Planck 2018 Results. VI. Cosmological Parameters

Citation

Why this reference is included

Cited in

• Book V — Categorical Macrocosm Part 1
  Chapter The Distance Ladder Re-Read

  Two classes of measurements of the Hubble constant H_0 yield persistently discrepant values: Early-universe (``indirect'') route. The Planck satellite measures the CMB temperature anisotropies and fits them to the ΛCDM model

• Book V — Categorical Macrocosm Part 1
  Chapter Boundary Data: CMB and CνB as Constraint Surfaces

  The CMB as Temporal-Epoch Constraint Surface The cosmic microwave background was discovered by Penzias and Wilson in 1965 and mapped with exquisite precision by COBE (1992) , WMAP (2003–2010) , and Planck (2013–2018)

• Book V — Categorical Macrocosm Part 1
  Chapter Boundary Data: CMB and CνB as Constraint Surfaces

  The six-parameter fit (Ω_b h^2, Ω_c h^2, θ_*, τ_reion, n_s, A_s) that Planck reports is a valid empirical summary of Σ_CMB

• Book V — Categorical Macrocosm Part 3
  Chapter Dark Energy as Readout Artifact

  CMB anisotropy (WMAP , Planck ): the angular power spectrum is consistent with a spatially flat universe (Ω_total ≈ 1), which requires Ω_Λ ≈ 0.68 to balance Ω_m ≈ 0.31

• Book V — Categorical Macrocosm Part 5
  Chapter H₀ Tension Resolution and the ΛCDM Re-Read

  For over a decade, two classes of measurement have yielded discrepant values: ``early-universe'' methods (CMB analysis via Planck , BAO calibration) give H_0 ≈ 67.4 ± 0.5 km/s/Mpc, while ``late-universe'' methods (Cepheid-calibrated Type Ia supernovae via SH0ES and related programmes) give H_0 ≈ 73.0 ± 1.0 km/s/Mpc

• Book V — Categorical Macrocosm Part 5
  Chapter H₀ Tension Resolution and the ΛCDM Re-Read

  Two classes of measurement yield discrepant values (see abstract for the key numbers): Early-universe: Planck CMB analysis gives H_0 = 67.4 ± 0.5 km/s/Mpc (Planck 2018) ; BAO confirms via the sound horizon

• Book V — Categorical Macrocosm Part 6
  Chapter Inflation-as-Regime: No Inflaton Sector

  The scalar amplitude of primordial perturbations is: A_s = α_τ · ι_τ^14 · (1 - ι_τ^33) = 121225 ι_τ^18 · (1 - ι_τ^(τ^3)(τ^3)) = 2.096 × 10^-9, at -1979 ppm from Planck (2.100 × 10^-9)

• Book V — Categorical Macrocosm Part 6
  Chapter Inflation-as-Regime: No Inflaton Sector

  The spectral index inherits: n_s = 1 - 2N_e = 1 - 257 = 0.96491, at +13 ppm from the Planck measurement n_s = 0.9649 ± 0.0042

• Book V — Categorical Macrocosm Part 6
  Chapter The Threshold Ladder: From Baryogenesis to Recombination

  Result: η_B,τ = 6.080 × 10^-10; Planck CMB-only : η_B = (6.104 ± 0.058) × 10^-10; deviation = -10 320 ppm (∼1.1σ)

• Book V — Categorical Macrocosm Part 6
  Chapter The Threshold Ladder: From Baryogenesis to Recombination

  The baryon-to-photon ratio satisfies η_B = α · ι_τ^15 · 56 = 121270 ι_τ^19 ≈ 6.041 × 10^-10, in agreement with the Planck 2018 value η_B^Planck = (6.104 ± 0.058) × 10^-10 at -1.03% accuracy (-1.09σ)

• Book V — Categorical Macrocosm Part 7
  Chapter General Relativity as Emergent Geometry

  The CMB angular power spectrum (Planck, 2018) confirms the Friedmann–Lema\^itre–Robertson–Walker metric to high precision

• Book V — Categorical Macrocosm Part 7
  Chapter Inflation, the CMB, and Primordial Nucleosynthesis

  CMB Anomalies The Planck data reveals several low-significance anomalies in the CMB: Low quadrupole. The C_2 power is approximately 7× lower than the ΛCDM expectation

• Book V — Categorical Macrocosm Part 7
  Chapter Inflation, the CMB, and Primordial Nucleosynthesis

  The Planck 2018 value A_s = (2.100 ± 0.030) × 10^-9 gives a deviation of -1979 ppm (-0.2%)

• Book V — Categorical Macrocosm Part 7
  Chapter Inflation, the CMB, and Primordial Nucleosynthesis

  The Scalar Spectral Index: n_s = 1 - 2/57 The scalar spectral index is n_s = 1 - 2N_e = 1 - 257 = 5557 = 0.96491… The Planck 2018 measurement gives n_s = 0.9649 ± 0.0042

• Book V — Categorical Macrocosm Part 7
  Chapter Inflation, the CMB, and Primordial Nucleosynthesis

  The observed value η_B = (6.104 ± 0.058) × 10^-10 (Planck 2018) gives a deviation of -1.03%

• Book V — Categorical Macrocosm Part 7
  Chapter The Dark Sector Dissolved

  CMB angular power spectrum (Planck, 2018) confirms FLRW to high precision

Bibliographic Details