Inflation from Covariant Signature Change: A Geometric Mechanism

Abstract

We present a covariant mechanism in which a smooth change of metric signature, from a Euclidean to a Lorentzian regime, drives a finite interval of accelerated expansion. The transition, encoded by a scalar interpolator along a timelike congruence, occurs on a codimension-one hypersurface where the continued metric is degenerate but curvature invariants remain finite, so the surface is curvature-regular. Using this covariant continuation, we rewrite the Einstein tensor of the continued metric as a localized, interpolator-dependent effective source for the post-transition Lorentzian branch, yielding a purely geometric stress tensor supported near the crossing. In the Lorentzian regime, we derive a model-independent, local criterion for acceleration: inflation persists while the interpolator's slope exceeds a critical value fixed by the extrinsic curvature and the spatial Ricci curvature on the initial hypersurface, and ends when this inequality is first saturated. Standard smooth profiles (tanh, generalized logistic, and power-law/arctan) admit closed-form expressions for the proper-time duration of the accelerated epoch, showing that, for fixed geometric data, the profile shape controls this duration. The construction provides a non-singular, inflaton-free route from a regular Euclidean origin to an early Lorentzian phase of accelerated expansion, in a manner compatible with no--boundary--type boundary conditions.