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A thermal interpretation of the stochastic formalism of a slow-rolling scalarfield in a de Sitter (dS) universe is given. By introducing a notion ofemergent particles and a dual description of scalar fields, we show that thestochastic evolution of the infrared part of the field is equivalent to theBrownian motion in an abstract space filled with a heat bath of masslessparticles. The 1st slow-roll condition and the Hubble expansion are alsoreinterpreted in the abstract space as the speed of light and a transfer ofconserved energy, respectively. Inspired by this, we sketch the quantumemergent particles, which may realize the Hubble expansion by an exponentialparticle production. This gives another meaning of dS entropy as entropy perHubble volume in the global dS universe.

Emergent particles of de Sitter universe: thermal interpretation of the stochastic formalism and beyond