The Large Number Coincidence, The Cosmic Coincidence and the Critical Acceleration

Abstract

The coincidence problem among the pure numbers of order near 10^{40} is resolved with the Raychaudhuri and Friedmann-Robertson-Lemaitre-Walker equations and a trivial relationship involving the fine structure constant. The fact that the large number coincidence occurs only in the same epoch in which other coincidences among cosmic parameters occur could be considered a distinct coincidence problem suggesting an underlying physical connection. A natural set of scaling laws for the cosmological constant and the critical acceleration are identified that would resolve the coincidence among cosmic coincidences.