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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Chern-Simons Modified General Relativity
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abstract
Chern-Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation in particle physics and string theory. In this review, we begin by providing a pedagogical derivation of the three distinct ways such an extension arises: (1) in particle physics, (2) from string theory and (3) geometrically. We then review many exact and approximate, vacuum solutions of the modified theory, and discuss possible matter couplings. Following this, we review the myriad astrophysical, solar system, gravitational wave and cosmological probes that bound Chern-Simons modified gravity, including discussions of cosmic baryon asymmetry and inflation. The review closes with a discussion of possible future directions in which to test and study gravitational parity violation.
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background 13representative citing papers
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.
In Ricci-coupled scalar-Gauss-Bonnet gravity, the change in scalar charge during binary black hole mergers generates a scalar memory contribution that modifies the total memory signal on observable timescales.
A reduction scheme transforms arbitrary N-term scalar and matrix recurrence relations from black hole perturbations in modified gravity into three-term relations solvable by continued fractions.
Leading-order deviations from general relativity in scalar quasinormal modes of rotating black holes are computed numerically up to dimensionless spins of 0.99 in quadratic-curvature scalar-tensor theories.
New quasi-universal relations connect static tidal deformability Λ⁰ to its dynamical correction Λ² and to Mω* with equation-of-state scatter below 5% and 2.8% respectively across 59 models.
Hierarchical Bayesian inference on 20 high-SNR simulated binary neutron star events shows a linear lnΛ-lnQ relation suffices and constrains dynamical Chern-Simons gravity length scale to ≤10 km.
GW250114 data confirm the remnant is consistent with a Kerr black hole and bound the dominant quadrupolar mode frequency to within a few percent of the GR prediction, with constraints tighter than prior multi-event catalogs.
γ-duality in the EPRL spinfoam model determines the relation between parity-even and parity-odd terms in an effective gravity theory, allowing the Barbero-Immirzi parameter to be measured from inflationary tensor observables.
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
Dyonic Ellis-Bronnikov wormholes supported by phantom dilaton, axion, and dyonic gauge fields arise from warped five-dimensional scalar-tensor theories via Kaluza-Klein reduction.
One-loop integration of a heavy fermion with inflaton-dependent mass in axion inflation generates localized gauge-field production and a detectable chiral gravitational-wave signal in the deci-hertz range.
Neural post-Einsteinian analysis of GWTC-3 finds no GR violation and sets constraints covering both post-Newtonian and beyond-post-Newtonian deviations in a single theory-agnostic setup.
In quadratic-EMSG the self-acceleration of self-gravitating bodies vanishes at 1PN order and total linear momentum is conserved, consistent with binary-pulsar bounds.
Applies parameterized dispersion to eccentric BBH burst waveforms, deriving a 2.5PN time-delay correction and Bessel amplitude modulation, then uses Fisher matrix to project LIGO constraints that are stronger than current bounds for Hořava-Lifschitz and extra-dimension models.
In dynamical Chern-Simons inflation the parity-odd trispectrum is a double copy of the mixed bispectrum and parity-odd power spectrum via a prior factorization formula.
Fuzzy dark matter induces frequency-dependent amplitude birefringence in gravitational waves with periodic time modulation set by the scalar mass, but no velocity birefringence.
Parameterized inspiral tests on GW230529 find consistency with GR, with |δφ̂_{-2}| ≲ 8×10^{-5} and ℓ_GB ≲ 0.51 M_⊙ in ESGB theories.
A CNN framework using response functions from gravitational wave mismatches classifies signals as GR or beyond-GR with 33 times better sensitivity than raw waveforms and detects massive gravity deviations at graviton masses around 10^{-23} eV/c².
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.
Magnetic fields lower the scalarization threshold for electromagnetic and gravitational Chern-Simons couplings but produce opposite trends on the two Gauss-Bonnet branches, with nonlinear terms converting exponential growth into bounded oscillations.
Analysis of GW231123 with IMRPhenomXPHM, IMRPhenomXO4a and NRSur7dq4 yields no waveform-independent evidence for polarization birefringence, with 90% upper limits on the derived coefficient of 0.378, 0.097 and 0.273 respectively.
Unitarity and torsion requirements in (3+1)-dimensional string effective actions introduce only a subleading four-derivative term that leaves the StRVM inflationary dynamics unchanged, confirming the model's phenomenological completeness within string theory.
A review summarizing modified theories of gravity, their effects on compact objects, existing bounds from astrophysical observations, and the promise of future gravitational wave tests for strong-field gravity.
citing papers explorer
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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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Chiral Gravitational Wave Background from Audible Axion via Nieh-Yan Term
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.
-
Scalar memory from compact binary coalescences
In Ricci-coupled scalar-Gauss-Bonnet gravity, the change in scalar charge during binary black hole mergers generates a scalar memory contribution that modifies the total memory signal on observable timescales.
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Beyond Three Terms: Continued Fractions for Rotating Black Holes in Modified Gravity
A reduction scheme transforms arbitrary N-term scalar and matrix recurrence relations from black hole perturbations in modified gravity into three-term relations solvable by continued fractions.
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Quadratic gravity corrections to scalar QNMs of rapidly rotating black holes
Leading-order deviations from general relativity in scalar quasinormal modes of rotating black holes are computed numerically up to dimensionless spins of 0.99 in quadratic-curvature scalar-tensor theories.
