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New Sensitivity Curves for Gravitational-Wave Signals from Cosmological Phase Transitions

Kai Schmitz

TL;DR

This work introduces Peak-Integrated Sensitivity Curves (PISCs) to quantify GW detector sensitivity to stochastic backgrounds from strong first-order cosmological phase transitions by embedding the expected signal shape into the sensitivity framework. It derives a model-independent peak sensitivity Omega_PIS and constructs six PISCs (and bands) per experiment for bubble collisions, sound waves, and turbulence, with cross-channel combinations, enabling direct SNR interpretation without repeated integrations. Semianalytical fits are provided for LISA, DECIGO, and BBO, and the method is demonstrated on a scalar-singlet xSM benchmark (BP #14) and a wide set of BSM models, showing how PISCs streamline cross-model comparisons and update as theory advances. The approach overcomes limitations of traditional PLISCs by preserving full SNR information while remaining agnostic to detailed spectral modeling, offering a practical toolbox for phenomenologists and experimentalists planning future GW searches.

Abstract

Gravitational waves (GWs) from strong first-order phase transitions (SFOPTs) in the early Universe are a prime target for upcoming GW experiments. In this paper, I construct novel peak-integrated sensitivity curves (PISCs) for these experiments, which faithfully represent their projected sensitivities to the GW signal from a cosmological SFOPT by explicitly taking into account the expected shape of the signal. Designed to be a handy tool for phenomenologists and model builders, PISCs allow for a quick and systematic comparison of theoretical predictions with experimental sensitivities, as I illustrate by a large range of examples. PISCs also offer several advantages over the conventional power-law-integrated sensitivity curves (PLISCs); in particular, they directly encode information on the expected signal-to-noise ratio for the GW signal from a SFOPT. I provide semianalytical fit functions for the exact numerical PISCs of LISA, DECIGO, and BBO. In an appendix, I moreover present a detailed review of the strain noise power spectra of a large number of GW experiments. The numerical results for all PISCs, PLISCs, and strain noise power spectra presented in this paper can be downloaded from the Zenodo online repository [https://doi.org/10.5281/zenodo.3689582]. In a companion paper [1909.11356], the concept of PISCs is used to perform an in-depth study of the GW signal from the cosmological phase transition in the real-scalar-singlet extension of the standard model. The PISCs presented in this paper will need to be updated whenever new theoretical results on the expected shape of the signal become available. The PISC approach is therefore suited to be used as a bookkeeping tool to keep track of the theoretical progress in the field.

New Sensitivity Curves for Gravitational-Wave Signals from Cosmological Phase Transitions

TL;DR

This work introduces Peak-Integrated Sensitivity Curves (PISCs) to quantify GW detector sensitivity to stochastic backgrounds from strong first-order cosmological phase transitions by embedding the expected signal shape into the sensitivity framework. It derives a model-independent peak sensitivity Omega_PIS and constructs six PISCs (and bands) per experiment for bubble collisions, sound waves, and turbulence, with cross-channel combinations, enabling direct SNR interpretation without repeated integrations. Semianalytical fits are provided for LISA, DECIGO, and BBO, and the method is demonstrated on a scalar-singlet xSM benchmark (BP #14) and a wide set of BSM models, showing how PISCs streamline cross-model comparisons and update as theory advances. The approach overcomes limitations of traditional PLISCs by preserving full SNR information while remaining agnostic to detailed spectral modeling, offering a practical toolbox for phenomenologists and experimentalists planning future GW searches.

Abstract

Gravitational waves (GWs) from strong first-order phase transitions (SFOPTs) in the early Universe are a prime target for upcoming GW experiments. In this paper, I construct novel peak-integrated sensitivity curves (PISCs) for these experiments, which faithfully represent their projected sensitivities to the GW signal from a cosmological SFOPT by explicitly taking into account the expected shape of the signal. Designed to be a handy tool for phenomenologists and model builders, PISCs allow for a quick and systematic comparison of theoretical predictions with experimental sensitivities, as I illustrate by a large range of examples. PISCs also offer several advantages over the conventional power-law-integrated sensitivity curves (PLISCs); in particular, they directly encode information on the expected signal-to-noise ratio for the GW signal from a SFOPT. I provide semianalytical fit functions for the exact numerical PISCs of LISA, DECIGO, and BBO. In an appendix, I moreover present a detailed review of the strain noise power spectra of a large number of GW experiments. The numerical results for all PISCs, PLISCs, and strain noise power spectra presented in this paper can be downloaded from the Zenodo online repository [https://doi.org/10.5281/zenodo.3689582]. In a companion paper [1909.11356], the concept of PISCs is used to perform an in-depth study of the GW signal from the cosmological phase transition in the real-scalar-singlet extension of the standard model. The PISCs presented in this paper will need to be updated whenever new theoretical results on the expected shape of the signal become available. The PISC approach is therefore suited to be used as a bookkeeping tool to keep track of the theoretical progress in the field.

Paper Structure

This paper contains 16 sections, 102 equations, 12 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Gravitational-wave signal from a cosmological phase transition
  3. Peak-integrated sensitivity curves
  4. Definition
  5. Benchmark point in the scalar-singlet extension
  6. Comparison of different BSM models
  7. Relaxing some of the underlying assumptions
  8. Runaway phase transitions in vacuum
  9. New signal predictions after theory updates
  10. Semianalytical fit functions
  11. Conclusions and outlook
  12. Review: Noise spectra of interferometer and pulsar timing experiments
  13. Formalism
  14. Transfer functions
  15. Detector noise power spectra
  16. ...and 1 more sections

Figures (12)

  • Figure 1: Top: Strain noise spectra. Bottom: PLISCs and GW signal for BP #14. See text.
  • Figure 2: PISCs for LISA, DECIGO, and BBO together with the predictions of BP #14. See text.
  • Figure 3: PLISCs and GW signals for all benchmark points listed in Tab. \ref{['tab:bp']}.
  • Figure 4: PISCs for LISA, DECIGO, and BBO together with the predictions of all BPs. See text.
  • Figure 5: PISC for LISA in the b-channel for different values of $\varrho_{\rm thr}$ and $t_{\rm obs}$. See Eq. \ref{['eq:OPISgen']}.
  • ...and 7 more figures