible for rigidly rot<strong>at</strong>ingdust (van Stockum metrics)Neill and DLW (in prepar<strong>at</strong>ion): new van Stockummetrics for empirically observed density pr<strong>of</strong>iles donot solve galaxy rot<strong>at</strong>ion curve problem(3) → (4) (galaxies → galaxy clusters):Newtonian gravity, viral theorem usually assumedVirial theorem studied formally only in GRRealistic solutions not known; given Lemaître–Tolman–Bondi (LTB) solutions inapplicable15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.11/143
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: Layers of coarse-g
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
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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