Future microhertz detections combined with nanohertz pulsar terms can serve as gravity echoes to measure supermassive black hole binary inspiral rates from hundreds to thousands of years in the past.
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Unveiling the Gravitational Universe at \mu-Hz Frequencies
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abstract
We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to $\mu$-Hz frequency range. By the 2040s', the $\mu$-Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a $\mu$-Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe.
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Radiative corrections from an asymmetric Dirac fermion generate a bias that collapses domain walls, producing gravitational waves that encode the asymmetry level and temperature.
Accounting for the minimal mass spread of primordial black holes from gravitational collapse suppresses the Poltergeist GW background to the level of generic scalar-induced signals and reopens ultra-light PBH parameter space.
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.
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.
Incorporating the general-relativity mass tail df_PBH/d ln M ∝ M^3.78 smooths PBH evaporation, suppresses the scalar-induced GW signal by orders of magnitude, and reopens the ultra-light PBH window for the hot Big Bang.
Tensor perturbations from first-order phase transitions and domain wall annihilation induce curvature fluctuations at second order that form primordial black holes, allowing asteroid-mass PBHs to comprise all dark matter for specific parameter ranges with associated gravitational wave peaks in LISA,
A framework is developed to test beyond-GR effects in nanohertz continuous waves from individual SMBHBs, deriving modified inter-pulsar correlations, antenna responses, and phase delays for three deviation classes, validated by injection-recovery simulations showing parameter recovery and no GR bias
Domain wall annihilation imprints a two-peaked spectrum on induced gravitational waves via an early matter-dominated phase and entropy dilution.
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.
Low-scale leptogenesis becomes viable in the neutrino seesaw framework when a first-order electroweak phase transition allows sphalerons to convert lepton asymmetry into baryon asymmetry at temperatures below the Standard Model decoupling point.
Axion-like particles in the trapped misalignment mechanism produce observable gravitational waves while generating intergalactic magnetic fields that exceed blazar lower bounds in the parameter space promising for gravitational wave detection.
ALP-assisted first-order phase transitions can explain observed intergalactic magnetic fields and produce detectable gravitational waves, linking cosmology with particle physics searches.
High-quality axion models with N_DW=1 and dark matter abundance requirement restrict the gauge breaking scale to 1.6e11-1e16 GeV, yielding a band of gravitational wave signals from two-step phase transitions consistent with current observations.
A spectator scalar field with strong portal coupling to the inflaton sources a stochastic gravitational wave background reaching Ω_GW h² ∼ 10^{-11} at frequencies 10^7-10^8 Hz for benchmark parameters σ/λ ≃ 10^4 and T_reh = 2×10^{14} GeV.
A dimension-six operator |H|^2|phi|^4 in a U(1)_D singlet extension relaxes the usual Higgs-portal and mixing-angle correlation, enabling strong first-order electroweak phase transitions driven primarily by the singlet VEV.
Lepton parity stabilizes a Majorana fermion as freeze-in dark matter produced via right-handed neutrino or Higgs decays, yielding detectable gravitational waves or ΔN_eff depending on scalar couplings.
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.
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.
In the minimal B-L gauge extension, Majorana neutrinos at high breaking scale produce flat GW spectra from cosmic strings, Dirac at low scale produce peaked spectra from first-order phase transitions, and pseudo-Dirac produce kink features from domain wall annihilation.
Lepton parity stabilizes a Majorana fermion dark matter candidate while an accidental Z2 symmetry in the scalar potential creates unstable domain walls whose decay produces observable gravitational waves.
3D simulations of cosmological first-order phase transitions find density perturbation spectra with k^3 and k^{-1.5} slopes and GW spectra with k^3 and k^{-2}, confirming slow transitions can produce PBHs.
TransitionListener v2.0 supplies an end-to-end pipeline from scalar potential to gravitational wave spectra with improved handling of transition dynamics and bubble separation.
Weak lensing surveys cannot detect nanohertz-microhertz gravitational waves from supermassive black hole binaries under realistic conditions; only unattainable idealized surveys could probe this band.
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Testing General Relativity with Individual Supermassive Black Hole Binaries
A framework is developed to test beyond-GR effects in nanohertz continuous waves from individual SMBHBs, deriving modified inter-pulsar correlations, antenna responses, and phase delays for three deviation classes, validated by injection-recovery simulations showing parameter recovery and no GR bias