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Inflationary potentials from the exact renormalisation group. (English) Zbl 1342.83533

Summary: 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 in the UV, which we take to be somewhere below the Planck scale to avoid discussing quantum gravity effects. We assume that the theory contains a scalar mode with suppressed coupling to other fields, and that higher derivative couplings are suppressed. In this framework the exact RG equation becomes a one-dimensional Schrödinger equation, which we solve. The effective IR potential is then dominated by the eigen-states of the RG Hamiltonian with the highest eigenvalues. We find that these potentials can generically give rise to slow-roll inflation, which is fully consistent with recent observations. As an example of how the proposed renormalisation group procedure works, we perform an explicit calculation in the \(\phi^4\) theory in an appendix.

MSC:

83F05 Relativistic cosmology
81T10 Model quantum field theories
81T17 Renormalization group methods applied to problems in quantum field theory
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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