AEDGE: Dark Matter & GW Exploration

• AEDGE is a space-based mission using cold-atom interferometry to investigate ultralight dark matter and its induced shifts in atomic transitions.
• It targets mid-frequency gravitational waves, detecting signals from sources like intermediate-mass black hole mergers and cosmic events.
• The mission integrates terrestrial advances in atom interferometry with space-based precision techniques to enhance multi-messenger cosmology and dark energy tests.

AEDGE (Atomic Experiment for Dark Matter and Gravity Exploration in Space) is a proposed space-based mission utilizing cold-atom interferometry to probe two major scientific frontiers: (1) the nature of ultra-light dark matter via its possible coupling to fundamental constants and induced frequency shifts in atomic transitions, and (2) gravitational-wave (GW) astrophysics and cosmology in the poorly explored mid-frequency band (∼0.01–10 Hz). AEDGE is conceived as a highly interdisciplinary project at the interface of particle physics, gravitational physics, astrophysics, and cosmology, leveraging advances from terrestrial atom interferometry, laser metrology, and space-based precision measurement techniques.

1. Scientific Objectives and Context

AEDGE has two principal scientific goals:

• Search for ultra-light dark matter: Many leading theories posit that dark matter may manifest as coherent oscillating fields (such as axion-like particles, scalars, or vectors) with masses below the eV scale. These fields can induce oscillatory or transient changes in fundamental constants including the fine-structure constant (α) and particle masses, shifting atomic transition frequencies and thus becoming detectable through high-precision atomic interferometry.
• Detection of gravitational waves in the mid-frequency (deci-Hertz) band: This band (∼10⁻² to a few Hz) lies between the optimal sensitivity ranges of current space-borne (LISA, <0.1 Hz) and terrestrial (LIGO/Virgo/KAGRA, >10 Hz) GW detectors. AEDGE is uniquely positioned to observe astrophysical sources such as the inspiral and merger of intermediate-mass black holes, early inspirals of stellar-mass systems, stochastic backgrounds from cosmic strings or first-order phase transitions, and potentially exotic compact object (ECO) mergers. The ability to access this unexplored band enables AEDGE to complement and synergize with the global network of GW and dark matter detectors (El-Neaj et al., 2019, Badurina et al., 2021, Banks et al., 2023).

AEDGE's design builds on the expertise developed in leading terrestrial atom-interferometer projects (MAGIS, AION, MIGA, ZAIGA, etc.) and incorporates technology demonstrated in microgravity environments (e.g., LISA Pathfinder, CAL/ISS experiments).

2. Experimental Design and Measurement Principles

AEDGE utilizes two widely separated cold atom interferometers on separate satellites in medium Earth orbit, forming a long-baseline arrangement (nominally up to 40,000 km). Ensembles of ultra-cold atoms (such as ⁸⁷Sr) serve as inertial references; their internal states are interrogated via ultrastable lasers tuned to narrow optical clock transitions.

The interferometric phase difference, sensitive to both variations in atom transition frequencies and changes in the light-travel time (baseline length), is expressed as: $\Delta\phi = \omega_a \cdot (2L)$ where $\omega_a$ is the atomic transition frequency and $L$ the separation of atomic clouds. Variations in $\omega_a$—potentially induced by dark matter coupling—or changes in $L$—such as GW-induced strain $\delta L = hL$—yield a time-varying differential phase shift. Differential inter-satellite measurements allow for common-mode rejection of laser phase noise and systematic errors, a capability demonstrated to the Standard Quantum Limit in prototype systems (Baynham et al., 12 Apr 2025).

Sensitivity is further enhanced by employing techniques such as large momentum transfer (LMT) and resonant pulse sequences. Resonant enhancement is characterized by: $$\Delta\phi_{res} = 2Q \cdot k_{eff} \cdot h \cdot L \cdot \operatorname{sinc}\left(\frac{\omega_r nL}{2c}\right)\cos\left(\frac{\omega_r (n-1)L}{2c}\right)$$ with $Q$ the resonant quality factor, $k_{eff}$ the effective wave number ($k_{eff} = n\omega_a/c$ for an $n$-pulse LMT), and $\omega_r = \pi/T$ with interrogation time $T$.

