H_0

The Hubble constant

The tension between the "Planck" value ($H_0 \approx 67.4$) and the "local" Cepheid/SH0ES value ($\approx 73$) is one of the open problems of modern cosmology.

In PT, the predicted value is:

$$ H_0 = 67.41 \pm 0.45\ \text{km/s/Mpc}. $$

That is, the Planck side of the tension, 0.08% from the Planck 2018 central value.

PT formula

$$ \rho_\Lambda = (1 + e^{-1}) \cdot m_e^4 \cdot (m_e/m_P)^{3/2} $$

where $m_e$ is the electron mass, $m_P$ the Planck mass. This dark-energy density (no fitted parameter) yields:

$$ \Omega_\Lambda = 0.6889, \quad \Omega_m = 0.3111, \quad H_0 = 67.41\ \text{km/s/Mpc}. $$

Epistemic status

In PT, $H_0$ is a consequence of cosmology at the fixed point $\mu^* = 15$, not a free cosmological parameter. It depends only on particle-physics constants ($m_e$, $m_P$) and sieve structure.

Prediction: the Planck/SH0ES tension will resolve on the Planck side. If SH0ES converges to ~73 with better systematics, PT falls.

Audit: see App. P §C9 for alternative Dark Energy routes and critique of the first promotion (route B downgraded to [PRED-candidate]).