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 second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
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abstract
We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of $4\%$. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of $60$ and a false alarm probability of about $0.1\%$ ($\gtrsim 3\sigma$ significance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The inferred spectrum from the latest EPTA data from new generation observing systems is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of ($2.5\pm0.7)\times10^{-15}$ at a reference frequency of $1\,{\rm yr}^{-1}$. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years.
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Calypso is a parameter-conditioned stochastic surrogate model for circumbinary accretion flows using PCA and multivariate Gaussian modeling, released as open-source software with a closed-form likelihood for parameter inference from time series.
Phase-resolved scalar distance bounds are derived for ekpyrotic, bouncing, and cyclic cosmologies, yielding a master condition that lower-bounds ε_ek from remaining distance after conversion and bounce.
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.
High-resolution lunar simulations reveal up to tenfold amplification of deci-hertz gravitational-wave signals in thick-crust regions via mode coupling.
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.
Axion-like fields coupled to the Nieh-Yan term generate a chiral GW background during radiation domination, with parameter space explored for detectability in PTA and space-based observatories.
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.
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
PTA statistical tests lose sensitivity to non-Gaussian GW features after decorrelation and cannot distinguish them model-agnostically.
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.
A phenomenological dipole anisotropy in primordial perturbations induces dipolar and quadrupolar anisotropies in SIGW energy density spectra, producing frequency-dependent PTA overlap reduction functions that depend on pulsar sky distribution, but NANOGrav 15-year data yields no significant evidence
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.
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.
Finite populations of inspiralling supermassive black hole binaries plus finite observation windows introduce non-Gaussian statistics in the pulsar timing array signal that are absent from the Gaussian approximation used in current analyses.
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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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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\texttt{calypso}: a Parameter-Conditioned Stochastic Surrogate Model for Circumbinary Accretion Time-Series
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Phase-resolved field-space distance bounds in ekpyrotic, bouncing and cyclic cosmologies
Phase-resolved scalar distance bounds are derived for ekpyrotic, bouncing, and cyclic cosmologies, yielding a master condition that lower-bounds ε_ek from remaining distance after conversion and bounce.
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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.
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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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Thick Lunar Crust Amplifies Deci-Hertz Gravitational-Wave Signal
High-resolution lunar simulations reveal up to tenfold amplification of deci-hertz gravitational-wave signals in thick-crust regions via mode coupling.
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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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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.
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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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Chiral Gravitational Wave Background from Audible Axion via Nieh-Yan Term
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Higher-order statistics of the stochastic gravitational wave background from supermassive black hole binaries
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