phenomenon 48.18 The Hubble tension

Rests on

• depends_on equation 48.26 eq:cosmo-acoustic-scale ¶
• depends_on equation 48.15 eq:cosmo-luminosity-distance ¶
• depends_on phenomenon 48.13 The anisotropy spectrum of the relic radiation ¶
  • depends_on equation 48.24 eq:cosmo-temperature-scaling ¶
  • depends_on phenomenon 48.12 The relic microwave background ¶
    • depends_on equation 48.2 eq:cosmo-redshift-scale-factor ¶
    • 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 equation 13.83 eq:mfd-ecsgauss ¶
        • depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
        • proves proof ch:11-manifolds-tensors-curvature@proof-49 ¶
      • 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 proposition 13.140 Killing's equation ¶
        • depends_on proposition 13.154 Symmetries of the curvature ¶
        • proves proof ch:11-manifolds-tensors-curvature@proof-48 ¶
      • proves proof ch:07-cosmology@proof-2 ¶
    • proves proof ch:07-cosmology@proof-9 ¶
  • proves proof ch:07-cosmology@proof-10 ¶
• depends_on proposition 48.7 Luminosity distance ¶
  • depends_on equation 48.13 eq:cosmo-chi-of-z ¶
  • depends_on equation 48.2 eq:cosmo-redshift-scale-factor ¶ ↺
  • depends_on theorem 48.3 The Robertson–Walker metric ¶ ↺
  • proves proof ch:07-cosmology@proof-5 ¶
• proves proof ch:07-cosmology@proof-15 ¶

Supports

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