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First detection of galaxies' transverse motion with the moving lens effect

This paper reports the first statistical detection ( $4.8\sigma$ ) of galaxies' transverse motion at cosmological distances by observing the "moving-lens effect"—a specific temperature shift in the cosmic microwave background caused by moving massive objects—thereby enabling the future mapping of the Universe's full three-dimensional velocity field.

Original authors: Selim Hotinli

Published 2026-07-30

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CC BY 4.0

Original authors: Selim Hotinli

Original paper licensed under CC BY 4.0 (https://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

Imagine the universe as a giant, invisible ocean of space, filled with islands of matter called galaxies. For a long time, astronomers could only tell if these islands were moving toward us or away from us, like a siren on a train getting louder or softer. This is called "line-of-sight" motion, and we've been able to measure it for decades. But what about the other way? What if a galaxy is zooming sideways, across our view, like a car speeding past on a highway? Until now, that sideways motion has been a ghost—impossible to catch because it doesn't change the color of the light coming from the galaxy in a way our eyes can easily spot.

To understand how we might catch this ghost, we need to look at the "background noise" of the universe. Imagine the entire sky is covered in a faint, ancient glow left over from the Big Bang, called the Cosmic Microwave Background (CMB). It's like the static on an old TV, but it's actually the oldest light in existence. When a massive object, like a cluster of galaxies, moves through this static, it drags its gravity along with it. Just as a moving car creates a wind that pushes dust differently in front of it versus behind it, a moving galaxy cluster pushes on the light passing by it. This creates a tiny, specific pattern: the light gets slightly hotter on one side and slightly colder on the other. This is the "moving lens effect," a cosmic trick of gravity that has been predicted for decades but was too faint to see until now.

This paper reports the first time scientists have successfully spotted this invisible sideways motion. The team, led by researchers at the Perimeter Institute and other institutions, acted like cosmic detectives. They didn't just look at the galaxies; they looked at the ancient static (the CMB) right next to them. They used a massive telescope in the Atacama Desert in Chile (the Atacama Cosmology Telescope) to map the temperature of the universe's background glow. Then, they cross-referenced this with a huge catalog of millions of galaxies from the Dark Energy Spectroscopic Instrument (DESI).

The scientists built a "template" of where the sideways winds should be blowing based on how the galaxies are clustered. They then asked: "Does the pattern of hot and cold spots in the ancient light match the direction the galaxies are supposed to be moving?" The answer was a resounding yes. By combining data from the northern and southern parts of the sky, they found a match with a statistical confidence of 4.8 sigma. In the world of science, this is a very strong signal—strong enough to say, "We are almost certainly seeing the real thing," rather than just a random fluke. Even when they used a smaller, more careful group of galaxies, the signal was still there at 3.7 sigma.

The researchers were very careful to make sure they weren't being fooled by other things, like dust or gas in space that could mimic the signal. They ran several "null tests," which are like checking if your shadow is actually you or just a trick of the light. They checked if the signal disappeared when they looked at the wrong type of pattern (a "curl" instead of a "gradient"), and it did. They checked if the signal vanished when they compared different frequencies of light, and it mostly did, leaving only a tiny, expected amount of noise. They even used computer simulations to prove that the signal they found couldn't be explained by known foreground contaminants.

This discovery is a big deal because it turns our view of the universe from a flat, one-dimensional movie into a full 3D experience. Before this, we could only see galaxies moving toward or away from us. Now, we have the first statistical proof that we can also see them moving sideways. This opens the door to mapping the entire three-dimensional velocity field of the universe, helping us understand how gravity pulls on the cosmic web and how the universe is growing. While the measurement is still a bit rough around the edges (it's a "statistical detection," meaning it's an average over millions of galaxies, not a photo of a single galaxy zooming by), it proves the method works. It's the first time we've successfully caught the universe's sideways shuffle, and it paves the way for future telescopes to map the cosmic dance in high definition.

Technical Summary: First Detection of Galaxies' Transverse Motion with the Moving Lens Effect

Problem Statement
Cosmic structure is dynamic, with galaxies and dark matter halos moving under gravity. While the line-of-sight (radial) component of these peculiar velocities has been measured via redshift-space distortions and the kinetic Sunyaev–Zel'dovich (kSZ) effect, the two transverse components (motion across the sky) at cosmological distances have remained inaccessible. Measuring these transverse velocities is crucial for converting cosmic-velocity surveys from one-dimensional probes into fully three-dimensional maps of the Universe's velocity field. This would allow for independent measurements of structure growth rates and help calibrate uncertainties in kSZ measurements, such as the optical-depth degeneracy.

