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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The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
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abstract
We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15-year pulsar-timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. The correlations follow the Hellings-Downs pattern expected for a stochastic gravitational-wave background. The presence of such a gravitational-wave background with a power-law-spectrum is favored over a model with only independent pulsar noises with a Bayes factor in excess of $10^{14}$, and this same model is favored over an uncorrelated common power-law-spectrum model with Bayes factors of 200-1000, depending on spectral modeling choices. We have built a statistical background distribution for these latter Bayes factors using a method that removes inter-pulsar correlations from our data set, finding $p = 10^{-3}$ (approx. $3\sigma$) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of inter-pulsar correlations yields $p = 5 \times 10^{-5} - 1.9 \times 10^{-4}$ (approx. $3.5 - 4\sigma$). Assuming a fiducial $f^{-2/3}$ characteristic-strain spectrum, as appropriate for an ensemble of binary supermassive black-hole inspirals, the strain amplitude is $2.4^{+0.7}_{-0.6} \times 10^{-15}$ (median + 90% credible interval) at a reference frequency of 1/(1 yr). The inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from a population of supermassive black-hole binaries, although more exotic cosmological and astrophysical sources cannot be excluded. The observation of Hellings-Downs correlations points to the gravitational-wave origin of this signal.
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representative citing papers
Hardening binaries experience deterministic self-acceleration of their center of mass, induced precession, and plane rotation in uniform isotropic media, driving outward spiraling and eccentricity growth in all cases rather than circularization.
A full-covariance formalism for PTA-astrometry ORF estimators forecasts graviton-mass upper limits of 4.41e-24 eV/c2 for current-like setups and 0.48e-24 eV/c2 for SKA/Theia-like future setups, with astrometry adding significant power in the latter case.
Pulsar timing arrays can probe supermassive black hole binaries that merged prior to observations via the pulsar term, with SKA potentially detecting a few such zombie binaries at SNR > 3.
A dipole pulsar timing array detects chiral nanohertz gravitational waves and extends PTA sensitivity into the microhertz regime.
A general relativistic derivation of gravitational wave response in an optically levitated cavity sensor reveals position-dependent strain sensitivity and suppressed input-mirror noise coupling.
Stupendously large black holes cast shadows on the CMB that rule out masses above 10^17 solar masses within the last scattering surface and limit their density parameter to below 10^-5 for masses 10^15 to 10^18 solar masses.
Black holes in ultralight dark matter solitons undergo quasi-periodic stone-skipping orbits driven by soliton dipole excitations, modifying inspiral dynamics when the black hole is much lighter than the soliton.
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.
Cross-correlating pulsar timing and polarimetry isolates the circular polarization of isotropic stochastic GW backgrounds and shares the Hellings-Downs angular pattern.
In pure axion inflation, detectable gravitational wave signals arise only in parameter regions with strong backreaction that violate the upper bound on ΔN_eff.
Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.
First astrometric constraints on parity-violating SGWB amplitude are reported as h70²ΩV = -0.020 ± 0.025 (Gaia) and -0.004 ± 0.010 (VLBA) at 2σ, consistent with zero, over 4.2e-18 Hz to 1.1e-8 Hz.
Proposes APTA with 6 satellites and 10^{-18} relative clock uncertainty at 1s averaging to achieve sensitivity for observing 10^3-10^4 solar-mass black hole mergers in the decihertz band.
PPO reinforcement learning accelerates identification of gravitational wave signals from supercooled phase transitions in a minimal dark U(1)_x sector compared to Monte Carlo sampling.
DarkAgents is an LLM-powered multi-agent framework for model building, pipeline computation, and assumption auditing in astroparticle physics, demonstrated on first-order phase transitions fitting NANOGrav gravitational wave data.
Self-consistent thermal regulation in circumbinary disks permits long-lived non-accretion phases that suppress binary feeding rates toward the Eddington limit while leaving optical/near-IR detectability intact.
Presents a new Fourier-expansion Bayesian hierarchical model with Lorentzian hyperprior for waveform-agnostic searches of nanohertz gravitational wave sources in pulsar timing array data.
