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Testing gravity and dark energy

A lensed gravitational wave is an experiment in how gravity propagates on a non-trivial space-time. Theories beyond Einstein predict distortions that no lens made of ordinary matter can produce.

Gravitational-wave birefringence. Top: the signal crosses a Vainshtein-screened lens, with a non-trivial scalar-field configuration. Note that the low-frequency inspiral is emitted earlier and is shown leading. The lens gives the two polarizations slightly different speeds, which also differ from the speed of light. The lower panels show the signal as recorded in the detector, split by polarization (middle) and the combined signal (bottom). The delay is short enough that the two copies overlap, so the waveform is scrambled rather than repeated, and no electromagnetic counterpart is needed to see it. Adapted from Ezquiaga & Zumalacárregui.[1]

Hearing gravity propagate

Gravitational waves are a direct probe of gravity in a way light is not:[2] they are gravity, and their propagation is directly determined by the dynamics of the gravitational sector. In contrast, the way light responds to gravity is very constrained, the main effect on modified theories being how light deflection responds to matter.

A gravitational wave traveling across the Universe can be subject to a wealth of additional effects: non-standard gravitational dynamics can affect the amplitude, and even the speed, of gravitational waves.[3] Deviations are routinely searched for, as a valuable test of the cosmological properties of gravity.[4]

More than a modified deflection

Gravitational waves will be lensed in alternative theories too, so a lensed signal is no surprise beyond general relativity, and a modified deflection is the least of what a lens can do. The presence of a lens dramatically expands the imprints that non-standard gravity can impart on a gravitational wave.

Alternative theories feature additional fields, which acquire non-trivial configurations in the presence of a lens. A wave passing through that region need not keep its polarization structure intact, and the signatures it picks up depend on both polarization and frequency: a lens can split the two components of a gravitational wave like an anisotropic crystal, or disperse them by frequency like a prism forming a rainbow.

The animation shows one example: birefringence. If the two polarization states travel at slightly different speeds, one pulls ahead of the other. When the delay is long, the signal is split into two. When it is short, the two copies overlap and the waveform is scrambled into something no unlensed source produces.[1]

The Universe as a gravitational prism

Related effects give the propagation a frequency dependence that ordinary matter in Einstein's theory can not produce.[5] The frequency-dependent propagation stems from very simple interaction with any new gravitational field (zero derivatives): we expect it to be a universal signature of any non-minimal theory beyond Einstein.

These are qualitatively distinct signatures, not effects that can be easily mistaken by changes in the source's properties. And because they distort the signal, these tests can be performed on the entire sample of events, not just rare multi-messenger ones.

Lensing tests of gravity, ordered by how strongly the effect depends on frequency. “Interactions tested” counts the derivatives the underlying interaction involves: the fewer it needs, the wider the class of theories in which the effect appears, which is what makes the dispersive term close to universal. Adapted from Menadeo & Zumalacárregui.[5]
Lensing beyond
Einstein		 Geometric optics Wave optics
f2 f0 f−2 any f
Effect speed amplitude phase all
Observable birefringence oscillations dispersion diffraction
Analogy birefringent crystal neutrino oscillations prism single slit
Interactions tested 2 derivatives 1 derivative 0 derivatives all

Connecting to dark energy

The same extra fields that would modify how a wave propagates past a lens are often invoked to explain the accelerating expansion of the Universe. A decisive advantage of gravitational-wave propagation tests is their capacity to constrain dark-energy theories,[6] offering routes complementary to supernovae, the cosmic microwave background or galaxy surveys, where the baryon acoustic oscillations measured by DESI now favor a dark energy that evolves with time.[7] In contrast, tests of gravitational-wave emission are often limited to theories that modify gravity in strong fields, the opposite regime from the one required to alter cosmological dynamics.

The project will release these constraints as likelihoods usable with Einstein–Boltzmann solvers, like the hi-class code, so that they can be combined with cosmological data rather than quoted beside it.

References

  1. J. M. Ezquiaga, M. Zumalacárregui, Gravitational wave lensing beyond general relativity: birefringence, echoes and shadows Phys. Rev. D 102, 124048 (2020)
  2. LIGO Scientific and Virgo Collaborations, B. P. Abbott et al., Observation of gravitational waves from a binary black hole merger Phys. Rev. Lett. 116, 061102 (2016)
  3. J. M. Ezquiaga, M. Zumalacárregui, Dark energy in light of multi-messenger gravitational-wave astronomy Front. Astron. Space Sci. 5, 44 (2018)
  4. LIGO Scientific, Virgo and KAGRA Collaborations, A. G. Abac et al., GWTC-5.0: tests of general relativity arXiv preprint (2026)
  5. N. Menadeo, M. Zumalacárregui, Gravitational wave propagation beyond general relativity: Geometric optic expansion and lens-induced dispersion Phys. Rev. D 111, 104022 (2025)
  6. J. M. Ezquiaga, M. Zumalacárregui, Dark energy after GW170817: dead ends and the road ahead Phys. Rev. Lett. 119, 251304 (2017)
  7. DESI Collaboration, M. Abdul Karim et al., DESI DR2 results II: measurements of baryon acoustic oscillations and cosmological constraints Phys. Rev. D 112, 083515 (2025)

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