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

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Past light cone averageInterpret solution <strong>of</strong> Buchert equ<strong>at</strong>ions by radial nullcone averageds 2 = −dt 2 + ā 2 (t) d¯η 2 + A(¯η,t) dΩ 2 ,where ∫ ¯η H0d¯η A(¯η,t) = ā 2 (t)V i (¯η H)/(4π).LTB metric but NOT an LTB solution15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.62/143
Physical interpret<strong>at</strong>ionConformally m<strong>at</strong>ch radial null geodesics <strong>of</strong> sphericalBuchert geometry to those <strong>of</strong> finite infinity geometrywith uniform local Hubble flow conditiondt = ā d¯η and dτ w = a w dη w . But dt = ¯γdτ w anda w = f wi −1/3 (1 − f v )ā. Hence on radial null geodesicsdη w =f wi 1/3 d¯η¯γ (1 − f v ) 1/3Define η w by integral <strong>of</strong> above on radial null-geodesics.Extend sp<strong>at</strong>ially fl<strong>at</strong> wall geometry to dressed geometryds 2 = −dτ 2 w+ a 2 (τ w ) [ d¯η 2 + r 2 w(¯η,τ w ) dΩ 2]where r w ≡ ¯γ (1 − f v ) 1/3 f wi −1/3 η w (¯η,τ w ), a = ā/¯γ.15th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.63/143
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Cosmic structure, averaging anddark
Page 3 and 4:
Lecture 1What is d
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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 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: 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
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Spherical averagesDetermine vari<st
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Analysis of COMPOS
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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
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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
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Comments on ISW amplitudeIntegr<str
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ConclusionApparent cosmic acceler<s
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