Grabby Aliens Expansion Model — Omega Centauri Society

Hanson et al. 2021: civilisations appear at rate ∝ t^n and expand at fraction s of c — compute the volume fraction colonised, expected nearest distance, and date of first contact

Model Parameters

Three parameters fully specify the grabby aliens model: n (hard steps), s (expansion speed as fraction of c), and k (appearance rate normalization)

Hard steps n6

2 (fast)6 (Hanson est.)12 (slow)

Expansion speed s (fraction of c)0.50

1% c50%c99%c

Appearance rate constant log₁₀(k)−27.0

10⁻³⁵10⁻²⁷10⁻¹⁸

Appearance rate: dN/dV/dt = k × t^(n−1) [Gly⁻³ Gyr⁻¹]. Hanson et al. estimate n ≈ 6 from Earth's hard-step history. The constant k is calibrated by assuming ~1 GA in the Hubble volume just ahead of us.

OBSERVATIONAL CONSTRAINT

We observe no grabby alien volumes in our sky → f_GA < 1. The tool shows whether current parameters violate this constraint.

Grabby Aliens Census

Current snapshot at t = 13.8 Gyr

N_GA in Hubble volume

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grabby civilisations (total ever)

Mean GA origin age

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Gyr after Big Bang

Fraction of universe colonised

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of observable volume

Observable constraint?

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f_GA should be ≲ 1

Nearest GA distance

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Gly (expected nearest)

Time to first contact

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Gyr from now

Expansion Map (schematic, 2D projection)

Expanding discs represent GA volumes at t = 13.8 Gyr. Our position (⊕) is at centre.

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What the model says

Hanson et al. (2021) divide alien civilisations into "grabby" (those that expand rapidly, making visible and permanent changes to the volumes they enter) and "quiet" (those that stay home and are hard to detect). Grabby aliens are important because their expanding spheres prevent the emergence of other intelligent life in the captured volume.

The model has three parameters: (1) n, the number of "hard steps" that evolution must pass through to produce intelligence — estimated from Earth history at ~6; (2) s, the expansion speed as a fraction of c; and (3) k, the rate at which grabby civilisations appear per unit volume per unit time.

Key formulas

Appearance rate: dN/dV/dt = k × t^(n−1) [Gly⁻³ Gyr⁻¹], giving a power-law increase with cosmic time. The total number of GAs born in the Hubble volume by time t is N(t) ≈ k × t^n × V_H / n.

Volume per GA: V_GA(t_born) = (4π/3) × (s × c × (t_now − t_born))³. GAs born earlier claim more volume today.

Universe fraction claimed: f = N_GA × V_GA / V_H (summed over the distribution of birth times). The observation that we haven't been colonised constrains f ≲ 1.

Nearest GA distance: d ≈ n_GA^(−1/3) where n_GA = N_GA/V_H.

Time to first contact: t_contact = d/s (the expanding front of the nearest GA reaches us).

Calibration

Hanson et al. calibrate k by requiring roughly one GA in the Hubble volume ahead of us: k × t_now^n / n × V_H ≈ 1. (The denominator is n, not n+1 — see the rate formula above: ∫k t^(n−1) dt = k t^n/n.) At n=6, this gives k ≈ 2.3×10⁻¹² Gly⁻³ Gyr⁻¹ (logk ≈ −11.6). The previous placeholder of 10⁻²⁷ was 15 orders of magnitude too small and produced zero grabby aliens in the tool's output.

Connection to OCS themes

If grabby aliens exist, their expanding spheres would encounter any IMBH-based civilisation in Omega Centauri (if one were there). The expected time-to-contact at s=0.5c and nearest distance ~1 Gly is ~2 Gyr — potentially comparable to the lifetime of an MTH civilisation aestivating near OC's IMBH.

References

Hanson, R. et al. (2021). ApJ 922:182. DOI: 10.3847/1538-4357/ac2369 Carter, B. (1983). Phil. Trans. R. Soc. London A310:347. (Hard steps model)

v1.0 — 2026-06-02