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Recombination
~42.7 Mly
Physical radius of the present observable volume at hydrogen recombination. Derived from the particle horizon and z*.
The universe used to be fog. When the fog cleared, the whole patch we can see today was only about forty-two million light-years across. Those first free photons are the cosmic microwave background.
What it supports
Standard ΛCDM arithmetic. Today the particle horizon is about 46.5 billion light-years. Planck 2018 puts photon decoupling at z* ≈ 1090, so a* ≈ 1/1091. 46.5 Gly / 1090 ≈ 42.7 Mly. Those photons are the cosmic microwave background. Age at last scattering is about 380,000 years (Planck: t* ≈ 373 kyr). The Book recovered the 42.7 on the archive plate beside GW231029 and M42.
What it does not
Not an exact 42. 46.5/1090 is 42.66, printed 42.7. The last-scattering surface today is a little inside the particle horizon, about 45.7 Gly, which scales to about 42 Mly. Two spheres. Parameters move with the cosmology.
Calculation
R_phys = a* · χ₀. χ₀ ≈ 46.5 Gly. a* = 1/(1+z*), z* ≈ 1090. 46.5 / 1090 ≈ 42.66 Mly ≈ 42.7 Mly. Last-scattering χ ≈ 45.7 Gly → ≈ 41.9 Mly.
ΛCDM particle horizon scaled by the recombination scale factor. Neighbor digits, not identity.
ExactnessDerived mathematics
Form42
UnitMly
Strengthhard
When~380 ka after the Big Bang