Full numerical N-body treatment is required for reliable gravitational wave predictions from nonspherical collapse in early matter-dominated eras, with resulting spectra mappable to detector sensitivities via horizon mass and reheating temperature.
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New Sensitivity Curves for Gravitational-Wave Signals from Cosmological Phase Transitions
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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.
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representative citing papers
Metastable cosmic strings produce a gravitational wave background that is best modeled with three parameters (string tension Gμ plus independent time scales t_LB and t_NC), yielding a compact analytical spectrum when t_LB greatly exceeds t_NC.
In massive self-gravitating black hole disks, magnetic turbulence damps the m=1 instability and gravitational waves when aligned with the spin, but strongly enhances both when the disk is antialigned.
Bubble collisions in a seesaw model produce right-handed neutrinos that source novel gravitational waves detectable by LISA, ET, and LVK while allowing the lightest RHN to explain dark matter or enable leptogenesis.
In pure axion inflation, detectable gravitational wave signals arise only in parameter regions with strong backreaction that violate the upper bound on ΔN_eff.
LISA auto-correlation SNR equals the square root of T_obs times the integral of (signal/(noise+signal))^2 and is therefore bounded by sqrt(T_obs(f_max-f_min)).
Scaling monopoles generate PBHs via stochastic overdensities and GWs with correlated spectra, potentially with magnetically charged PBHs as a signature if the scaling ends via gauge boson mass.
Periodic warm inflation imprints one log-periodic feature on the curvature spectrum that saturates asteroid-mass PBHs, generates dual-band GW backgrounds, and offsets the bispectrum phase by a quarter cycle fixed by spectral running.
Composite dark matter from a keV–MeV confining phase transition sources an IR-enhanced curvature spectrum that competes with free-streaming suppression, yielding concrete CMB and Lyman-α bounds on transition strength and temperature.
The end of thermal inflation proceeds by nucleating true-vacuum bubbles rather than by global phase mixing, and the resulting gravitational-wave background can reach BBO and DECIGO sensitivities for low flaton mass scale gamma.
Domain wall annihilation imprints a two-peaked spectrum on induced gravitational waves via an early matter-dominated phase and entropy dilution.
A chiral U(1) gauge symmetry generates an accidental Peccei-Quinn symmetry broken by mirror QCD, solving the strong CP problem without a light axion while supplying WIMP dark matter, stochastic gravitational waves, and LHC-testable colored pNGBs.
Schwinger fermion production in axion inflation damps gauge fields, enabling observable primordial gravitational waves in LISA/ET bands while satisfying ΔN_eff limits and identifying a new damped-oscillation backreaction regime.
Temperature-dependent DM couplings mediated by a scalar field's VEV that drops after a first-order phase transition allow sufficient early-universe annihilations for the observed relic density while evading current direct detection bounds.
Extends diagrammatic approach for scalar-induced gravitational waves to arbitrary-order local PNG, deriving semi-analytic spectra for energy density, anisotropies, bispectrum and trispectrum up to quartic terms.
Lattice simulations of bumpy axion U(1) inflation in the strong backreaction regime generate curvature perturbations large enough for primordial black holes to comprise all dark matter.
HydroGrav code computes self-similar fluid profiles and GW spectra using exact EOS from effective potentials for EWPT models, identifying parameter regions in a Z2 SM extension where simplified EOS differ in amplitude and shape, with LISA SNR estimates.
Finite-duration domain-wall nucleation during inflation produces a curvature power spectrum peaked at nanohertz frequencies whose scalar-induced gravitational waves match NANOGrav and EPTA data in a two-field model.
Radiative barriers in SUSY flat directions enable supercooled PTs yielding Ω_GW h² up to ~3e-10 for M_λ̃/v_X in 0.05-0.23, with the hidden sector also reproducing Ω_CDM h²=0.12 for m_q ~30-800 keV.
An SU(5) GUT model uses an intermediate breaking to SO(3)_C × SO(2)_L realized by adjoint, symmetric tensor, and singlet scalars plus singlet fermions so that monopoles annihilate via cosmic strings, with possible first-order restoration producing detectable GWs.
A model in which inflaton energy goes exclusively to a dark sector, delaying SM thermalization until a false-vacuum decay produces a GW background with present-day Omega_GW up to 3e-8.
Bubble collisions during a first-order phase transition at the end of inflation can generate the observed dark matter abundance in a restricted region of parameter space via direct production and spectator decays.
A transient parity-violating phase during inflation generates a robust blue-tilted (n_T ≃ 2) primordial gravitational wave spectrum at small scales with nearly maximal helicity coherence and linear polarization, offering a cosmological template for PTA data distinct from astrophysical sources.
Soft-wall warped geometries yield rapid, mildly supercooled phase transitions whose TeV-scale gravitational wave signals are accessible to space-based interferometers.
citing papers explorer
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Gravitational wave emission from nonspherical collapse in an early matter-dominated era using N-body simulations
Full numerical N-body treatment is required for reliable gravitational wave predictions from nonspherical collapse in early matter-dominated eras, with resulting spectra mappable to detector sensitivities via horizon mass and reheating temperature.
