remark 13.161 rem:mfd-schur
open in the book ·
parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:7104
· p. 536
- remark -- no derivation owed by its kind
Rests on
No declared or derived dependency edges point away from this node yet.
Supports
-
depends_on
theorem 48.3
The Robertson–Walker metric
¶
-
depends_on
phenomenon 48.12
The relic microwave background
¶
-
depends_on
phenomenon 48.13
The anisotropy spectrum of the relic radiation
¶
- depends_on phenomenon 48.18 The Hubble tension ¶
-
tests
experiment
The Cosmic Microwave Background
¶
- cites (method) derived bib 24 Detection ofB-Mode Polarization at Degree Angular Scales by BICEP2 ¶
- cites (evidence) derived bib 24 Detection ofB-Mode Polarization at Degree Angular Scales by BICEP2 ¶ ↺
- cites (evidence) derived bib 10 Joint Analysis of BICEP2/Keck ArrayandPlanckData ¶
- cites (evidence) derived bib 10 Joint Analysis of BICEP2/Keck ArrayandPlanckData ¶ ↺
- cites (method) derived bib 15 Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season ¶
- cites (evidence) derived bib 15 Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season ¶ ↺
- cites (evidence) derived bib 15 Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season ¶ ↺
- cites (evidence) derived bib 15 Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season ¶ ↺
- cites (context) derived bib 15 Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season ¶ ↺
- cites (evidence) derived bib 15 Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season ¶ ↺
- cites (evidence) derived bib Planck 2018 results. VI. Cosmological parameters ¶
- cites (method) derived bib Planck 2018 results. VI. Cosmological parameters ¶ ↺
- … 109 more
-
depends_on
phenomenon 48.13
The anisotropy spectrum of the relic radiation
¶
- depends_on phenomenon 48.1 The Hubble–Lemaître law ¶
-
depends_on
phenomenon 51.6
Acoustic peaks, and a spatially flat universe
¶
- depends_on phenomenon 51.7 E-mode polarization, and no primordial B mode ¶
-
depends_on
proposition 48.7
Luminosity distance
¶
-
depends_on
corollary 48.8
Angular-diameter distance and the duality relation
¶
-
depends_on
phenomenon 48.15
A standard ruler in the galaxy distribution
¶
- depends_on phenomenon 103.68 The sum of the neutrino masses is bounded ¶
-
depends_on
phenomenon 48.15
A standard ruler in the galaxy distribution
¶
- depends_on phenomenon 48.17 The expansion is accelerating ¶
- depends_on phenomenon 48.18 The Hubble tension ¶ ↺
-
depends_on
corollary 48.8
Angular-diameter distance and the duality relation
¶
-
depends_on
phenomenon 48.12
The relic microwave background
¶
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 |
|---|---|---|---|---|
depends_on |
← | The Robertson–Walker metric | declared | parts/05-general-relativity-cosmology/07-cosmology.tex:240 |