⚛️ general relativity

Probing Dark Matter with Strongly Lensed Binary Black Hole Mergers: Prospects in the Near Future

This paper forecasts that upcoming observations from the upgraded LIGO-Virgo-KAGRA network, particularly by the sixth observing run (O6), will enable competitive constraints on the mass of warm dark matter particles using strongly lensed binary black hole mergers, offering a complementary and independent probe to existing astrophysical methods.

Original authors: Koustav N. Maity, Souvik Jana, Ankur Barsode, Tejaswi Venumadhav, Parameswaran Ajith

Published 2026-09-07

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CC BY 4.0

Original authors: Koustav N. Maity, Souvik Jana, Ankur Barsode, Tejaswi Venumadhav, Parameswaran Ajith

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is filled with invisible stuff that holds galaxies together, a substance scientists call dark matter. For decades, the leading theory has been that this matter is "cold," meaning its particles move slowly and clump together easily to form a vast cosmic web of tiny, dense halos. But there is another possibility: that these particles are "warm," moving fast enough to smooth out the smallest clumps, leaving the universe with fewer small galaxies than the cold theory predicts. Distinguishing between these two ideas is one of the great challenges in modern cosmology, because the difference lies in the faintest, smallest structures that are incredibly difficult to see with traditional telescopes.

A new approach to solving this puzzle involves listening to the universe rather than looking at it. When two black holes spiral into each other and merge, they send out ripples in space-time known as gravitational waves. Occasionally, a massive galaxy or cluster of galaxies sits directly between Earth and these merging black holes. This massive object acts like a lens, bending the path of the gravitational waves and creating multiple copies of the same signal that arrive at our detectors at slightly different times. Because these waves pass through the lens without interacting with anything else, their timing carries a pristine record of the mass and structure of the lensing object. If dark matter is warm, the smallest lenses simply do not exist, and the pattern of these time delays will look different than if the matter is cold.

Researchers Koustav Maity and his colleagues have now mapped out how future gravitational-wave detectors could use this phenomenon to weigh the particles of dark matter. They focused on the upcoming observing runs of the global network of detectors, including the upgraded LIGO, Virgo, and KAGRA facilities. By simulating millions of potential black hole mergers and accounting for the specific limitations of these instruments, the team calculated how many of these lensed events would be detectable in the coming years. Their work shows that while the next few years of observation will yield only a handful of these rare, time-delayed signals, the data will already be powerful enough to set strict limits on the nature of dark matter.

The study reveals that by the time the detectors reach their sixth major observing run, the data will be sensitive enough to rule out dark matter particles that are lighter than about 5 to 10 kiloelectron-volts. This is a significant milestone, as it would make gravitational-wave observations competitive with the tightest constraints currently available from electromagnetic astronomy, such as studies of ancient starlight and the distribution of satellite galaxies. The researchers found that the key to this measurement lies in the shortest time delays. If dark matter is warm, the smallest gravitational lenses are missing, which means the shortest delays—those lasting only minutes or hours—would be absent from the data. If the matter is cold, those short delays would be present. By counting how many short delays appear, the detectors can effectively weigh the dark matter particles.

Looking further ahead, the potential for discovery grows dramatically. The team forecasts that as detector networks expand in the following decades, the precision of these measurements will improve by roughly an order of magnitude. This means that within a decade or two, gravitational-wave astronomy could not only confirm whether dark matter is warm or cold but could potentially measure the exact mass of the particles responsible. The researchers also demonstrated that this method is robust against confusion with other cosmic variables, such as the expansion rate of the universe, because the signature of warm dark matter affects only the smallest scales, leaving the larger time delays untouched.

This work represents a shift in how scientists might probe the invisible universe. Instead of relying solely on the light from distant stars or the distribution of visible galaxies, the field is moving toward using the timing of gravitational ripples to count the smallest building blocks of the cosmos. The upcoming observing runs will serve as a critical test, determining whether the universe is populated by the tiny, numerous halos predicted by cold dark matter or the smoother, sparser landscape suggested by warm dark matter. As the detectors come online and begin to hear the echoes of colliding black holes, they will provide a direct, independent check on the fundamental nature of the dark matter that shapes our reality.

Problem Statement
The nature of dark matter (DM) remains one of the most significant open questions in cosmology. While the standard $\Lambda$ CDM model successfully explains large-scale observations, it lacks direct detection of cold dark matter (CDM) particles. Warm dark matter (WDM) offers a compelling alternative, consisting of thermal relic particles (e.g., sterile neutrinos) that decouple while relativistic. WDM introduces a free-streaming scale that suppresses the formation of low-mass dark matter halos compared to CDM. This suppression alters the mass function of halos, leading to shallower gravitational potentials and fewer low-mass structures.

Current constraints on the WDM particle mass ( $m_{\text{wdm}}$ ) rely heavily on electromagnetic (EM) probes, such as the Lyman- $\alpha$ forest, high-redshift quasar absorption, and strong-lensing flux ratios, yielding bounds generally in the range $m_{\text{wdm}} \gtrsim 6\text{--}10$ keV. However, these constraints often depend on complex astrophysical modeling (e.g., star formation efficiency, baryonic physics). This paper investigates whether gravitational-wave (GW) observations of strongly lensed binary black hole (BBH) mergers can provide a complementary, independent, and purely gravitational probe of the DM nature. Specifically, the authors aim to forecast the ability of upcoming GW observing runs (O5, O6, and beyond) to constrain $m_{\text{wdm}}$ by analyzing the time-delay distribution of lensed events, while rigorously accounting for detector selection effects.