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New gravitational-wave templates for metastable cosmic strings: Loop breaking versus network collapse
Metastable cosmic strings produce a gravitational wave background that is best modeled with three parameters (string tension Gμ plus independent time scales t_LB and t_NC), yielding a compact analytical spectrum when t_LB greatly exceeds t_NC.
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Multimessenger Signatures of Tilted, Self-Gravitating, Black Hole Disks
In massive self-gravitating black hole disks, magnetic turbulence damps the m=1 instability and gravitational waves when aligned with the spin, but strongly enhances both when the disk is antialigned.
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Cosmic Collider Gravitational Waves sourced by Right-handed Neutrino production from Bubbles: Testing Seesaw, Leptogenesis and Dark Matter
Bubble collisions in a seesaw model produce right-handed neutrinos that source novel gravitational waves detectable by LISA, ET, and LVK while allowing the lightest RHN to explain dark matter or enable leptogenesis.
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Gravitational waves from axion inflation in the gradient expansion formalism. Part I. Pure axion inflation
In pure axion inflation, detectable gravitational wave signals arise only in parameter regions with strong backreaction that violate the upper bound on ΔN_eff.
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Signal-to-Noise Ratio Contours for LISA
LISA auto-correlation SNR equals the square root of T_obs times the integral of (signal/(noise+signal))^2 and is therefore bounded by sqrt(T_obs(f_max-f_min)).
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PBHs and GWs from Scaling Monopoles
Scaling monopoles generate PBHs via stochastic overdensities and GWs with correlated spectra, potentially with magnetically charged PBHs as a signature if the scaling ends via gauge boson mass.
-
One Feature, Three Clocks: Phase-Locked Gravitational Waves, Primordial Black Holes, and Non-Gaussianity from Periodic Warm Inflation
Periodic warm inflation imprints one log-periodic feature on the curvature spectrum that saturates asteroid-mass PBHs, generates dual-band GW backgrounds, and offsets the bispectrum phase by a quarter cycle fixed by spectral running.
-
Probing Confining Dark Sectors with Cosmological Perturbations
Composite dark matter from a keV–MeV confining phase transition sources an IR-enhanced curvature spectrum that competes with free-streaming suppression, yielding concrete CMB and Lyman-α bounds on transition strength and temperature.
-
Phase Transitions and Gravitational Wave Production at the End of Thermal Inflation
The end of thermal inflation proceeds by nucleating true-vacuum bubbles rather than by global phase mixing, and the resulting gravitational-wave background can reach BBO and DECIGO sensitivities for low flaton mass scale gamma.
-
Imprint of domain wall annihilation on induced gravitational waves
Domain wall annihilation imprints a two-peaked spectrum on induced gravitational waves via an early matter-dominated phase and entropy dilution.
-
Accidental Peccei-Quinn Symmetry from Chiral Gauge Symmetry and Mirror QCD
A chiral U(1) gauge symmetry generates an accidental Peccei-Quinn symmetry broken by mirror QCD, solving the strong CP problem without a light axion while supplying WIMP dark matter, stochastic gravitational waves, and LHC-testable colored pNGBs.
-
Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation
Schwinger fermion production in axion inflation damps gauge fields, enabling observable primordial gravitational waves in LISA/ET bands while satisfying ΔN_eff limits and identifying a new damped-oscillation backreaction regime.
-
Reviving WIMP dark matter with temperature-dependent couplings
Temperature-dependent DM couplings mediated by a scalar field's VEV that drops after a first-order phase transition allow sufficient early-universe annihilations for the observed relic density while evading current direct detection bounds.
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Isotropy, anisotropies and non-Gaussianity in the scalar-induced gravitational-wave background: diagrammatic approach for primordial non-Gaussianity up to arbitrary order
Extends diagrammatic approach for scalar-induced gravitational waves to arbitrary-order local PNG, deriving semi-analytic spectra for energy density, anisotropies, bispectrum and trispectrum up to quartic terms.
-
Lattice study of primordial black hole formation in bumpy axion inflation
Lattice simulations of bumpy axion U(1) inflation in the strong backreaction regime generate curvature perturbations large enough for primordial black holes to comprise all dark matter.
-
HydroGrav: Precise hydrodynamics and gravitational waves for cosmological phase transitions
HydroGrav code computes self-similar fluid profiles and GW spectra using exact EOS from effective potentials for EWPT models, identifying parameter regions in a Z2 SM extension where simplified EOS differ in amplitude and shape, with LISA SNR estimates.
-
Nanohertz gravitational waves from domain walls nucleated during inflation
Finite-duration domain-wall nucleation during inflation produces a curvature power spectrum peaked at nanohertz frequencies whose scalar-induced gravitational waves match NANOGrav and EPTA data in a two-field model.
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Natural Supercooling and Reheating along Supersymmetric Flat Directions and Observable Gravitational Waves at the Einstein Telescope and the Cosmic Explorer
Radiative barriers in SUSY flat directions enable supercooled PTs yielding Ω_GW h² up to ~3e-10 for M_λ̃/v_X in 0.05-0.23, with the hidden sector also reproducing Ω_CDM h²=0.12 for m_q ~30-800 keV.
