Standard Cosmology (ΛCDM)
What it claims: The standard cosmological model (ΛCDM: cosmological constant + cold dark matter) describes the universe’s large-scale expansion using GR’s Friedmann equations, $H^2=\frac{8\pi G}{3}\rho+\frac{\Lambda c^2}{3}$, with two components that dominate the energy budget but aren’t ordinary matter: cold dark matter (~27%) and dark energy via the cosmological constant $\Lambda$ (~68%).
Catalog status: split. The expansion framework itself is Proven Systems — Hubble’s original 1929 redshift-distance relation, the discovery of the Cosmic Microwave Background (Penzias & Wilson, 1965), and its precisely-measured acoustic peak structure (COBE, WMAP, and Planck) all confirm the broad expanding, cooling-universe picture with extraordinary precision, as does Big Bang nucleosynthesis’s match to observed light-element abundances. Accelerating expansion itself is directly measured (Riess et al., 1998; Perlmutter et al., 1999, 2011 Nobel Prize). But the literal nature of dark matter and dark energy — what they actually are, physically — is Unknowns: no dark matter particle has ever been directly detected, and $\Lambda$’s physical mechanism is unexplained. There’s also a real, currently unresolved discrepancy in the expansion rate itself: Planck’s CMB-based measurement gives $H_0\approx67.4$ km/s/Mpc, while local distance-ladder measurements (SH0ES) give $\approx73.0$ km/s/Mpc — the “Hubble tension,” a genuine open problem, not a rounding difference.
Where PBT touches this: Paper 9 uses the real Friedmann equation directly, proposing PBT’s own residual hierarchical energy density as the source of both $\rho_{eff}$ and $\Lambda$ — i.e., PBT’s specific hypothesis for what dark energy and dark matter’s effects physically are (see also Dark Matter Is the Medium). This is a genuine attempt at the real Unknown above, not a borrowed proven result — it hasn’t been tested against real lensing/CMB data. The 2026-07-21 audit found the paper’s derived $H_0\approx70$ km/s/Mpc doesn’t distinctly match either the Planck or SH0ES value (it sits between them, off both by ~4%), so it doesn’t currently resolve or align cleanly with either side of the tension.
References
- Hubble, E. (1929). “A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae.” PNAS 15, 168–173.
- Penzias, A.A., Wilson, R.W. (1965). “A Measurement of Excess Antenna Temperature at 4080 Mc/s.” Astrophys. J. 142, 419.
- Riess, A.G. et al. (1998). “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant.” Astron. J. 116, 1009.
- Perlmutter, S. et al. (1999). “Measurements of Ω and Λ from 42 High-Redshift Supernovae.” Astrophys. J. 517, 565.
- Planck Collaboration. (2020). “Planck 2018 results. VI. Cosmological parameters.” Astron. Astrophys. 641, A6.