The Big Idle: Emergent Late-Time Acceleration from Informational Saturation of a Scalar Field

We propose an effective scalar-field realization of the “Big Idle” framework, in whichlate-time cosmic acceleration is not attributed to a fundamental cosmological constant butto the asymptotic relaxation of a dynamical scalar field toward a state of maximal informational saturation. The scalar is related phenomenologically to a bounded informationalsaturation fraction I ∈ [0, 1), and evolves under a plateau potential that approaches a finiteconstant at large field values. In this limit, the field kinetic energy is damped by Hubblefriction, the equation of state approaches wϕ → −1, and the background expansion becomesasymptotically de Sitter-like. The cosmological equations are derived consistently from anaction principle, removing the dimensional ambiguities of earlier phenomenological versionsof the Big Idle idea. We show explicitly that the plateau regime satisfies ϵV , ηV → 0 andtherefore admits a controlled late-time slow-roll limit. The framework yields a simple dynamical dark-energy scenario with a natural informational interpretation and a potentiallytestable prediction: a small late-time deviation of w(z) from −1 as the field relaxes towardits asymptotic idle state.