For a cosmic string in de Sitter spacetime, scalar particle creation probabilities are exponential Boltzmann factors, P = e^{-2π(Qq+(ε-qC0)/H)} for a point charge and P = e^{-2π ε/H} for a neutral string.
Vilenkin, Cosmic strings as gravitational lenses, The Astr
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Quantum Particle Creation by Cosmic Strings in de Sitter Spacetime
For a cosmic string in de Sitter spacetime, scalar particle creation probabilities are exponential Boltzmann factors, P = e^{-2π(Qq+(ε-qC0)/H)} for a point charge and P = e^{-2π ε/H} for a neutral string.