Methodology
The authors employ a Bayesian inference framework to forecast constraints on the inverse WDM mass ( $m^{-1}_{\text{wdm}}$ ) using simulated populations of lensed BBH mergers. The methodology involves several key steps:

Modeling the Lens Population: The authors model the suppression of the halo mass function (HMF) in WDM scenarios relative to CDM using the rescaling prescription of Schneider et al. (2012). Lenses are approximated as singular isothermal spheres (SISs), parameterized by velocity dispersion $\sigma$ . The number density of lenses is derived from the HMF, where lower $m_{\text{wdm}}$ values suppress the low- $\sigma$ (low-mass) end of the distribution.
Strong Lensing Probability: The optical depth for strong lensing is calculated by integrating the lens number density over redshift and velocity dispersion. The probability of a source being lensed at least once is derived using Poisson statistics.
Detector Selection Effects: Unlike previous studies assuming next-generation (XG) detectors sensitive to all mergers, this work explicitly models the selection function for current and near-future detectors (O4 through Voyager/XG). The authors calculate the detectable lensing fraction ( $u_{\text{det}}$ ) and the time-delay distribution ( $dP_{\text{det}}/d\Delta t$ ) by convolving the intrinsic merger rates (using Dominik et al. and Madau & Dickinson models) with the detector sensitivity and the strong-lensing probability.
Time-Delay Signature: The core physical signature is that WDM suppresses the abundance of low-mass halos, which are responsible for short time delays ( $\Delta t$ ). Consequently, the WDM time-delay distribution exhibits a depletion in the short- $\Delta t$ tail compared to CDM. The authors derive an approximate scaling relation showing that the suppression threshold $\Delta t_{\text{min}}$ scales as $m_{\text{wdm}}^{-4.44}$ .
Bayesian Inference: The authors construct a likelihood function combining two observables: the observed lensing fraction ( $u_{\text{det}}$ ) and the distribution of measured time delays $\{\Delta t_i\}$ . They assume a uniform prior on $m^{-1}_{\text{wdm}}$ and marginalize over cosmological parameters ( $H_0, \Omega_m, \sigma_8$ ) to test for degeneracies.

Key Contributions

Incorporation of Selection Effects: The paper provides a rigorous treatment of detector selection effects for current-generation (O5) and near-future (O6) networks, demonstrating that these effects are critical for accurate forecasting, unlike in idealized XG scenarios.
Dual-Observable Constraint: The analysis combines the lensing fraction and the time-delay distribution, showing that while the fraction alone offers modest constraints, the inclusion of the time-delay distribution significantly tightens the bounds.
Degeneracy Analysis: The authors explicitly demonstrate that the WDM signature (suppression of the short- $\Delta t$ tail) is distinct from the effects of varying cosmological parameters, which distort the distribution across the entire $\Delta t$ range. This confirms that $m_{\text{wdm}}$ can be constrained independently of $H_0, \Omega_m,$ and $\sigma_8$ .
Forecasting for Near-Term Runs: The study provides specific forecasts for the LIGO-Virgo-KAGRA (LVK) network upgrades, moving beyond theoretical XG projections to practical near-future expectations.

Results

O5 Run: The fifth observing run is expected to yield only a modest constraint ( $m^{-1}_{\text{wdm}} \lesssim 0.30 \text{ keV}^{-1}$ , or $m_{\text{wdm}} \gtrsim 3.3 \text{ keV}$ ) due to the low expected number of lensed pairs.
O6 Run: By the sixth observing run, the forecasted bound tightens to $m^{-1}_{\text{wdm}} \lesssim 0.1\text{--}0.2 \text{ keV}^{-1}$ ( $m_{\text{wdm}} \gtrsim 5\text{--}10 \text{ keV}$ ). This is comparable to the tightest existing astrophysical constraints derived from EM probes.
Future Runs (Voyager/XG): Networks operating beyond O6 are projected to improve the constraint by approximately an order of magnitude, reaching $m^{-1}_{\text{wdm}} \lesssim 0.036 \text{ keV}^{-1}$ ( $m_{\text{wdm}} \gtrsim 28 \text{ keV}$ ), surpassing current EM limits in many scenarios.
Robustness: The results are shown to be robust against variations in the BBH merger-rate models (Dominik vs. MD-nodelay) and rate calibrations. Furthermore, marginalizing over cosmological parameters does not significantly degrade the constraints on $m_{\text{wdm}}$ .
Mass Measurement: If DM is indeed warm (e.g., $m_{\text{wdm}} = 8.6 \text{ keV}$ ), the authors show that future runs could not only set upper limits but potentially measure the particle mass with increasing precision as the sample size grows.

Significance
The paper claims that strongly lensed GWs offer a "complementary, competitive, and independent probe of dark matter." By relying solely on gravitational interactions, this method bypasses the astrophysical uncertainties (such as baryonic feedback and star formation efficiency) that plague EM-based constraints. The authors emphasize that by the O6 observing run, GW observations will reach a level of precision competitive with the best current EM bounds, and future runs will provide significantly tighter constraints. This establishes strongly lensed GWs as a viable and powerful tool for testing the fundamental nature of dark matter in the near future.

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