A simple mechanism for the enhancement of the inflationary power spectrum

TL;DR

The paper addresses how to generate large localized enhancements in the primordial curvature power spectrum without spoiling CMB observables. It introduces a minimal two-field inflation model with two energy-scale plateaux connected by a sharp transition, during which a sequence of turns transfers power from isocurvature to adiabatic modes, producing a peaked spectrum $\mathcal{P}_{\mathcal{R}}(k)$. The main contributions are the demonstration of the assisted enhancement mechanism, a detailed analysis of parameter dependencies, and the exploration of the resulting phenomenology for primordial black holes and scalar-induced gravitational waves, including non-Gaussianity considerations. The results suggest this mechanism is generic across a wide class of multi-field models and yields testable predictions for PTA and LISA, linking microphysical inflationary dynamics to small-scale structure and gravitational-wave signals.

Abstract

The background evolution in two-field inflation can feature two distinct stages, corresponding to the evolution along two successive field directions. When the second stage occurs at a significantly lower energy scale, the inflationary trajectory includes a sharp transition, accompanied by a series of rapid turns in field space. Fluctuations crossing the Hubble horizon during this turning phase can experience amplification by several orders of magnitude. This mechanism is very intuitive and can be implemented even in simple two-field models. It produces a peak in the scalar power spectrum that can lead to significant abundances of primordial black holes and secondary gravitational waves.

Figures (7)

• Figure 1: A schematic illustration of the proposed minimal mechanism, showing the qualitative shape of the inflationary potential and the corresponding field-space trajectory, with a zoom into the transition region. The two stages of inflation are indicated in the plot.
• Figure 2: The background solutions for $\chi(N)$ (black) and $\psi(N)$ (blue) for the model \ref{['equ:xsq']} with parameters $m_{\chi}^2=8 \times 10^{-12}$, $m_{\psi}^2=4 \times 10^{-7}$ and $c_w=4 \times 10^{-3}.$
• Figure 3: Left panel: The field trajectory shown on a logarithmic scale for the potential \ref{['equ:xsq']}, highlighting its evolution across different energy scales. Right panel: A zoomed-in view of the trajectory in field space during the transition stage, highlighting the multiple turns that characterize the two-field dynamics. Both axes are in Planck units.
• Figure 4: Left panel: The evolution of the parameter $W$ defined in \ref{['equ:cond']}. It is negative during the first stage of evolution, while large positive pulses occur during the transition stage. Right panel: For the Fourier mode $k_{\rm p} = 7.6 \times 10^{10} \ {\rm Mpc}^{-1}$ we plot $\mathcal{P}_{\mathcal{R}}(N)$ (blue) and $\mathcal{P}_{\mathcal{F}}(N)$ (yellow) for the same model.
• Figure 5: Left panel: A representative shape of the scalar power spectrum. Right panel: Three power spectra whose phenomenological implications for GWs and PBHs are discussed in Section \ref{['sec:PBHGW']}.