theorem 48.14 Linear growth of density perturbations
open in the book ·
parts/05-general-relativity-cosmology/07-cosmology.tex:1117
· p. 1332
Rests on
- depends_on equation 48.6 eq:cosmo-friedmann-1 ¶
- depends_on equation 31.10 eq:fluid-continuity ¶
- depends_on equation 31.19 eq:fluid-euler ¶
-
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 13.117 Metric tensor of signature $(p,q)$ ¶
- depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
-
depends_on
definition 13.153
Contractions
¶
-
depends_on
definition 44.2
Einstein tensor
¶
- proves proof ch:07-cosmology@proof-4 ¶
- proves proof ch:07-cosmology@proof-11 ¶
Supports
- depends_on phenomenon 48.16 Flat rotation curves and the missing mass ¶
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 |
→ | eq:cosmo-friedmann-1 | declared | parts/05-general-relativity-cosmology/07-cosmology.tex:1135 |
depends_on |
→ | eq:fluid-continuity | declared | parts/05-general-relativity-cosmology/07-cosmology.tex:1135 |
depends_on |
→ | eq:fluid-euler | declared | parts/05-general-relativity-cosmology/07-cosmology.tex:1135 |
depends_on |
→ | The Friedmann equations | declared | parts/05-general-relativity-cosmology/07-cosmology.tex:1135 |
depends_on |
← | Flat rotation curves and the missing mass | declared | parts/05-general-relativity-cosmology/07-cosmology.tex:1362 |
proves |
← | ch:07-cosmology@proof-11 | declared | parts/05-general-relativity-cosmology/07-cosmology.tex:1139 |