Ancient light
CMB · Planck
67.4 km/s/Mpc
Nearby stars
Distance ladder · SH0ES
73.0 km/s/Mpc
Share of total energy density (%) · vs scale factor a
Bare power law
With cut-off shell
Exponent n
3.5
No illusions, and no grand claims of solving the Hubble tension. What remains is an equation, an honest set of caveats, and an open question for anyone with the tools to test it.
The prediction
A structured bulk imprints a dark-radiation term scaling as a−n, not the a−4 of an empty bulk. For 3 < n < 4 it leaves a distinct shape evolving by (3.1)4−n between equality and recombination.
The honest catch
This is a background-expansion argument only — it tracks H(a), not the CMB power spectrum, where the proposals ultimately stand or fall. The profile ρ₅ ∝ (r₀/r)n is an ansatz imposed, not solved from the 5D field equations.
Not quite EDE
Early Dark Energy redshifts away faster than radiation after its peak. A bare power law with 3 < n < 4 dilutes more slowly — so it resembles EDE in name, not behaviour, unless the cut-off shell is engineered to mimic it.
In a Randall–Sundrum braneworld, assuming a power-law distribution for the bulk matter density, could the resulting generalised dark radiation, given a suitably structured bulk, behave in a way relevant to the Hubble tension?
Dr Mehzeb Chowdhury · June 2026 · CC BY 4.0
Builds on the modified Friedmann equation of Apostolopoulos & Tetradis (2004). DOI: 10.5281/zenodo.20602920
Regardless of what you find, please do let this non-physicist dreamer know.
Builds on the modified Friedmann equation of Apostolopoulos & Tetradis (2004). DOI: 10.5281/zenodo.20602920
Regardless of what you find, please do let this non-physicist dreamer know.