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A simple solution to the monopole problem: SU(5) GUT with symmetry breaking into special subgroup
An SU(5) GUT model uses an intermediate breaking to SO(3)_C × SO(2)_L realized by adjoint, symmetric tensor, and singlet scalars plus singlet fermions so that monopoles annihilate via cosmic strings, with possible first-order restoration producing detectable GWs.
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A New Origin of the Big Bang from Dark-Sector-Induced Vacuum Decay and Its Gravitational-Wave Signal
A model in which inflaton energy goes exclusively to a dark sector, delaying SM thermalization until a false-vacuum decay produces a GW background with present-day Omega_GW up to 3e-8.
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Dark Matter Production from Bubble Collisions during a First-Order Phase Transition at the End of Inflation
Bubble collisions during a first-order phase transition at the end of inflation can generate the observed dark matter abundance in a restricted region of parameter space via direct production and spectator decays.
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Transient Parity Violation during Inflation: Implications for PTA Gravitational Waves
A transient parity-violating phase during inflation generates a robust blue-tilted (n_T ≃ 2) primordial gravitational wave spectrum at small scales with nearly maximal helicity coherence and linear polarization, offering a cosmological template for PTA data distinct from astrophysical sources.
-
Uncool soft-wall transitions and gravitational waves
Soft-wall warped geometries yield rapid, mildly supercooled phase transitions whose TeV-scale gravitational wave signals are accessible to space-based interferometers.
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Exponential Quintessence Model: Analytical Quantification of the Fine-Tuning Problem in Dark Energy
Exponential quintessence with an assumed kination epoch relaxes the dark energy fine-tuning problem by dozens of orders of magnitude relative to a cosmological constant.
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Dark Matter Freeze-in from a $Z^\prime$ Reheaton
Dark matter freezes in from non-thermal Z' decays before reheating ends in an inflationary model with a secluded U(1)_D gauge sector, Z' reheaton, and lattice treatment of non-perturbative effects, opening viable parameter space with GW probes.
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Stochastic Gravitational Waves from Modulated Reheating
A spectator scalar in modulated reheating with large Higgs-like couplings generates detectable scalar-induced stochastic gravitational waves for BBO and DECIGO, but only outside perturbative low-energy extrapolations.
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Observable CMB B-modes from Cosmological Phase Transitions
Phase transitions in dark sectors can generate CMB B-modes with amplitudes competitive with inflation but peaking at smaller angular scales.
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Probing radiative electroweak symmetry breaking with colliders and gravitational waves
Radiative electroweak symmetry breaking with a logarithmic potential yields analytical vacuum solutions, four thermal history patterns, and supercooled FOPT gravitational waves whose signals combined with collider data can probe conformal scales to 10^5-10^8 GeV.
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Gravitational Waves from Multiple First-Order Phase Transitions in a Scenario with Early Matter Domination
Early matter domination with time-dependent decay rates produces multiple first-order phase transitions whose gravitational wave signatures encode the transition and reheating temperatures.
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Strong First-Order Electroweak Phase Transition and Gravitational Waves in a $\mathbb{Z}_4$ Fermion-Scalar Dark Matter Model
In a Z4 fermion-scalar dark matter model, strong first-order electroweak phase transitions and gravitational wave signals occur only in the thermal two-component regime with Mψ < MS < 2Mψ or the decay-driven WIMP-FIMP regime with MS > 2Mψ after dark matter constraints.
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Majoron Dark Matter, High-Scale Seesaw, and Leptogenesis
Majoron dark matter is viable for sub-MeV masses in high-scale seesaw models with thermal leptogenesis, produced via misalignment and cosmic strings in pre- and post-inflationary scenarios and constrained by CMB, X-ray, and gravitational wave observations.
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Accretion Effects on Primordial Black Hole Reheating Constraints
Accretion on primordial black holes prolongs matter domination and shifts reheating constraints from isocurvature gravitational waves and mergers toward smaller formation masses and initial abundances.
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Metastable strings at PTAs: classical stability analysis
Classical instabilities in metastable strings from two-step symmetry breaking can restrict the viable parameter space for explaining the PTA gravitational wave signal.
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Gravitational waves from CP domain wall collapse and electron EDM in a complex singlet model with dimension-five Yukawa interactions
In a complex singlet model with dimension-five Yukawa couplings, current electron EDM bounds already restrict part of the parameter space where gravitational waves from CP domain wall collapse would be detectable.
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Precision Analysis for $\boldsymbol{H_0}$ Using Upcoming Multi-band Gravitational Wave Observations
Multi-band GW observations of PBHs can reduce H0 uncertainty to ≲2 km/s/Mpc (conservative) or O(0.1) km/s/Mpc (optimistic) via Fisher forecasts on M_PBH and f_PBH.
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ACT DR6+Planck impact on inflation with non-zero vacuum expectation value and the post-inflationary behavior
Updated constraints on non-zero VEV parameter M from ACT+Planck data, plus lattice simulations showing oscillon formation and reheating implications.