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Khronon inflation

Paolo Creminelli, Jorge Noreña, Manuel Peña, Marko Simonović

TL;DR

This paper investigates inflation with a full time-reparametrization (khronon) symmetry, promoting the inflaton redefinition to a symmetry that constrains the low-energy EFT to two leading derivative operators. In the decoupling limit, scalar perturbations exhibit Minkowski-like dynamics with a scale-invariant spectrum and a curvature perturbation $\zeta = -H\pi$, while the decaying mode decays as $1/a$, enabling potential but symmetry-suppressed deviations in squeezed limits. The 3-point function is dominated by a single equilateral-shaped contribution with amplitude $f_{NL}^{eq} = \frac{5}{108} \frac{1}{c_s^2}$, where $c_s^2 = M_\lambda^2/M_\alpha^2$, and the 4-point function arises only from exchange diagrams, with no leading contact-term contribution; the symmetry ensures consistency relations are preserved at leading order. Overall, Khronon inflation offers a highly constrained, ghost-inflation–like corner of the EFT of inflation, with sharp predictions tied to $P_\zeta$ and $c_s$, and observational signatures that pose a challenge to detect but remain conceptually distinctive.

Abstract

We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t \to \tilde t(t), or equivalently under field redefinition of the inflaton φ\to \tildeφ(φ). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k_L in the squeezed limit k_L \to 0 compared to the local shape.

Khronon inflation

TL;DR

This paper investigates inflation with a full time-reparametrization (khronon) symmetry, promoting the inflaton redefinition to a symmetry that constrains the low-energy EFT to two leading derivative operators. In the decoupling limit, scalar perturbations exhibit Minkowski-like dynamics with a scale-invariant spectrum and a curvature perturbation , while the decaying mode decays as , enabling potential but symmetry-suppressed deviations in squeezed limits. The 3-point function is dominated by a single equilateral-shaped contribution with amplitude , where , and the 4-point function arises only from exchange diagrams, with no leading contact-term contribution; the symmetry ensures consistency relations are preserved at leading order. Overall, Khronon inflation offers a highly constrained, ghost-inflation–like corner of the EFT of inflation, with sharp predictions tied to and , and observational signatures that pose a challenge to detect but remain conceptually distinctive.

Abstract

We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t \to \tilde t(t), or equivalently under field redefinition of the inflaton φ\to \tildeφ(φ). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k_L in the squeezed limit k_L \to 0 compared to the local shape.

Paper Structure

This paper contains 8 sections, 39 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Derivation of the action
  3. Power spectrum
  4. The 3-point function
  5. The 4-point function
  6. Conclusions and outlook
  7. Evolution after the field redefinition invariant phase
  8. Constraints and the validity of the decoupling limit

Figures (1)

  • Figure 1: We plot the shape of the part proportional to $1/c_s^2$ of the 3-point function, equation \ref{['3pf']}, as a function of the ratios between momenta $r_2 \equiv k_2/k_1$ and $r_3 \equiv k_3/k_1$, multiplied by $r_2^2 r_3^2$. The shape is normalized such that its amplitude is one at the equilateral point $r_2 = r_3 = 1$.