Why the Universe Is Flat: The Flatness Problem from Wave Information

The observed flatness of the universe is one of the classic fine-tuning problems in cosmology. In standard Big Bang cosmology, the curvature density grows with time, requiring the early universe to be flat to one part in 10^60 to match today's limits. Inflation solves this by exponential expansion, but requires an inflaton field and 60 e-folds of slow-roll.

The canvas model provides a different solution. Flatness follows directly from the wave information postulate. At the Planck epoch, the cosmic horizon had an area of order the Planck length squared, giving an information capacity of only about 10 bits. These bits were required to specify the existence of spacetime itself—the formation of the voxel lattice and the cosmological constant. No information remained to specify spatial curvature. The universe began exactly flat because there was no information capacity to be otherwise.

Once flat, the Friedmann equations preserve flatness. Could quantum fluctuations generate curvature later? The amplitude of any fluctuation is bounded by the same information limit that sets the cosmological constant. The maximum possible curvature from fluctuations is one part in 10^122—completely negligible.

The universe is flat because it cannot be otherwise. No inflation required. No fine-tuning. Just the finite information capacity of the cosmic horizon at the Planck epoch. This joins the cosmological constant, the arrow of time, and the low initial entropy as consequences of the same principle.