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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.