phenomenon 51.7 E-mode polarization, and no primordial B mode
open in the book ·
parts/05-general-relativity-cosmology/10-exp-cmb.tex:824
· p. 1382
- phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt
Rests on
-
depends_on
phenomenon 51.6
Acoustic peaks, and a spatially flat universe
¶
-
depends_on
phenomenon 65.3
Thomson scattering
¶
- proves derived proof ch:08-radiation-scattering@proof-2 ¶
-
depends_on
theorem 48.3
The Robertson–Walker metric
¶
-
depends_on
proposition 13.162
Curvature induced on the quadric
¶
-
depends_on
definition 13.119
Induced metric
¶
- depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
- depends_on equation 13.83 eq:mfd-ecsgauss ¶
-
depends_on
theorem 13.152
Riemann tensor; Ricci identity with torsion
¶
- depends_on definition 13.145 Affine connection ¶
- depends_on definition 13.147 Torsion ¶
- depends_on proposition 7.105 Clairaut–Schwarz ¶
- proves proof ch:11-manifolds-tensors-curvature@proof-42 ¶
- proves proof ch:11-manifolds-tensors-curvature@proof-49 ¶
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depends_on
definition 13.119
Induced metric
¶
- depends_on remark 13.161 rem:mfd-schur ¶
-
depends_on
theorem 13.160
Maximal symmetry forces constant curvature
¶
-
depends_on
definition 13.153
Contractions
¶
- depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
- depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶ ↺
-
depends_on
proposition 13.140
Killing's equation
¶
- depends_on definition 13.139 Killing vector ¶
- depends_on definition 13.149 Metric compatibility ¶
- depends_on proposition 13.127 Component formulas ¶
- depends_on theorem 13.150 Levi-Civita connection and contorsion ¶
- depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶ ↺
- proves proof ch:11-manifolds-tensors-curvature@proof-37 ¶
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depends_on
proposition 13.154
Symmetries of the curvature
¶
- depends_on definition 13.149 Metric compatibility ¶ ↺
- depends_on proposition 13.157 Bianchi identities ¶
- depends_on theorem 13.150 Levi-Civita connection and contorsion ¶ ↺
- depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶ ↺
- proves proof ch:11-manifolds-tensors-curvature@proof-43 ¶
- proves proof ch:11-manifolds-tensors-curvature@proof-48 ¶
-
depends_on
definition 13.153
Contractions
¶
- proves proof ch:07-cosmology@proof-2 ¶
-
depends_on
proposition 13.162
Curvature induced on the quadric
¶
-
depends_on
theorem 48.5
The Friedmann equations
¶
- depends_on equation 48.3 eq:cosmo-flrw-metric ¶
- depends_on equation 48.5 eq:cosmo-perfect-fluid ¶
-
depends_on
postulate 44.3
Einstein field equations
¶
-
depends_on
definition 44.2
Einstein tensor
¶
- depends_on definition 13.153 Contractions ¶ ↺
-
depends_on
definition 44.2
Einstein tensor
¶
- proves proof ch:07-cosmology@proof-4 ¶
- proves proof ch:10-exp-cmb@proof-5 ¶
-
depends_on
phenomenon 65.3
Thomson scattering
¶
- depends_on phenomenon 65.3 Thomson scattering ¶ ↺
- proves proof ch:10-exp-cmb@proof-6 ¶
Supports
Nothing declares a dependency on this node yet.
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
cites
(evidence) |
→ | Detection ofB-Mode Polarization at Degree Angular Scales by BICEP2 | derived | parts/05-general-relativity-cosmology/10-exp-cmb.tex:838 |
cites
(evidence) |
→ | Joint Analysis of BICEP2/Keck ArrayandPlanckData | derived | parts/05-general-relativity-cosmology/10-exp-cmb.tex:840 |
cites
(evidence) |
→ | Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season | derived | parts/05-general-relativity-cosmology/10-exp-cmb.tex:841 |
cites
(evidence) |
→ | Planck 2018 results. VI. Cosmological parameters | derived | parts/05-general-relativity-cosmology/10-exp-cmb.tex:834 |
cites
(evidence) |
→ | NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: FINAL MAPS AND RESULTS | derived | parts/05-general-relativity-cosmology/10-exp-cmb.tex:834 |
cites
(evidence) |
→ | Detection ofB-Mode Polarization in the Cosmic Microwave Background with Data from the South Pole Telescope | derived | parts/05-general-relativity-cosmology/10-exp-cmb.tex:836 |
cites
(evidence) |
→ | Detection of polarization in the cosmic microwave background using DASI | derived | parts/05-general-relativity-cosmology/10-exp-cmb.tex:828 |
depends_on |
→ | Acoustic peaks, and a spatially flat universe | declared | parts/05-general-relativity-cosmology/10-exp-cmb.tex:842 |
depends_on |
→ | Thomson scattering | declared | parts/05-general-relativity-cosmology/10-exp-cmb.tex:842 |
proves |
← | ch:10-exp-cmb@proof-6 | declared | parts/05-general-relativity-cosmology/10-exp-cmb.tex:845 |