Sampling the four-sphere

Hybrid Monte Carlo for λφ4 theory on Euclidean de Sitter space, S4. Every frame is a field configuration from the chain.

φ/H

Above: the field on the equatorial 2-sphere of S4 (drag to rotate). Below it: the same configuration on 2-spheres at latitudes χ, drawn to scale with radius R sin χ.

Zero mode φ̄ along the chain

chainhistogram of visited valuesStarobinsky–Yokoyama distribution

Running estimates after N configurations

running estimateits current valuepredictionprediction per shell68% and 95% of independent chains

trajectory 0 / — accepted — φ̄ = — ⟨φ̄²⟩ = — U = —
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