With a physically motivated z_min cutoff, higher-order moments of the SGWB from SMBH binaries depend on the mass function solely via <M^{10/3}>, giving a variance-to-mean ratio for <M^{10/3}>/<M^{5/3}> and a kurtosis-skewness consistency relation independent of redshift evolution.
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
AM-CW lunar laser ranging achieves μHz SGWB sensitivity of 5.29×10^{-9} D_cov (80 μm range uncertainty) or 2.07×10^{-9} D_cov (50 μm) over 5 years, with discovery possible if covariance degradation stays below ~3.6-13.7.
Analytic gravitational waveforms from radial test-particle infall into a thin-shell traversable wormhole exhibit a characteristic pulse-gap structure from repeated throat crossings and lie within reach of ground-based detectors at ~500 Mpc.
Domain wall annihilation imprints a two-peaked spectrum on induced gravitational waves via an early matter-dominated phase and entropy dilution.
citing papers explorer
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Gravity Echoes from Supermassive Black Hole Binaries
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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Self-acceleration of Hardening Binaries
Hardening binaries experience deterministic self-acceleration of their center of mass, induced precession, and plane rotation in uniform isotropic media, driving outward spiraling and eccentricity growth in all cases rather than circularization.
-
Forecasting graviton-mass constraints from the full covariance of PTA-astrometry ORF estimators
A full-covariance formalism for PTA-astrometry ORF estimators forecasts graviton-mass upper limits of 4.41e-24 eV/c2 for current-like setups and 0.48e-24 eV/c2 for SKA/Theia-like future setups, with astrometry adding significant power in the latter case.
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Probing Supermassive Black Hole Mergers with Pulsar Timing Arrays
Pulsar timing arrays can probe supermassive black hole binaries that merged prior to observations via the pulsar term, with SKA potentially detecting a few such zombie binaries at SNR > 3.
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Detecting Chiral Gravitational Wave Background with a Dipole Pulsar Timing Array
A dipole pulsar timing array detects chiral nanohertz gravitational waves and extends PTA sensitivity into the microhertz regime.
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Gravitational wave signal and noise response of an optically levitated sensor in a Fabry-P\'erot cavity
A general relativistic derivation of gravitational wave response in an optically levitated cavity sensor reveals position-dependent strain sensitivity and suppressed input-mirror noise coupling.
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Shadows of Giants: Constraints on Stupendously Large Black Holes from Negative Sources against the Cosmic Microwave Background
Stupendously large black holes cast shadows on the CMB that rule out masses above 10^17 solar masses within the last scattering surface and limit their density parameter to below 10^-5 for masses 10^15 to 10^18 solar masses.
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Stone Skipping Black Holes in Ultralight Dark Matter Solitons
Black holes in ultralight dark matter solitons undergo quasi-periodic stone-skipping orbits driven by soliton dipole excitations, modifying inspiral dynamics when the black hole is much lighter than the soliton.
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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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Detecting Parity-Violating Gravitational Wave Backgrounds with Pulsar Polarization Arrays
Cross-correlating pulsar timing and polarimetry isolates the circular polarization of isotropic stochastic GW backgrounds and shares the Hellings-Downs angular pattern.
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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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Quantum production of gravitational waves after inflation
Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.
-
First astrometric constraints on parity-violation in the gravitational wave background
First astrometric constraints on parity-violating SGWB amplitude are reported as h70²ΩV = -0.020 ± 0.025 (Gaia) and -0.004 ± 0.010 (VLBA) at 2σ, consistent with zero, over 4.2e-18 Hz to 1.1e-8 Hz.
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Artificial Precision Timing Array: bridging the decihertz gravitational-wave sensitivity gap with clock satellites
Proposes APTA with 6 satellites and 10^{-18} relative clock uncertainty at 1s averaging to achieve sensitivity for observing 10^3-10^4 solar-mass black hole mergers in the decihertz band.
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Supercool with PPO: Exploring Supercooled Phase Transitions via Reinforcement Learning
PPO reinforcement learning accelerates identification of gravitational wave signals from supercooled phase transitions in a minimal dark U(1)_x sector compared to Monte Carlo sampling.
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DarkAgents
DarkAgents is an LLM-powered multi-agent framework for model building, pipeline computation, and assumption auditing in astroparticle physics, demonstrated on first-order phase transitions fitting NANOGrav gravitational wave data.
