Gravity as Temporal Geometry IV: Origin of Time via Temporal Vacuum Decay

Description (concise)

A calculable “how” for a beginning of time.
In a time-first (lapse-first) formulation of gravity where one temporal potential Φ sets both proper time and expansion via dτ=eΦdt, a=e−Φ, and H=−Φ′, the Big Bang is not a singular point to evolve through. It is a boundary + transition: the high-Φ limit (Φ ⁣→ ⁣+∞) is a kinematic boundary where proper time is undefined; a universe begins when a finite-Φ region nucleates and Φ subsequently rolls, yielding ordinary FRW evolution with finite, selected initial data (no ad-hoc “just-so” start).

Abstract (technical, compact)

Paper IV in the Gravity as Temporal Geometry series. We formalize a time-first map in which a single lapse field Φcontrols both proper time and expansion (dτ=eΦdt,  a=e−Φ,  H=−Φ′). In this dictionary, the “origin of time” is a kinematic boundary at Φ→+∞; cosmology begins via a quantum nucleation-and-roll transition that selects finite FRW initial data {Φin,Φin′} by extremizing a Euclidean action in V(Φ). We give thin- and thick-wall rates (including the determinant prefactor) and treat the Hawking–Moss limit in dimensionally correct, equivalent forms.

Operationally, we derive a Birkhoff-style flux law in spherical symmetry that calibrates the time dial: changes in Φ are driven by energy flux across a sphere (full SI factors provided), yielding clean “no self-restart in spherical vacuum” corollaries and suggesting clock-network probes (flux-modulated redshift drift; universal dephasing). The FRW handoff is justified by symmetry/regularity at the bounce center: the induced 3-metric and extrinsic curvature are isotropic at leading order, so the first proper-time slice is an FRW representative without circular assumptions. We exhibit gauge-equivalence to Eddington–Finkelstein/Vaidya.

No new graviton DOFs: lapse and shift remain constraints (ADM); only the usual TT modes propagate. The result is a selection principle for initial conditions—finite and calculable—that replaces “singularity crossing” and ad-hoc starts with a boundary-plus-transition mechanism tied to observational and laboratory handles.

Significance: This work provides a concrete, testable mechanism for how time can start (boundary + quantum nucleation with selected FRW data) while remaining fully consistent with GR’s propagating content.

Series context

• Paper I: Gravity as Temporal Geometry: A Quantizable Reformulation of General Relativity (Zenodo: 10.5281/zenodo.16878019)

• Paper II: Experimental Signatures of Quantum Temporal Geometry (Zenodo: 10.5281/zenodo.16879129)

• Paper III: FRW Equivalence and Background Constraints (Zenodo: 10.5281/zenodo.16884232)