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Trapped Inflation

Daniel Green, Bart Horn, Leonardo Senatore, Eva Silverstein

TL;DR

Trapped inflation proposes a distinctive mechanism where particle production at many closely spaced points slows a scalar inflaton on a steep potential, enabling sustained inflation and a calculable perturbation spectrum. The authors develop novel methods to account for fluctuations in the produced particle ensemble and derive conditions under which $60$ e-folds with Gaussian perturbations are achieved, while predicting a significant equilateral non-Gaussian signal with $f_{\rm NL}^{\rm equilateral} \sim (\tilde{m}/H)^2$ (bounded by Planck data). In the concrete $V(\phi)=\frac{1}{2}m^2\phi^2$ case, they identify a viable parameter window with sub-Planckian field ranges and negligible tensor modes, and show how the mechanism can be embedded in string theory via monodromy in angular moduli. The framework yields a mildly red tilt $n_s \approx 0.99$ for $N_e \sim 55$, an extremely small $r$, and an equilateral-dominated non-Gaussian signature, offering a testable link between UV-complete string constructions and CMB observables.

Abstract

We analyze a distinctive mechanism for inflation in which particle production slows down a scalar field on a steep potential, and show how it descends from angular moduli in string compactifications. The analysis of density perturbations -- taking into account the integrated effect of the produced particles and their quantum fluctuations -- requires somewhat new techniques that we develop. We then determine the conditions for this effect to produce sixty e-foldings of inflation with the correct amplitude of density perturbations at the Gaussian level, and show that these requirements can be straightforwardly satisfied. Finally, we estimate the amplitude of the non-Gaussianity in the power spectrum and find a significant equilateral contribution.

Trapped Inflation

TL;DR

Trapped inflation proposes a distinctive mechanism where particle production at many closely spaced points slows a scalar inflaton on a steep potential, enabling sustained inflation and a calculable perturbation spectrum. The authors develop novel methods to account for fluctuations in the produced particle ensemble and derive conditions under which e-folds with Gaussian perturbations are achieved, while predicting a significant equilateral non-Gaussian signal with (bounded by Planck data). In the concrete case, they identify a viable parameter window with sub-Planckian field ranges and negligible tensor modes, and show how the mechanism can be embedded in string theory via monodromy in angular moduli. The framework yields a mildly red tilt for , an extremely small , and an equilateral-dominated non-Gaussian signature, offering a testable link between UV-complete string constructions and CMB observables.

Abstract

We analyze a distinctive mechanism for inflation in which particle production slows down a scalar field on a steep potential, and show how it descends from angular moduli in string compactifications. The analysis of density perturbations -- taking into account the integrated effect of the produced particles and their quantum fluctuations -- requires somewhat new techniques that we develop. We then determine the conditions for this effect to produce sixty e-foldings of inflation with the correct amplitude of density perturbations at the Gaussian level, and show that these requirements can be straightforwardly satisfied. Finally, we estimate the amplitude of the non-Gaussianity in the power spectrum and find a significant equilateral contribution.

Paper Structure

This paper contains 11 sections, 97 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Background Solution
  3. Perturbations
  4. Gaussian Perturbations
  5. Non-Gaussian Perturbations
  6. The case $V(\phi)= \frac{1}{2} m^2 \phi^2$
  7. Observational predictions
  8. $n_s$ and $r$
  9. Non-Gaussianity
  10. Trapped Inflation from String Theory
  11. Discussion

Figures (3)

  • Figure 1: A look at the contributions of the Green's function in eq. (\ref{['gftntilde']}) to the late-time power spectrum, for $\frac{\tilde{m}}{H} = 10$.
  • Figure 2: A numerical study of the shape $x_2^2 x_3^2 F(1,x_2,x_3)\over F(1,1,1)$ for the choice of parameters $\frac{\tilde{m}}{H} = 10$, plotted in the region $0 \leq x_2 \leq 1; 1 - x_2 \leq x_3 \leq x_2$. The peak in the equilateral limit is clearly visible.
  • Figure 3: Top: The allowed parameter window for the $m^2 \phi^2$ model. The red zones are forbidden by eq. (\ref{['conditions']}); the blue zones are forbidden by eq. (\ref{['deltacondition']}) and by the constraint (\ref{['NGconstraintm']}) on the size of the non-Gaussianities, to be discussed in the next section. The dashed line indicates the range of parameters for which $\phi/M_P\sim 1$, with super-Planckian field ranges above and sub-Planckian ranges below. Bottom: Same plot as above for a model with potential equal to $\mu^3\phi$. We do not give explicitly the constraints in the paper as they are very similar to the ones for the $m^2\phi^2$ model.