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Dynamics and detectability of long-lived non-accretion phases for massive black hole binaries in cold, thermally regulating disks
Self-consistent thermal regulation in circumbinary disks permits long-lived non-accretion phases that suppress binary feeding rates toward the Eddington limit while leaving optical/near-IR detectability intact.
-
Searching for a waveform-agnostic gravitational wave signal in pulsar timing arrays
Presents a new Fourier-expansion Bayesian hierarchical model with Lorentzian hyperprior for waveform-agnostic searches of nanohertz gravitational wave sources in pulsar timing array data.
-
Higher-order statistics of the stochastic gravitational wave background from supermassive black hole binaries
With a physically motivated z_min cutoff, higher-order moments of the SGWB from SMBH binaries depend on the mass function solely via <M^{10/3}>, giving a variance-to-mean ratio for <M^{10/3}>/<M^{5/3}> and a kurtosis-skewness consistency relation independent of redshift evolution.
-
Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls
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,
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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
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High-Power AM-CW Lunar Laser Ranging as a $\mu$Hz SGWB Detector
AM-CW lunar laser ranging achieves μHz SGWB sensitivity of 5.29×10^{-9} D_cov (80 μm range uncertainty) or 2.07×10^{-9} D_cov (50 μm) over 5 years, with discovery possible if covariance degradation stays below ~3.6-13.7.
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Gravitational Waves from a Black Hole Falling Radially into a Thin-Shell Traversable Wormhole
Analytic gravitational waveforms from radial test-particle infall into a thin-shell traversable wormhole exhibit a characteristic pulse-gap structure from repeated throat crossings and lie within reach of ground-based detectors at ~500 Mpc.
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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.
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Spectral Butterfly Effect and Resilient Ringdown in Thick Braneworlds
Thick braneworlds feature fragile quasinormal mode spectra due to a butterfly effect but maintain a resilient early ringdown, keeping the standard gravitational wave fingerprint usable.
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The Heavy Tailed Non-Gaussianity of the Supermassive Black Hole Gravitational Wave Background
The gravitational wave background from supermassive black hole binaries has a universal heavy-tailed amplitude distribution with power-law index -4, causing divergent higher moments and dominance of the strongest signals by few loud sources.
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Two types of quasinormal modes of Casadio-Fabbri-Mazzacurati brane-world black holes
Quasinormal modes of massive scalars in CFM brane-world black holes split into two types, with modes disappearing at critical masses where real or imaginary frequency parts reach zero.
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Reaching diffraction-limited localization with coherent PTAs
Coherent map-making with pulsar distances in PTAs reaches diffraction-limited angular resolution of ~2 arcmin for GW sources at SNR=10 using roughly 9 pulsars.
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Stochastic gravitational-wave background search using data from five pulsar timing arrays
Combined five-PTA dataset yields posterior on SGWB power-law amplitude and index consistent with nonzero signal but below 5-sigma significance, with reconstructed angular correlations matching the Hellings-Downs prediction.
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Addressing prior dependence in hierarchical Bayesian modeling for PTA data analysis II: Noise and SGWB inference through parameter decorrelation
A reparametrized hierarchical Bayesian approach using normalizing flows and orthogonal projection of hyperparameters yields tighter noise constraints and partially breaks the red-noise-SGWB degeneracy in a minimal 3-pulsar PTA analysis.
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Finding Supermassive Black Hole Binary Mergers in Pulsar Timing Array Data
A complete SMBHB waveform model enables unified PTA searches for mergers and memory signals, with parameter recovery shown on simulated data for 10^8-10^10 solar mass systems.
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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.
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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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Late-time Quantum Vacuum Decay and its Cosmological Implications
Phenomenological late-time vacuum-tunneling models are fit to DESI DR2, supernova, and CMB data, allowing up to 50% vacuum-energy drop for z_t < 1 and a preferred z_t ~7 model that converts ~10% dark matter while easing cosmological tensions.
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Whispers of Supergravity in Gravitational Wave Backgrounds: Determining the Gravitino Mass from Cosmic Thermal History
Gravitino masses in the 100 TeV to 10^10 TeV range can be inferred from two frequency features in the stochastic gravitational wave spectrum produced by an early matter-dominated phase.