3. Gravitational Wave Science in the Mid-Band

AEDGE's most distinctive astrophysical role is coverage of the 0.01–10 Hz GW band. This enables several advances beyond current laser interferometric observatories:

• Intermediate-mass black holes (IMBHs): AEDGE can observe the late inspiral and merger phases of IMBH binaries with total masses between $10^2$ and $10^5\ M_\odot$, using both broadband and resonant modes to maximize SNR and parameter estimation accuracy. The short, high-frequency resonant mode is especially effective at characterizing the final merger (Torres-Orjuela, 2023). The sensitivity allows precise sky localization and extraction of source parameters.
• Stochastic gravitational wave backgrounds (SGWB): AEDGE's frequency range overlaps with predicted peaks from cosmological phase transitions at $T_* \sim 10^4$–$10^6$ GeV and with the flat ($f^{2/3}$) background from compact binary inspirals. The mid-band is also ideal for constraining cosmic string tension $G\mu$ via the spectral turnover or plateau, and for detecting signatures from dark sector ECOs (Ellis et al., 2020, Barish et al., 2020, Banks et al., 2023).
• Multi-messenger and cosmological applications: By capturing long-duration GW signals (months–years), AEDGE is positioned to provide early warnings of mergers (notably white dwarf binaries relevant for SN Ia), as well as serve as a source of "bright" and "dark" standard sirens for cosmology (Sala et al., 22 Oct 2025, Pujolas et al., 2021, Yang et al., 2021). Simulations suggest that with as few as 5–10 golden dark siren events, AEDGE can constrain the Hubble constant $H_0$ to ∼2%, meeting the precision required to resolve the Hubble tension.

AEDGE's power-law–integrated and combined sensitivity curves illustrate up to two orders-of-magnitude improved reach in $\Omega_{\mathrm{GW}}$ at its target band, enabling unparalleled discrimination between cosmological and astrophysical backgrounds (Barish et al., 2020, Badurina et al., 2021).

4. Dark Matter Searches and Fundamental Constant Variations

Through atomic clock transitions, AEDGE probes both non-gravitational and gravitational signatures of dark matter:

• Non-gravitational signatures (coupled scalars/vectors): Oscillations in fundamental constants due to dark matter fields induce modulations of the atomic transition energies. Both linear (dimension-5) and quadratic (dimension-6) couplings to electrons, photons, and the Higgs sector are probed via phase measurements in atomic interferometers:
  • Linear: $$\mathcal{L}_{\rm linear} = \kappa\phi\left[\frac{1}{4}d_e^{(1)} F_{\mu\nu}F^{\mu\nu} - d_{m_e}^{(1)} m_e \bar{\psi}_e\psi_e\right]$$
  • Quadratic: $$\mathcal{L}_{\rm quadratic} = \kappa^2\phi^2\left[\frac{1}{4}d_e^{(2)} F_{\mu\nu}F^{\mu\nu} - d_{m_e}^{(2)} m_e \bar{\psi}_e\psi_e\right]$$

With linear couplings nearly excluded by existing torsion-balance results, AEDGE is optimally suited to constrain or detect quadratic couplings—probing possible quantum gravity-induced operators in the effective theory (Calmet et al., 2022).

• Purely gravitational signatures (gravitational redshift): AEDGE's gradiometer configuration allows it to detect ultralight dark matter through its induced spacetime metric perturbations (e.g., $\sim$10⁻¹⁷ eV scalar fields) and transient signals from passing compact dark matter clumps (masses $10^6$–$10^{10}$ kg). The observable phase shift is dominated by the differential gravitational redshift between distant atomic clouds, a regime where atom interferometers display parametric sensitivity advantages over laser interferometers for rapid spacetime fluctuations (Badurina et al., 1 May 2025).

