The Hubble parameter of the Local Distance Ladder from dynamical dark energy with no free parameters

Abstract: Our cosmology contains Big Bang relic fluctuations by a loss of time-translation symmetry on a Hubble time scale. The contribution to the vacuum is identified with dynamical dark energy $\Lambda\simeq \alpha_p\Lambda_0$ by an IR coupling $\alpha_p\sim \hbar$ of the bare cosmological constant $\Lambda_0\sim\hbar^{-1}$ consistent with general relativity, where $\hbar$ is the Planck constant. Described by the trace $J=(1-q)H^2$ of the Schouten tensor derived from a path integral formulation with gauged global phase, the proposed $J$CDM takes us beyond the $\Lambda$CDM limit of frozen $J=\Lambda$. The Hubble constant $H_0$ in $J$CDM is effectively $\sqrt{6/5}$ times the {\em Planck} value in $\Lambda$CDM analysis of the CMB according to $H(z)=H_0\sqrt{1+(6/5)\Omega_{M,0} Z_5(z) + \Omega_{r,0}Z_6(z)}/(1+z)$, where $Z_n=(1+z)^n-1$ given densities of matter $\Omega_{M,0}$ and radiation $\Omega_{r,0}$. With no free parameters, $J$CDM hereby agrees with the Local Distance Ladder when satisfying the BAO measured by {\em Planck}. On this cosmological background, galaxies possess an essentially $C^0$-transition to anomalous dynamics due to reduced inertia below the de Sitter scale of acceleration $a_{dS}=cH$, where $c$ is the velocity of light. This is confirmed in SPARC over a 6$\sigma$ tension in $\Lambda$CDM galaxy models, pointing to ultra-light CDM of mass $m_Dc^2<3\times 10^{-21}$eV. Sensitivity to this cosmological background explains the JWST 'Impossible galaxies' at cosmic dawn by rapid gravitational collapse. We comment on an outlook on future confrontations with observations by {\em Euclid}.