The Universal Expansion Clock (UEC) is a dimensionless, logarithmic spacetime coordinate derived from the cosmological scale factor in standard ΛCDM cosmology. Anchored at photon decoupling (recombination, redshift z ≈ 1089.92, scale factor a_dec ≈ 1/1100), the UEC is defined using the natural logarithm of the ratio between the cosmic scale factor at a given time and its value at recombination: UEC(t) = ln(a(t) / a_dec).

The UEC provides an observer-independent, timezone-free temporal reference for labeling moments across cosmic history. It reparameterizes existing cosmological time coordinates — including cosmic proper time, conformal time, and redshift — into an expansion-based clock, without introducing new physics, new laws, or new observables.

• Monotonic behaviour fully consistent with FLRW cosmology
• Compression of early-universe epochs with increased resolution at late times
• Applicability restricted to post-inflationary epochs where the cosmic scale factor is observationally constrained

For practical human-facing use, a non-normative projection layer termed the Human Epoch Window (HEW) is introduced. The HEW corresponds to a narrow decimal range of the UEC that spans the portion of cosmic expansion occurring over a typical human lifetime. The HEW does not alter the UEC definition and serves only as a conventional display and indexing scheme that bridges the cosmological coordinate to human temporal intuition for civil, archival, and educational contexts.

• Long-term archival timestamping
• Synchronization for interplanetary and interstellar missions
• Cosmology education and visualization
• Philosophical discussions of time
• Labeling in cosmic-scale simulations
The Human Epoch Window enables optional human-scale representations within these applications without compromising the universality of the underlying coordinate.

An optional high-precision unit system, termed Expansion Seconds (εs), subdivides the logarithmic expansion into fixed increments for scientific and archival use. At the present cosmic epoch, this subdivision is approximately comparable in magnitude to SI seconds through the Hubble rate (1 Earth second ≈ 2.18 εs), while remaining strictly a dimensionless refinement of the expansion coordinate.

Anchor εc: 6.99478 εc
Base εs: 6.99478012345678 × 10¹⁸ εs
Anchor date: 2 February 2026 — 20:20:00 UTC
Tick rate: 2.18 εs per Earth second
H₀: 67.4 km/s/Mpc (Planck 2018)

Photon Decoupling: −∞ (reference limit)
First Stars (z ≈ 18.45): −2.97 εc
Solar System (z ≈ 0.42): −0.35 εc
Present epoch: 6.99478 εc

This work is presented as a technical standard proposal intended to encourage discussion, implementation, and potential adoption of the Universal Expansion Clock as a universal expansion-based temporal reference.

Explore the entire history of the universe on an interactive 3D expanding spiral — from photon decoupling (0 εc) to the far future (7.5+ εc).

1 Earth second = 2.18 εs
1 εc = 10¹⁸ εs
The mapping is monotonically increasing and deterministic — every moment in cosmic history has a unique εc coordinate.

Convert any Earth date and time into Archival Precision (Es) — the full-resolution UEC timestamp with all decimal places.

For inquiries about the Universal Expansion Clock project, research collaboration, or technical questions:

Marko Misic
Universal Expansion Clock Project