5. Multi-Messenger and Precision Cosmology

AEDGE enables precision cosmology via GW standard sirens:

• Bright sirens: Events with EM counterparts (e.g., BNS–GRB associations) provide direct $d_L$–$z$ measurements. Projections indicate $\sim$30 such detections in a 5-year mission, yielding a $\sim$2.1% determination of $H_0$—adequate to arbitrate the current Hubble tension (Pujolas et al., 2021).
• Golden dark sirens: Exceptional localization, achieved through the orbital modulation of the detector and extended observation time (due to source longevity in the mid-band), allows unique host galaxy identification even without EM signals. Analyses show $\sim$1.5–2% $H_0$ precision with $5$–$10$ golden dark BBH sirens, facilitating independent, ladder-free measurements of cosmic expansion (Yang et al., 2021, Yang et al., 2022).
• Testing modified gravity and dark energy: AEDGE's determination of the GW luminosity distance, cross-compared with EM distances, allows tests of modified GW propagation (parameterized, e.g., by $\Xi_0$ or effective friction terms), constraining deviations from GR at the 5–6% level.

Accurate waveform modeling—including effects from source eccentricity which dramatically improve $d_L$ and localization inference—further refine cosmological analyses and multi-messenger alert performance (Yang et al., 2022).

6. Synergies with Other Detectors and Global Network Impact

AEDGE is designed for maximal complementarity with both ground and space-based GW and DM searches:

• Global frequency coverage: AEDGE's mid-frequency band bridges a gap not optimally accessible to LIGO/Virgo/KAGRA/ET (high-frequency) and LISA/TianQin/Taiji (low-frequency). This facilitates multi-band GW astronomy—monitoring sources from early inspiral through merger across observatories (Torres-Orjuela, 2023, Ellis et al., 2023).
• SGWB and foreground discrimination: Through combined power-law sensitivity curves, AEDGE, when included in a global detector network, substantially enhances the detection and separation of cosmological SGWB (from cosmic strings, phase transitions, inflationary preheating) from astrophysical backgrounds (e.g., unresolved binaries), notably improving constraints on cosmic string tension and phase transition parameters (Barish et al., 2020, Ellis et al., 2020, Cui et al., 2021).
• Quadrupolar correlation identification: By cross-correlating the time-varying antenna response of AEDGE (scalar–longitudinal basis) with those of other space missions (tensor basis, e.g., TianQin), the quadrupolar pattern of the SGWB can be robustly verified via orbital modulation signatures, providing crucial evidence for the stochastic GW background’s tensorial (GR) origin (Chen et al., 9 Oct 2024).

These networked measurements will assist in distinguishing astrophysical from cosmological sources, probing the nature of black hole seeds, and searching for non-standard gravitational-wave polarizations or relics of early Universe physics.

7. Collaboration, Technological Trajectory, and Future Prospects

AEDGE is organized as a broad international collaboration spanning Europe, the USA, China, and other regions, bringing together experts in quantum optics, atomic physics, gravitational wave data analysis, and cosmology (El-Neaj et al., 2019). The mission leverages ongoing developments from terrestrial projects, microgravity experiments, and advances in laser stabilization, clock interrogation, and long-baseline phase noise rejection (demonstrated in current prototypes (Baynham et al., 12 Apr 2025)).

Future directions for AEDGE and the field include:

• Further optimization of atom interferometer architectures (e.g., "inside" vs. "outside" atom cloud configurations, LMT enhancement), baseline increases, and clock transition selection for broader sensitivity.
• Algorithmic and pipeline advances for extracting cosmological and particle physics parameters from GW and DM signal catalogs, including degeneracy breaking via multi-band observations.
• Exploration of network configurations and mission designs for robust cross-correlation and background subtraction in the SGWB context.
• Continued technology transfer and synergy with related atom interferometric and optical GW missions.

AEDGE is positioned to play a pivotal role in the next generation of gravitational-wave astrophysics and dark matter research, providing new experimental access to fundamental physics at the intersection of quantum measurement, gravity, and cosmology.