Tensor-Induced Backreaction in Ultra-Slow-Roll Inflation

Abstract

We discuss the impact of tensor-induced backreaction at second order in perturbation theory on primordial black holes production in single-field inflationary models, where the comoving curvature power spectrum is amplified by a transient ultra-slow-roll phase. Although the leading perturbative correction is mostly negligible in standard slow-roll evolution, it becomes important in non-attractor regimes, going in the direction of limiting the suppression of the first slow-roll parameter $\varepsilon$ and reducing the enhancement of the scalar power spectrum. We then go beyond the standard perturbative analysis by considering the background parameters as effective quantities with evolution self consistently determined by a closed system of backreaction equations. This analysis, which leads to a partial resummation of the effect beyond the perturbative treatment, confirms the limitation of the suppression of $\varepsilon$ by consistently showing how the effect remains important even after accounting for the effective evolution of the background in the evaluation of the backreaction itself. Finally, we discuss how, taking into account the tensor-induced backreaction, the fine-tuning associated with the value of the peak amplitude of the scalar power spectrum is strongly reduced.