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Stochastic gravitational wave background anisotropies from inflation with non-Bunch-Davies states

Shingo Akama, Shin'ichi Hirano, Shuichiro Yokoyama

TL;DR

This work analyzes stochastic gravitational-wave background (SGWB) anisotropies generated during inflation from squeezed scalar-tensor-tensor (STT) non-Gaussianities in Horndeski theory with non-Bunch-Davies states. It develops a consistent framework that avoids Trans-Planckian and strong-coupling problems, derives the primordial STT bispectrum across seven cubic interactions, and connects these to SGWB anisotropies via a non-Gaussian coupling $F^{ss'}_{\rm NL}$. The authors explore two Bogoliubov configurations—a peaked tensor spectrum and a nearly scale-invariant spectrum—and compute the resulting SGWB auto- and cross-correlations with the CMB, demonstrating potential observability with DECIGO/BBO and SKA under backreaction and perturbativity constraints. The results suggest that inflationary non-Bunch-Davies states can significantly enhance SGWB anisotropies, potentially surpassing late-time Sachs-Wolfe contributions, and provide a novel avenue to probe the inflationary vacuum state with future GW observations.

Abstract

It is known that stochastic gravitational wave backgrounds (SGWBs) have anisotropies generated by squeezed-type tensor non-Gaussianities originating from scalar-tensor-tensor (STT) and tensor-tensor-tensor cubic interactions. While the squeezed tensor non-Gaussianities in the standard slow-roll inflation with the Bunch-Davies vacuum state are suppressed due to the so-called consistency relation, those in extended models with the violation of the consistency relation can be enhanced. Among such extended models, we consider the inflation model with the non-Bunch-Davies state that is known to enhance the squeezed tensor non-Gaussianities. We explicitly formulate the primordial STT bispectrum induced during inflation in the context of Horndeski theory with the non-Bunch-Davies state and show that the induced SGWB anisotropies can be enhanced. We then discuss the detectability of those anisotropies in future gravitational wave experiments.

Stochastic gravitational wave background anisotropies from inflation with non-Bunch-Davies states

TL;DR

This work analyzes stochastic gravitational-wave background (SGWB) anisotropies generated during inflation from squeezed scalar-tensor-tensor (STT) non-Gaussianities in Horndeski theory with non-Bunch-Davies states. It develops a consistent framework that avoids Trans-Planckian and strong-coupling problems, derives the primordial STT bispectrum across seven cubic interactions, and connects these to SGWB anisotropies via a non-Gaussian coupling . The authors explore two Bogoliubov configurations—a peaked tensor spectrum and a nearly scale-invariant spectrum—and compute the resulting SGWB auto- and cross-correlations with the CMB, demonstrating potential observability with DECIGO/BBO and SKA under backreaction and perturbativity constraints. The results suggest that inflationary non-Bunch-Davies states can significantly enhance SGWB anisotropies, potentially surpassing late-time Sachs-Wolfe contributions, and provide a novel avenue to probe the inflationary vacuum state with future GW observations.

Abstract

It is known that stochastic gravitational wave backgrounds (SGWBs) have anisotropies generated by squeezed-type tensor non-Gaussianities originating from scalar-tensor-tensor (STT) and tensor-tensor-tensor cubic interactions. While the squeezed tensor non-Gaussianities in the standard slow-roll inflation with the Bunch-Davies vacuum state are suppressed due to the so-called consistency relation, those in extended models with the violation of the consistency relation can be enhanced. Among such extended models, we consider the inflation model with the non-Bunch-Davies state that is known to enhance the squeezed tensor non-Gaussianities. We explicitly formulate the primordial STT bispectrum induced during inflation in the context of Horndeski theory with the non-Bunch-Davies state and show that the induced SGWB anisotropies can be enhanced. We then discuss the detectability of those anisotropies in future gravitational wave experiments.

Paper Structure

This paper contains 31 sections, 155 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Primordial power spectra with non-Bunch-Davies states
  3. Quadratic action and primordial power spectra with non-Bunch-Davies states
  4. On the scale-dependence of the tensor power spectrum with non-Bunch-Davies state
  5. Peaked spectrum
  6. Nearly scale-invariant spectrum
  7. Non-Bunch-Davies bispectrum
  8. Trans-Planckian and strong coupling problems
  9. STT bispectrum
  10. SGWB anisotropies
  11. General expression for the anisotropies
  12. Angular correlation for the SGWB anisotropies
  13. SGWB anisotropies from inflation with the non-Bunch-Davies states
  14. Peaked spectrum
  15. Nearly scale-invariant spectrum
  16. ...and 16 more sections

Figures (3)

  • Figure 1: Left: The plot of $C_\ell^{\rm GW}$ normalized by $\mathcal{P}_\zeta f^{ss}_{{\rm NL},0}(k)^2$. Right: The plot of $C_\ell^{\rm GW-T}$ normalized by $\mathcal{P}_\zeta f^{ss}_{{\rm NL},0}(k)$.
  • Figure 2: Left: The allowed values of $C_\ell^{\rm GW}$ for the peaked spectrum. Right: The allowed values of $C_\ell^{\rm GW-T}$ for the peaked spectrum.
  • Figure 3: Left: The allowed values of $C_\ell^{\rm GW}$ for the scale-invariant spectrum. Right: The allowed values of $C_\ell^{\rm GW-T}$ for the scale-invariant spectrum.