A Geometric Origin for the Cosmic Baryon Fraction

The cosmic baryon fraction is derived here from horizon geometry once the cosmological horizon is admitted as a thermodynamic boundary.

Starting from

ΛR_H² = π³/15

with

R_H = c/H₀,

one has

Ω_Λ,0 = π³/45

and, under spatial flatness,

Ω_m,0 = 1 − π³/45.

The baryonic fraction is then written as

Ω_b,0 = Ω_m,0 / 2π,

which gives

Ω_b,0 = (1 − π³/45) / 2π ≈ 0.04949.

The complementary non-baryonic fraction follows as

Ω_c,0 = Ω_m,0 − Ω_b,0,

and the corresponding sector ratio is

Ω_c,0 / Ω_b,0 = 2π − 1.

In this form, the baryon fraction is not introduced as an independent fitted parameter, but follows once the horizon construction has fixed the total matter sector and the baryonic share is identified with the one-sided radiative domain of the boundary. The derived value of Ω_b,0 lies at the level of the measured cosmological baryon abundance.