Strongly Coupled Perturbations in Two-Field Inflationary Models

TL;DR

This work analyzes two-field inflation with non-canonical kinetic terms to understand how strong curvature–isocurvature coupling reshapes perturbation dynamics and EFT decoupling. By introducing a gelaton-like mechanism and a simple toy model, it shows that decoupling to a single-field EFT occurs when a heavy isocurvature mode is effectively integrated out, producing a reduced sound speed $c_s$ and altered power spectra, with the onset of the EFT governed by $\max\{m_{gel}/H, \sqrt{\xi}\}$. It reveals two distinct observational routes: horizon crossing inside the EFT yields DBI-like predictions with $\mathcal{P}_{\mathcal{R}} \propto 1/c_s$, while crossing outside yields coupling-dominated enhancements or suppressions, and it derives a lower bound $c_s^2 \gtrsim 1/(4\xi)$ under EFT validity. The results highlight that large couplings can drive significant, model-dependent deviations from canonical single-field expectations and motivate further exploration of nonlinear and UV-complete realizations.

Abstract

We study models of inflation with two scalar fields and non-canonical kinetic terms, focusing on the case in which the curvature and isocurvature perturbations are strongly coupled to each other. In the regime where a heavy mode can be identified and integrated out, we clarify the passage from the full two-field model to an effectively single-field description. However, the strong coupling sets a new scale in the system, and affects the evolution of the perturbations as well as the beginning of the regime of validity of the effective field theory. In particular, the predictions of the model are sensitive to the relative hierarchy between the coupling and the mass of the heavy mode. As a result, observables are not given unambiguously in terms of the parameters of an effectively single field model with non-trivial sound speed. Finally, the requirement that the sound horizon crossing occurs within the regime of validity of the effective theory leads to a lower bound on the sound speed. Our analysis is done in an extremely simple toy model of slow-roll inflation, which is chosen for its tractability, but is non-trivial enough to illustrate the richness of the dynamics in non-canonical multi-field models.

Figures (4)

• Figure 1: Numerical results for the evolution of perturbations calculated in the full two-field system (from (\ref{['eomgel0']}) in the limit of constant $\xi$ and $3\eta_{ss}$) for the first set of parameters in Table \ref{['tab:par']}: $\xi=300$ and $m^2_\mathrm{gel}/H^2=100$. For this case $c_s^2=2.7\cdot10^{-4}$. Left panel: black lines are the real and imaginary parts of both components of the solution of eq. (\ref{['eomgel0']}), corresponding to final curvature perturbations. Gray lines show the real and imaginary parts of the effective single-field solution $u_\mathrm{eff}$ given by (\ref{['expa3']}). Normalizations and overall phases are chosen so that the imaginary parts vanish toward the end of inflation. Right panel: evolution of the instantaneous curvature and isocurvature perturbations shown in terms of the instantaneous power spectra, as described in the text. $N=0$ corresponds to the Hubble radius exit. Shaded areas, labeled A, B and C, indicate the ranges $-k\tau<\xi$, $-k\tau<1/c_s$ and $-k\tau< m_\mathrm{gel}/H$, respectively, while the vertical dotted line corresponds to $-k\tau = \sqrt\xi$. The black solid (gray dashed) lines correspond to curvature (isocurvature) perturbations; the short-dashed (green) line is the solution (\ref{['expa3']}) with normalization satisfying the Wronskian condition. All results are normalized to the final value of the single-field, $c_s=1$ solution, which is shown as the solid gray (orange) line ending at 1.
• Figure 2: The same as in Figure \ref{['fgel2']}; numerical results for the evolution of perturbations calculated from (\ref{['eomgel0']}) in the limit of constant $\xi$ and $3\eta_{ss}$ for the second set of parameters in Table \ref{['tab:par']}: $\xi=300$ and $m^2_\mathrm{gel}/H^2=5000$ (corresponding to $c_s^2=1.4\cdot10^{-2}$).
• Figure 3: Predictions for the power spectrum of the curvature perturbations (normalized to the single-field result) as a function of the gelaton mass parameter $m_\mathrm{gel}^2=(3\eta_{ss}-2\xi^2)H^2$ for different values of $\xi=10,\,30,\,100,\,300,\,1000$. Black solid lines show the numerical results for the evolution of the perturbations in the full two-field system, calculated from (\ref{['eomgel0']}) in the limit of constant $\xi$ and $3\eta_{ss}$. Red dotted lines correspond to our analytic estimates (\ref{['sest']}) and (\ref{['sest1']}) (with the proportionality constant in (\ref{['sest1']}) set to 3). Green short-dashed lines correspond to the estimate (\ref{['sest']}) outside the limits of its applicability.
• Figure 4: Left panel: Evolution of the instantaneous curvature and isocurvature perturbations, obtained by solving (\ref{['eomgel0']}), shown in terms of the instantaneous power spectra, as described in the text. Solid (dashed) lines are the (iso)curvature perturbations. We show results for $\xi=10$ and $3\eta_{ss}=100,\,200.1,\,210,\,10^3,\,10^4$ (top to bottom for the curvature perturbations, left to right for the isocurvature perturbations). The overall normalization is such that 1 corresponds to a late-time power spectrum for a massless scalar field in the de Sitter space. Right panel: Predictions for the curvature perturbations normalized to the single-field result given in (\ref{['psf']}), obtained by solving (\ref{['eomgel0']}). In both panels $N=0$ corresponds to the Hubble radius exit, the results are obtained in the limit of constant $\xi$ and $\eta_{ss}$.