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Gravitational positivity bounds

Junsei Tokuda, Katsuki Aoki, Shin'ichi Hirano

TL;DR

The paper analyzes how positivity bounds, foundational for linking low-energy EFTs to UV completions, survive in the presence of a massless graviton by invoking Regge behavior to cancel the graviton t-channel pole. It shows that strict positivity can be violated by a finite, UV-sensitive amount suppressed by M_pl^{-2} α', making the bounds most reliable when the EFT cutoff is far below the Regge scale and demonstrates how to derive approximate positivity for scalar-tensor EFT at one loop. Through detailed mapping to general scalar-tensor actions and DHOST theories, the work provides explicit conditions on EFT coefficients and DHOST functions, with implications for cosmology and gravitational phenomenology, including GW constraints. The results offer a framework for applying positivity bounds to gravity-coupled EFTs while highlighting the need for knowledge of UV completion to interpret potential violations.

Abstract

We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic $t$-channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with "wrong" sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. This violation is suppressed by $M_{\rm pl}^{-2}α'$ where $α'$ is the scale of Reggeization. This implies that the positivity bounds can be applied only when the cutoff scale of EFT is much lower than the scale of Reggeization. We then obtain the positivity bounds on scalar-tensor EFT at one-loop level. Implications of our results on the degenerate higher-order scalar-tensor (DHOST) theory are also discussed.

Gravitational positivity bounds

TL;DR

The paper analyzes how positivity bounds, foundational for linking low-energy EFTs to UV completions, survive in the presence of a massless graviton by invoking Regge behavior to cancel the graviton t-channel pole. It shows that strict positivity can be violated by a finite, UV-sensitive amount suppressed by M_pl^{-2} α', making the bounds most reliable when the EFT cutoff is far below the Regge scale and demonstrates how to derive approximate positivity for scalar-tensor EFT at one loop. Through detailed mapping to general scalar-tensor actions and DHOST theories, the work provides explicit conditions on EFT coefficients and DHOST functions, with implications for cosmology and gravitational phenomenology, including GW constraints. The results offer a framework for applying positivity bounds to gravity-coupled EFTs while highlighting the need for knowledge of UV completion to interpret potential violations.

Abstract

We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic -channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with "wrong" sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. This violation is suppressed by where is the scale of Reggeization. This implies that the positivity bounds can be applied only when the cutoff scale of EFT is much lower than the scale of Reggeization. We then obtain the positivity bounds on scalar-tensor EFT at one-loop level. Implications of our results on the degenerate higher-order scalar-tensor (DHOST) theory are also discussed.

Paper Structure

This paper contains 21 sections, 118 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Review: positivity bounds for scalar theories without gravity
  3. Positivity bounds in the presence of gravity
  4. Unavoidable problems caused by gravitons
  5. Violation of strict positivity and the Regge behavior
  6. An example: superstring amplitude
  7. Bound on negativity and the approximate positivity
  8. Bounds on scalar-tensor EFT
  9. Frame-independence: example
  10. Ghost-freeness v.s. EFT point of view
  11. General action
  12. Positivity bounds on scalar-tensor EFT
  13. Application to phenomenological models
  14. Conclusion and discussions
  15. Extension to the positivity with $t$-derivative
  16. ...and 6 more sections

Figures (3)

  • Figure 1: Analytic structure of $F(s,t)$ in the complex $s$-plane and the integration contours. The light-blue "$\times$" and the wavy lines are simple poles associated with a stable particle $\phi$ and branch cuts generated by loops, respectively. The integration contour $\mathcal{C}$ can be deformed into the one on the right panel, leading to the dispersion relation \ref{['eq:twdisp']}.
  • Figure 2: The deformation of the integration contours, parameterized by an angle $\varepsilon>0$. Simple poles associated with the Regge states are denoted by $\times$.
  • Figure 3: The $s$-channel loop diagram.