Redshift-Dependent Expansion: Visualizing the Distance–CMB Difference

Same synthetic tracers, different fitted expansion histories

difference display ×8 z ≤ 1.8 constrained

ILLUSTRATIVE — radial differences exaggerated; not a literal spatial model of the Big Bang. Blue and red points show the same synthetic tracer projected through two fitted expansion histories. Connecting lines exaggerate the inferred radial difference for visibility. This is an illustrative embedding; cosmic expansion is not literally an explosion into surrounding space.

Space pause/resume · ←→ step redshift · R restart · S save PNG · C C2 reference · L pair lines · G graphs · E exaggeration · H help · drag rotate · wheel zoom

z = … … R distance sector C1 Planck reference C2 sensitivity ref

Expansion histories H(z) [km/s/Mpc]

Fitted endpoint histories. Blue band: constrained domain (z ≤ 1.8). Amber band: continuation-test region up to the z = 2.33 anchor. C2 is a sensitivity check on the same reference sky, not an independent confirmation.

Endpoint difference fields Δ = ln H − ln Href

Dashed gray: compact five-coordinate approximation (order 3). It captures the broad trend but not the exact ∼0.65 peak.

Validation: constrained order selection

Held-out error above the raw minimum (orders 2–6, constrained domain only). Dashed line: predeclared within-2 parsimony threshold — order 3 is selected although order 4 is lower by ∼0.13.

selected representationorder 3
constrained bootstrapP(select ≥ m3) = 0.216
projected Jacobianrank 5/5
condition number≈ 27
extra scaling = 0Δχ² = 0.124
ruler ratio R/C1≈ 0.92
Lyα z = 2.33continuation FAILED