How LISA Will Unveil the Secrets of Ultralight Dark Matter with Quadratic Coupling
Ultralight dark matter interacts with Standard Model particles gravitationally and non-gravitationally, which can produce characteristic signals in gravitational-wave experiments. Signals induced by quadratic coupling are studied in the LISA detector. Due to the quadratic nature of the coupling, the signal appears at two frequencies: twice the dark matter mass and frequencies below its typical kinetic energy. The analysis showed that LISA outperforms current limits from ground-based and astrophysical methods in certain mass ranges. A key advantage is the absence of shielding effects, which severely limit the sensitivity of Earth-based experiments.
Context
The nature of dark matter is one of the central problems in modern physics. If it consists of ultralight bosons (with mass less than 1 eV), such particles can form coherent classical waves whose coherence length exceeds astrophysical scales. These waves can interact with ordinary matter through the Standard Model not only gravitationally but also directly—via quadratic scalar couplings. The quadratic nature of the interaction is a common feature of many theories: from the axion to dilatonic scalars. The future space-based interferometer LISA, designed to detect gravitational waves, could prove to be an ideal tool for searching for such particles in the vicinity of the Solar System. The existence of dark matter was first hypothesized by Fritz Zwicky and later compellingly demonstrated by Vera Rubin.
Methods
To evaluate LISA's sensitivity, a Bayesian analysis was performed on synthetic data simulating a 4-year mission with a 75% duty cycle. Data were generated as time series for channels A, E, T—orthogonal combinations of interferometric signals constructed using Time-Delay Interferometry (TDI), which suppresses laser noise. The noise model included instrumental sources (shot noise from the optical system and test-mass acceleration) and the astrophysical background from unresolved binary systems, mostly white dwarfs. The signal from dark matter was calculated through perturbations of test-mass motion (acceleration effect) and the Shapiro gravitational delay as the laser beam propagates in the field potential, taking into account relativistic corrections such as time dilation (suppressed in TDI). The interaction obeys the law of universal gravitation for gravitational coupling and an analogous structure for direct couplings. Freely falling test masses realize Einstein's equivalence principle, allowing the pure dark matter effect to be isolated. The quadratic nature of the coupling leads to a doubling of the oscillation frequency, equivalent to a Doppler shift of the original wave.
Results
The analysis revealed two distinct signals in frequency. The coherent signal (fast mode) appears as an almost monochromatic peak at a frequency equal to twice the particle mass (f = m/π), slightly broadened due to the Doppler spread of velocities (~160 km/s). The stochastic signal (slow mode) covers frequencies below the characteristic kinetic energy of the field (ω ≪ mσ²) and has a power-law falling spectrum. LISA will be able to probe two mass ranges: from 10^{-19} eV to 10^{-15} eV via the coherent signal and from 10^{-14} eV to 10^{-9} eV via the stochastic one. For gravitational interaction, even a single LISA constellation will constrain the local dark matter density down to ~10^4 times the standard value (ρ₀ = 0.4 GeV/cm³) for masses ~10^{-13} eV, and down to ~10^{10} for masses ~10^{-9} eV. For direct quadratic couplings (e.g., to electrons or photons), sensitivity reaches coupling constants d_i ~ 10^{10}–10^{16} (in units of inverse Planck mass), surpassing current limits from ground-based interferometers and experiments like MICROSCOPE, especially for masses above 10^{-14} eV. Key result: LISA's space-based platform completely removes the screening problem that suppresses signals in Earth-based searches at |g| > 10^9.
Implications
These results reinforce the role of gravitational-wave detectors as multipurpose observatories for fundamental physics. LISA will not only register mergers of supermassive black holes but also, for the first time, directly measure the local dark matter density in the Solar System's vicinity—a quantity that still lacks direct observational confirmation. Constraints on quadratic scalar couplings will close a significant portion of parameter space for QCD-type axion models, although they won't reach the minimal predicted line for the standard axion. Nevertheless, for axion-like particles with suppressed mass, this will provide a unique test. Moreover, the analysis showed that cross-correlation between different space missions (LISA, TianQin, Taiji) will be effective only for gravitational signals due to the long-range nature of the interaction.
Future development
In the future, combining LISA data with other experiments such as pulsar timing arrays, astrometric observations, and atomic clocks on satellites will enable a multi-messenger investigation of ultralight dark matter. Of particular interest is the development of cross-correlation methods between LISA and the Chinese Taiji project or the European Decigo, which could enhance sensitivity to the stochastic signal. Also promising is the study of nonlinear screening effects near the Sun and planets, which may create additional features in the spectrum. Theoretical refinement of the signal shape accounting for a realistic field profile in the Sun's gravitational potential (instead of the plane-wave approximation) will improve the precision of future analyses.
Impact
The results will impact cosmic-ray physics, high-energy astrophysics, and fundamental symmetries, as quadratic couplings modify effective particle masses and interaction constants. This is especially important for testing models with violation of the equivalence principle on cosmic scales.
Next steps
Next steps will include detailed simulations with non-stationary noise and accounting for possible systematics, as well as developing algorithms to extract the signal from real data after LISA's launch in 2035.
Key open problems
The work directly addresses the unsolved problem of the nature of dark matter and measuring its local density, as well as the question of the existence of new scalar fields beyond the Standard Model. The lack of knowledge about non-gravitational interactions of dark matter leaves open the possibility of the quadratic scenario, which can only be tested in space experiments free from screening.
🎯 The quadratic coupling makes the dark matter signal sound in two octaves at once: a high-frequency 'note' at twice the particle mass and a low-frequency 'hum' of stochastic fluctuations. LISA's virtuosity is such that it will be able to hear this duet through the noise of its own lasers and even separate it from the background of white-dwarf binaries, like picking out a quiet whisper in a noisy orchestra.
Key numbers
- local dark matter density (standard value): 0.4 GeV/cm³
- dark matter particle velocity dispersion: ~160 km/s
- mass range accessible to LISA: 10^{-19} – 10^{-9} eV
- LISA arm length: 2.5·10^6 km
- screening threshold for ground-based experiments: |g| ~ 10^9