Anthropic Landscape 2D: Cosmological Constant Selection

Landscape Sampling

Vacua sampled 800

Prior range (decades of Λ) 4.0

Structure must form by z 4.0

Anthropic Selection

Vacua allowed

0 / 800

Allowed fraction

Median allowed Λ (× observed)

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How it works

Each point is a candidate vacuum drawn from a flat prior in the cosmological constant Λ, spanning a landscape of size 10^R × Λ_obs — this is the actual statistical assumption behind Weinberg's 1987 anthropic bound: because the string-theory landscape has an astronomical number of nearly-continuous vacua, a flat measure near Λ = 0 is the natural default, and it puts almost all vacua at large Λ.

Λ_i = U(0, 1) · 10^R · Λ_obs

Λ dominates expansion once (1+z_Λ)³ = (Λ / ρ_m0)
Galaxies need matter domination to survive to redshift z_gal, so:

  allowed  ⇔  Λ_i ≤ Λ_obs · (1+z_gal)³ / K,   K = (1+z_Λ,obs)³

with z_Λ,obs ≈ 0.3 calibrated to our own universe.

Vacua sampled — how many landscape points to draw each resample.
Prior range — how many decades of Λ the flat prior spans; wider ranges dilute the anthropically-allowed sliver.
Structure must form by z — how early galaxies need to condense; a higher redshift requirement tightens the bound and shrinks the allowed fraction.
Resample — draws a fresh landscape; glowing green points are anthropically allowed (a universe like ours could exist there), dim orange/red ones are Λ-dominated too early for any observer to form.
Scatter panel — drag to pan, scroll/pinch to zoom. The histogram below shows the same vacua binned by Λ with the anthropic threshold marked.

This is the actual logic behind Steven Weinberg's pre-1998 prediction that Λ should be small but nonzero — made before the accelerating expansion was observed. Only vacua that permit observers can ever be observed, so the fact we measure a tiny Λ is not surprising once the enormous majority of the landscape is anthropically sterile.

Anthropically allowed Λ too large — sterile

drag to pan · scroll to zoom