Renormalization-group techniques for single-field inflation in
  primordial cosmology and quantum gravity
  We study inflation as a "cosmic" renormalization-group flow. The flow, which
encodes the dependence on the background metric, is described by a running
coupling $\alpha $, which parametrizes the slow roll, a de Sitter free,
analytic beta function and perturbation spectra that are RG invariant in the
superhorizon limit. Using RG invariance as a guiding principle, we classify the
main types of flows according to the properties of their spectra, without
referring to their origins from specific actions or models. Novel features
include spectra with essential singularities in $\alpha $ and violations of the
relation $r+8n_{\text{t}}=0$ to the leading order. Various classes of
potentials studied in the literature can be described by means of the RG
approach, even when the action includes a Weyl-squared term, while others are
left out. In known cases, the classification helps identify the models that are
ruled out by data. The RG approach is also able to generate spectra that cannot
be derived from standard Lagrangian formulations.