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Recombination Thickness as an Uncertainty in Inflationary Observables
Finite recombination thickness introduces Gaussian smoothing in ln k to the primordial power spectrum, producing non-trivial differences between TT and EE spectral indices that may be detectable in future CMB data.
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Positive Running of the Spectral Index for Scalar Theory and Modified Gravity
Positive running of the spectral index is achievable in Einstein-Gauss-Bonnet gravity with viable inflation, unlike standard scalar field and F(R) models which face challenges.
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Fixing the Renormalization of Inflationary Loops via Ward Identities
Ward identities from large gauge symmetry impose model-independent constraints on renormalizing inflationary loops and non-perturbatively govern the infrared power spectrum evolution.
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One Merge to Rule Them All: From Galaxy Interactions to Black Hole Mergers Using Horizon-AGN
Horizon-AGN shows galaxy and black hole merger rates both rise with stellar mass and fall with redshift, peaking near z=2-3, establishing a direct evolutionary link from galaxy interactions to black hole coalescences.
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Reviving Motivated Inflationary Potentials with $K$-inflation in the light of ACT
K-inflation with non-canonical kinetic term G(φ) shifts α-attractor T-models and natural inflation into the Planck-ACT-LB-BK18 allowed region while satisfying Swampland conjectures and producing testable GW spectra.
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Purely Quadratic Non-Gaussianity from Tachyonic Instability: Primordial Black Holes and Scalar-Induced Gravitational Waves
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Hawking area law in quantum gravity
Exact Hawking area law from black hole mergers restricts quantum gravity to singular Ricci-flat or specific regular black holes in Stelle and nonlocal theories, derives the standard entropy-area law, and realizes Barrow fractal black holes.
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Reconstructing inflationary features on large scales using genetic algorithm
Genetic algorithm reconstructs single-field inflationary models with features in the scalar power spectrum that fit Planck 2018 CMB data better by Δχ² ≲ -10 and suggest alternative background parameters.
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Grand Unified Origin of Enhanced Scalar Couplings: Connecting Radiative Electroweak Symmetry Breaking to SO(10) Dynamics
SO(10) scalar threshold corrections generate the Higgs quartic enhancement factor k≈6 required by radiative electroweak symmetry breaking, placing the Landau pole at 1.5-2×10^16 GeV near the GUT scale.
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Dark QCD Origin of the NANOGrav Signal and Self-Interacting Dark Matter
A dark QCD model with a first-order phase transition at 5-6 MeV produces the NANOGrav SGWB amplitude while supplying self-interacting dark matter via a 40 GeV baryon and 20-50 MeV dilaton, linked by entropy dilution.
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LISA as a probe of pre-big-bang physics: a nested sampling analysis
Nested sampling analysis indicates LISA could constrain H1, m, sigma_i and beta in the pre-big-bang model to relative uncertainties of about 18 percent under favorable conditions when including foregrounds.
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Measuring gravitational wave spectrum from electroweak phase transition and Higgs self-couplings
Frequency-domain simulations of the Taiji mission, including noise and foregrounds, demonstrate that the stochastic gravitational wave background from an electroweak phase transition can constrain Higgs cubic and quartic self-couplings in a singlet-extended Standard Model despite degeneracies.
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Sensitivity forecasts for gravitational-wave detectors to dark matter decaying into gravitons
Model-independent forecasts for the stochastic gravitational-wave background from ultralight dark matter decaying into gravitons and the sensitivity of current and future detectors to this signal.
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Expectations for the first supermassive black-hole binary resolved by PTAs II: Milestones for binary characterization
Simulations of continuous-wave searches show that PTA data first constrain GW frequency and strain amplitude together, then sky location, with chirp mass and inclination following later for evolving sources, with precision depending on source frequency and sky position.
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Expectations for the first supermassive black-hole binary resolved by PTAs I: Model efficacy
Simulations of PTA data show that a full gravitational-wave signal template achieves the highest Bayes factors and most robust parameter estimation for individual supermassive black hole binaries compared to an Earth-term template and a novel Spike Pixel cross-correlation model.