The Present Hubble Horizon as a Radiative Decoupling Boundary

Hawking (1975) established that the Schwarzschild horizon has a thermal Planckian spectrum. In the ideal blackbody luminosity limit, this gives the reduced spherical normalization

X = (L / R²T⁴)(ℏ³c² / k_B⁴) = π³ / 15,

the Stefan–Boltzmann normalization reduced by the area of the unit sphere.

In spatially flat FLRW cosmology, the Hubble radius R_H = c/H coincides with the apparent horizon, and the standard definition of the vacuum fraction gives the dimensionless identity

Λ R_H² = 3Ω_Λ.

The proposal made here is not a modification of the Einstein or Friedmann equations, and not a determination of Λ alone. It is a boundary value for this existing dimensionless horizon combination:

Λ₀ R²_H,0 = π³ / 15.

The numerical coefficient is supplied by the reduced spherical blackbody normalization, while the cosmological slot in which it is placed is the standard combination Λ R_H².

It follows immediately that

Ω_Λ,0 = π³ / 45 ≃ 0.689,

Ω_m,0 = 1 − π³ / 45 ≃ 0.311.

Standard flat-FLRW kinematics then give

z_acc ≃ 0.643,

q₀ ≃ −0.534,

H₀t₀ ≃ 0.954,

corresponding to t₀ ≃ 13.85 Gyr for H₀ = 67.4 km s⁻¹ Mpc⁻¹.

The product Λ R_H²(z) follows the standard monotonic trajectory

0 → 1 → π³/15 → 3,

corresponding respectively to the matter-dominated past, the acceleration threshold, the present boundary value, and the asymptotic de Sitter limit. In this framework, the Schwarzschild horizon supplies the established thermal radiative anchor, while the Hubble horizon supplies the cosmological boundary on which the same reduced spherical normalization is tested.