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Universal Relations with Dynamical Tides
New quasi-universal relations connect static tidal deformability Λ⁰ to its dynamical correction Λ² and to Mω* with equation-of-state scatter below 5% and 2.8% respectively across 59 models.
-
Inferring neutron-star Love-Q relations from gravitational waves in the hierarchical Bayesian framework
Hierarchical Bayesian inference on 20 high-SNR simulated binary neutron star events shows a linear lnΛ-lnQ relation suffices and constrains dynamical Chern-Simons gravity length scale to ≤10 km.
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Black Hole Spectroscopy and Tests of General Relativity with GW250114
GW250114 data confirm the remnant is consistent with a Kerr black hole and bound the dominant quadrupolar mode frequency to within a few percent of the GR prediction, with constraints tighter than prior multi-event catalogs.
-
Spinfoams, $\gamma$-duality and parity violation in primordial gravitational waves
γ-duality in the EPRL spinfoam model determines the relation between parity-even and parity-odd terms in an effective gravity theory, allowing the Barbero-Immirzi parameter to be measured from inflationary tensor observables.
-
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
-
Dyonic Ellis-Bronnikov wormholes from warped extra dimensions
Dyonic Ellis-Bronnikov wormholes supported by phantom dilaton, axion, and dyonic gauge fields arise from warped five-dimensional scalar-tensor theories via Kaluza-Klein reduction.
-
Axion Inflation from Heavy-Fermion One-Loop Effects
One-loop integration of a heavy fermion with inflaton-dependent mass in axion inflation generates localized gauge-field production and a detectable chiral gravitational-wave signal in the deci-hertz range.
-
Neural Post-Einsteinian Test of General Relativity with the Third Gravitational-Wave Transient Catalog
Neural post-Einsteinian analysis of GWTC-3 finds no GR violation and sets constraints covering both post-Newtonian and beyond-post-Newtonian deviations in a single theory-agnostic setup.
-
Dynamics of the $N$-body system in energy-momentum squared gravity: II. Existence of a Self-Acceleration
In quadratic-EMSG the self-acceleration of self-gravitating bodies vanishes at 1PN order and total linear momentum is conserved, consistent with binary-pulsar bounds.
-
Probing modified gravitational-wave dispersion with bursts from eccentric black-hole binaries
Applies parameterized dispersion to eccentric BBH burst waveforms, deriving a 2.5PN time-delay correction and Bessel amplitude modulation, then uses Fisher matrix to project LIGO constraints that are stronger than current bounds for Hořava-Lifschitz and extra-dimension models.
-
A Match Made in Heaven: Linking Observables in Inflationary Cosmology
In dynamical Chern-Simons inflation the parity-odd trispectrum is a double copy of the mixed bispectrum and parity-odd power spectrum via a prior factorization formula.
-
Gravitational Wave Birefringence from Fuzzy Dark Matter
Fuzzy dark matter induces frequency-dependent amplitude birefringence in gravitational waves with periodic time modulation set by the scalar mass, but no velocity birefringence.
-
Tests of General Relativity with GW230529: a neutron star merging with a lower mass-gap compact object
Parameterized inspiral tests on GW230529 find consistency with GR, with |δφ̂_{-2}| ≲ 8×10^{-5} and ℓ_GB ≲ 0.51 M_⊙ in ESGB theories.
-
Testing General Relativity Through Gravitational Wave Classification: A Convolutional Neural Network Framework
A CNN framework using response functions from gravitational wave mismatches classifies signals as GR or beyond-GR with 33 times better sensitivity than raw waveforms and detects massive gravity deviations at graviton masses around 10^{-23} eV/c².
-
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.
-
Scalarizations of magnetized Reissner-Nordstr\"om black holes induced by parity-violating and parity-preserving interactions
Magnetic fields lower the scalarization threshold for electromagnetic and gravitational Chern-Simons couplings but produce opposite trends on the two Gauss-Bonnet branches, with nonlinear terms converting exponential growth into bounded oscillations.
-
Polarization Birefringence and Waveform Systematics in GW231123
Analysis of GW231123 with IMRPhenomXPHM, IMRPhenomXO4a and NRSur7dq4 yields no waveform-independent evidence for polarization birefringence, with 90% upper limits on the derived coefficient of 0.378, 0.097 and 0.273 respectively.
-
The most general four-derivative Unitary String Effective Action with Torsion and Stringy-Running-Vacuum-Model Inflation: Old ideas from a modern perspective
Unitarity and torsion requirements in (3+1)-dimensional string effective actions introduce only a subleading four-derivative term that leaves the StRVM inflationary dynamics unchanged, confirming the model's phenomenological completeness within string theory.
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Testing General Relativity with Present and Future Astrophysical Observations
A review summarizing modified theories of gravity, their effects on compact objects, existing bounds from astrophysical observations, and the promise of future gravitational wave tests for strong-field gravity.
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The Confrontation between General Relativity and Experiment
Experiments confirm general relativity to high precision in weak-field and strong-field regimes, with gravitational wave damping matching predictions to better than 0.5 percent.
- Theoretical and Observational Bounds on Dynamical Chern-Simons Gravity as an Effective Field Theory