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Bounds on Gravitational Wave Production from Unitarity in an Early NEC-Violating Model

Pavel Petrov, Jianing Wang

TL;DR

This work investigates whether an early NEC-violating phase within a Horndeski/kinetic gravity braiding framework can generate a sizable stochastic gravitational-wave background without violating perturbative unitarity. The authors estimate the strong-coupling scale from cubic perturbations using dimensional analysis and then derive exact unitarity bounds via the optical theorem in the high-energy limit, focusing on the center-of-mass frame. They find that leading cubic operators cancel in all channels, leaving subleading interactions to set the bounds, which in turn tightly constrain the possible GW amplitude $A_T$ and tensor tilt $n_T$, typically decreasing the viable $A_T$ by several orders of magnitude. The results apply broadly to NEC-violating early-Universe scenarios and motivate non-perturbative or EFT-based extensions to capture dynamics beyond perturbation theory across more general cosmologies.

Abstract

We study a cosmological scenario featuring an early phase of null energy condition (NEC) violation. Within this framework, we show that perturbative unitarity bounds place strong constraints on both the amplitude and the spectral tilt of primordial gravitational waves. Our analysis is largely insensitive to the detailed realization of the transition between the NEC-violating phase and subsequent cosmological phases, allowing our results to be extended to a broader class of models. Finally, the perturbative unitarity approach employed here is applicable to a wide range of cosmological scenarios.

Bounds on Gravitational Wave Production from Unitarity in an Early NEC-Violating Model

TL;DR

This work investigates whether an early NEC-violating phase within a Horndeski/kinetic gravity braiding framework can generate a sizable stochastic gravitational-wave background without violating perturbative unitarity. The authors estimate the strong-coupling scale from cubic perturbations using dimensional analysis and then derive exact unitarity bounds via the optical theorem in the high-energy limit, focusing on the center-of-mass frame. They find that leading cubic operators cancel in all channels, leaving subleading interactions to set the bounds, which in turn tightly constrain the possible GW amplitude and tensor tilt , typically decreasing the viable by several orders of magnitude. The results apply broadly to NEC-violating early-Universe scenarios and motivate non-perturbative or EFT-based extensions to capture dynamics beyond perturbation theory across more general cosmologies.

Abstract

We study a cosmological scenario featuring an early phase of null energy condition (NEC) violation. Within this framework, we show that perturbative unitarity bounds place strong constraints on both the amplitude and the spectral tilt of primordial gravitational waves. Our analysis is largely insensitive to the detailed realization of the transition between the NEC-violating phase and subsequent cosmological phases, allowing our results to be extended to a broader class of models. Finally, the perturbative unitarity approach employed here is applicable to a wide range of cosmological scenarios.
Paper Structure (19 sections, 118 equations, 5 figures)

This paper contains 19 sections, 118 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The Model
  3. Estimation of the Strong Coupling Scale
  4. The Method
  5. Most Relevant Terms
  6. Unitarity Bounds from the Optical Theorem
  7. Matrix Element for the Leading-Order Action
  8. (1) $s$-channel (two incoming legs and outgoing propagator).
  9. (2) $t$-channel (one incoming leg, one outgoing leg and outgoing propagator).
  10. (3) $u$-channel (one incoming leg, one outgoing leg and outgoing propagator).
  11. Constraints on the Model Parameters
  12. Conclusion
  13. The Cubic Actions for All Sectors
  14. Scalar Sector
  15. Mixed and Tensor Sectors
  16. ...and 4 more sections

Figures (5)

  • Figure 1: Values of $\log_{10}\mathcal{F}$ over the region of the $(p,q)$ plane that satisfies the conditions of stability and sub-luminal propagation.
  • Figure 2: Maximum allowed value of $n_T$ as a function of $\log_{10}(m/M_{\mathrm{Pl}})$ for different $e$-folding numbers $N$ during the inflationary stage.
  • Figure 3: Allowed parameter range in the $(p,q)$ plane for $N = 30$ and $\log_{10}(m/M_{\mathrm{Pl}}) = -9$.
  • Figure 4: The blue area corresponds to the stability requirements, $\mathcal{F}_S>0$ and $\mathcal{G}_S>0$, while the orange area corresponds to $c_S>1$.
  • Figure 5: The blue region corresponds to the allowed values of the tensor spectral index $n_T$ and the tensor amplitude $A_T$.