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Conventional and Unitarity-Conserving Peccei-Quinn Inflation Models and ACT

J. McDonald

Abstract

We compare conventional non-minimally coupled Peccei-Quinn (PQ) inflation with a version of the model in which unitarity conservation is imposed by additional Jordan frame interactions. Assuming instantaneous reheating, the unitarity-conserving model is within 1$σ$ agreement with the central value of the scalar spectral index reported by the ACT collaboration, whereas conventional PQ inflation is more than 2$σ$ below the ACT central value. In the case where dark matter is composed of axions and PQ symmetry is not restored after inflation, the axion isocurvature constraint of the unitarity-conserving model typically allows a much larger axion decay constant $f_{a}$ than the conventional model, with the conventional model upper bound being larger only if the PQ scalar self-coupling is extremely small, $λ< 10^{-12}$. For $λ= 0.1$, the axion isocurvature upper bounds are $f_{a} \leq 1.1 \times 10^{9} $ GeV for conventional PQ inflation and $f_{a} \leq 6.4 \times 10^{13}$ GeV for unitarity-conserving PQ inflation, with the latter bound being independent of $λ$. We also find a new isocurvature upper bound for conventional PQ inflation which is 650 times smaller than the existing bound. A modest reduction of the reheating temperature of the unitarity-conserving model from its maximum possible value will ensure that the PQ symmetry is not restored after inflation, allowing values of $f_{a}$ up to $6.4 \times 10^{13}$ GeV. Thus only the unitarity-conserving PQ inflation model allows $f_{a}$ to access values greater than the symmetry restoration cosmological upper bound $\sim 10^{12}$ GeV with naturally large values of the PQ scalar self-coupling.

Conventional and Unitarity-Conserving Peccei-Quinn Inflation Models and ACT

Abstract

We compare conventional non-minimally coupled Peccei-Quinn (PQ) inflation with a version of the model in which unitarity conservation is imposed by additional Jordan frame interactions. Assuming instantaneous reheating, the unitarity-conserving model is within 1 agreement with the central value of the scalar spectral index reported by the ACT collaboration, whereas conventional PQ inflation is more than 2 below the ACT central value. In the case where dark matter is composed of axions and PQ symmetry is not restored after inflation, the axion isocurvature constraint of the unitarity-conserving model typically allows a much larger axion decay constant than the conventional model, with the conventional model upper bound being larger only if the PQ scalar self-coupling is extremely small, . For , the axion isocurvature upper bounds are GeV for conventional PQ inflation and GeV for unitarity-conserving PQ inflation, with the latter bound being independent of . We also find a new isocurvature upper bound for conventional PQ inflation which is 650 times smaller than the existing bound. A modest reduction of the reheating temperature of the unitarity-conserving model from its maximum possible value will ensure that the PQ symmetry is not restored after inflation, allowing values of up to GeV. Thus only the unitarity-conserving PQ inflation model allows to access values greater than the symmetry restoration cosmological upper bound GeV with naturally large values of the PQ scalar self-coupling.

Paper Structure

This paper contains 16 sections, 82 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Conventional and Unitarity-Conserving PQ Inflation
  3. Conventional PQ Inflation
  4. Unitarity Violation in Conventional PQ inflation
  5. Unitarity-Conserving PQ Inflation
  6. Inflation predictions
  7. Conventional PQ inflation
  8. Unitarity-conserving PQ inflation
  9. General Analysis of Inflation
  10. Axion Isocurvature Constraints
  11. Conventional PQ inflation
  12. Unitarity-conserving PQ inflation
  13. PQ Symmetry Non-Restoration
  14. Conventional PQ Inflation
  15. Unitarity-Conserving PQ Inflation
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Scalar spectral index $n_{s}$ as a function of the non-minimal coupling $\xi$ for the conventional PQ inflation model (dotted curve, C) and for the unitarity-conserving model (solid curve, UC). The central value and 1$\sigma$ and 2$\sigma$ bounds from the ACT collaboration P-ACT-LB2 analysis are also shown.
  • Figure 2: Tensor-to-scalar ratio $r$ as a function of the non-minimal coupling $\xi$ for the conventional PQ inflation model (dotted curve, C) and the unitarity-conserving model (solid curve, UC). Dashed lines show the present observational upper bound, $r < 0.036$, and the magnitude that will be probed by next generation CMB experiments, $r = 10^{-3}$.
  • Figure 3: Inflaton self-coupling $\lambda$ as a function of the non-minimal coupling $\xi$ for the conventional PQ inflation model (dotted curve, C) and the unitarity-conserving model (solid curve, UC).
  • Figure 4: Axion isocurvature upper bound on $f_{a}$ in GeV for conventional PQ inflation (dotted line, C) and for unitarity-conserving PQ inflation (solid line, UC). The dashed line at $f_{a} = 10^{9} {\rm \ GeV}$ indicates the astrophysical lower bound and the dashed line at $f_{a} = 10^{12} {\rm \ GeV}$ indicates the cosmological upper bound in the case where PQ symmetry is restored after inflation.