Large power spectrum and primordial black holes in the effective theory
  of inflation
  We study the generation of a large power spectrum, necessary for primordial
black hole formation, within the effective theory of single-field inflation.
The mechanisms we consider include a transition into a ghost-inflation-like
phase and scenarios where an exponentially growing mode is temporarily turned
on. In the cases we discuss, the enhancement in the power spectrum results from
either a swift change in some effective coupling or a modification of the
dispersion relation for the perturbations, while the background evolution
remains unchanged and approximately de Sitter throughout inflation. The
robustness of the results is guaranteed thanks to a weakly broken galileon
symmetry, which protects the effective couplings against large quantum
corrections. We discuss how the enhancement of the power spectrum is related to
the energy scale of the operators with weakly broken galileon invariance, and
study the limits imposed by strong coupling and the validity of the
perturbative expansion.
