Speaker
Description
Addressing the Hubble Tension via Granular Metric Anchoring of Early Baryonic Gravitational Self-Energy
Stephan Walrand stephan.walrand@uclouvain.be ORCID: 0000-0002-0120-684X
In a recent publication, we derived a general relativity gauge-invariant solution modelling a granular universe composed of spherical bodies with a radial Gaussian density profile. In this framework, a cosmological constant (\Lambda ) emerges natively from the gravitational self-energy of these discrete nodes. Energy conservation dictates a uniform compactness ratio (M/R^2) across all bodies, a relation closely met by the elliptical galaxies containing most of the universe's stellar mass as shown in the GAMA survey. This setup yields:(\Lambda \approx \frac{1}{12 \pi^3} \left( \kappa c^2 \frac{M}{\sigma^2} \right)^2) which evaluates to (\Lambda = 0.9 \times 10^{-52}\text{ m}^{-2}) using the (\frac{M}{(1.17 \sigma)^2} \approx 7.1\text{ kg/m}^2) compactness measured in the GAMA survey. This predicted (\Lambda ) value is close to modern observations. Furthermore, the model predicts the (R = (1 + z)^{-1.5}) scaling confirmed by the 3D-HST+CANDELS survey and, unlike (\Lambda )CDM theory, the model preserves total energy conservation.
Shortly after the Big Bang, baryons moved freely between collisions, as did hydrogen atoms post-recombination until they became gravitationally bound to form clouds, and later, stars and galactic structures. In this early era, they can be considered independent metric sources like modern galaxies. Thus, conditions are met to apply the (\Lambda ) formula, which evaluates to (\Lambda_p = 7.37 \times 10^{-44}\text{ m}^{-2}) when using the proton compactness ratio obtained from the QCD gluon core radius containing most of the mass of the proton and hydrogen atoms. At (z \approx 500), growing density perturbations cross the Jeans instability threshold, initiating structured cloud formation that starts to relax the metric tension down to the modern baseline of (\Lambda = 1.24 \times 10^{-52}\text{ m}^{-2}).
Integrating the metric expansion across this dual regime, with the unbound-to-bound threshold chosen at (z \approx 125) while targeting the current Hubble constant of (H_0 = 73\text{ km/s/Mpc}), yields a perfect validation against the Planck cosmic microwave background angular scale (\theta^* = 0.010410\text{ rad}). The model also accurately predicts the DESI BAO data for the three more recent epochs, but less accurately for the Lyman-(\alpha ) forest epoch (14% deviation). However, this tension was cleared using a blackholes & quasars collapsing correction to the Hubble parameter modelled by the Lemaître-Tolman-Bondi metric. The model bypasses the need for an unexplained, speculative dark energy burst.