Chern-Simons Gravity Theories and Gravitational Waves

Chern-Simons gravity theories represent a class of extensions to general relativity in which a topological term, the Chern-Simons three-form, couples to curvature or to a pseudoscalar field. This modification introduces parity-violating interactions that leave the background cosmology largely unaltered but can induce distinctive signatures in the propagation and generation of gravitational waves. In particular, left- and right-handed circular polarisations acquire different dispersion relations, leading to amplitude and phase birefringence over cosmological distances. The theory also supports novel black-hole and black-string solutions in which the Cotton tensor contributes non-trivially to the field equations. Experimentally, gravitational-wave observatories provide a unique arena to probe these parity-violating effects: measurements of waveform polarisation, velocity birefringence and deviations from standard dispersion relations can constrain the energy scale of Chern-Simons couplings. At the same time, model-dependent implementations involving axion-like fields or torsion extend the framework into teleparallel or Nieh–Yan modified gravity, enriching the landscape of potential observational signatures and offering connections to high-energy physics and quantum gravity scenarios.

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Technical terms

Chern–Simons term: A topological density coupling a pseudoscalar field to the Pontryagin invariant, leading to parity-violating modifications of gravity.

Parity violation: The breaking of mirror symmetry in physical interactions, here manifested as different dynamics for left- and right-handed gravitational-wave modes.

Cotton tensor: A three-dimensional analogue of the Weyl tensor that arises in Chern–Simons gravity field equations, encoding the parity-violating contributions.

Torsion: A geometric property characterising the antisymmetric part of the connection, which can couple to scalar or pseudoscalar fields in teleparallel and Nieh–Yan gravity models.

Circular polarisation modes: The left- and right-handed helicity states of gravitational waves, whose differential propagation can signal parity-violating physics.

Birefringence: The phenomenon in which different polarisation states travel at different speeds, producing relative phase and amplitude shifts detectable in precision waveform analyses.

References

1. Static and rotating black strings in dynamical Chern–Simons modified gravity. European Physical Journal C (2019).
2. Model-independent test of the parity symmetry of gravity with gravitational waves. European Physical Journal C (2020).
3. Search for the Birefringence of Gravitational Waves with the Third Observing Run of Advanced LIGO-Virgo. The Astrophysical Journal (2022).