Inflationary Potentials from the Exact Renormalisation Group

We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian for the UV theory at the Planck scale. We assume that the theory contains a scalar mode with suppressed coupling to other UV fields, and that higher derivative couplings are suppressed. The resulting effective potential gives rise to slow-roll inflation, which is fully consistent with the recent observations. As an example of how the proposed renormalisation group procedure works, we perform an explicit calculation in the $ϕ^4$ theory.

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