The "moving-lens effect," first predicted by Birkinshaw and Gull (1983), offers a pathway to detect this motion. As a massive object moves transversely across the line of sight, its changing gravitational potential induces a time-varying shift in Cosmic Microwave Background (CMB) photons. Photons passing the trailing side of the moving potential are blueshifted (hotter), while those on the leading side are redshifted (colder), creating a characteristic temperature dipole aligned with the motion. However, the signal amplitude is extremely small (order of 0.1 µK for massive clusters), and previous attempts have been hindered by foreground contamination that mimics the signal's morphology.

Methodology
The authors developed a harmonic-space estimator to cross-correlate CMB temperature maps with a transverse-velocity template derived from galaxy surveys.

Data Sources:
- CMB: Temperature maps from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6), specifically a foreground-cleaned map generated via a needlet internal linear combination (NILC) of 90, 150, and 220 GHz channels. Single-frequency maps were also used for consistency checks.
- Galaxies: Luminous Red Galaxies (LRGs) from the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys (DR9). Two samples were analyzed: a conservative "main" sample (5.1 million galaxies) and a higher-density "extended" sample (13.2 million galaxies) covering the northern (NGC) and southern (SGC) Galactic caps.
Velocity Template Construction:
- A 3D galaxy density field was reconstructed from the DESI-LS catalog, accounting for survey masks, photometric redshift errors, and completeness weights.
- A linear velocity reconstruction filter was applied to the density field to infer the large-scale bulk flow (transverse velocity field). Crucially, the reconstruction was limited to large scales ( $k < 0.05 \, \text{Mpc}^{-1}$ ) to capture bulk flows while excluding small-scale astrophysical physics (e.g., gas dynamics, satellite motions) that could introduce foreground correlations.
- This velocity field was projected onto the sky to create a transverse-velocity template ( $X_a$ ), which was decomposed into gradient (parity-even) and curl (parity-odd) components in harmonic space.
Estimator and Signal Extraction:
- The moving-lens signal is predicted to appear exclusively in the parity-even (gradient) component of the cross-correlation between the CMB temperature ( $T$ ) and the velocity template ( $X$ ), denoted as $C^{TG}_\ell$ . The parity-odd (curl) component ( $C^{TC}_\ell$ ) must vanish due to the parity symmetry of the effect.
- The analysis utilized a scale separation strategy: the velocity template was constructed from large scales, while the CMB dipole signal was measured on smaller angular scales ( $\ell \approx 2500\text{--}6000$ ). This separation minimizes contamination from foregrounds (like the Cosmic Infrared Background and thermal SZ effect) which are dominated by small-scale, local astrophysics.
Validation and Null Tests:
- Parity Test: The curl-mode cross-spectrum was measured to ensure it was consistent with zero.
- Frequency Tests: Frequency-difference maps (e.g., 150–90 GHz) were analyzed. Since the moving-lens effect is a gravitational blackbody shift, it cancels in frequency differences, whereas foregrounds (which have non-blackbody spectra) would remain.
- Spatial Consistency: Results from the NGC and SGC were compared to ensure the signal was consistent across different sky regions.
- External Constraints: High-frequency Planck maps (353 and 545 GHz) were used to empirically bound the contribution of the Cosmic Infrared Background (CIB) to the signal.

Key Results

Detection Significance: The cross-correlation between the foreground-cleaned ACT NILC map and the extended DESI-LS sample yielded a detection of the moving-lens signal at 4.8 $\sigma$ significance. A more conservative analysis using the main DESI-LS sample resulted in a 3.7 $\sigma$ detection.
Amplitude: The measured amplitude parameter $b_{ML}$ (the ratio of the observed signal to the $\Lambda$ CDM prediction) was found to be $1.24 \pm 0.26$ for the extended sample and $0.93 \pm 0.25$ for the main sample. Both are consistent with the General Relativity prediction of $b_{ML} = 1$ .
Null Tests:
- The curl-mode (parity-odd) correlation was consistent with zero ( $< 1\sigma$ ), confirming the signal's parity symmetry.
- Frequency-difference maps (150–90 GHz) showed no significant signal, indicating that the detection is not driven by frequency-dependent foregrounds.
- Empirical bounds using Planck high-frequency data suggested that CIB contamination contributes negligibly ( $\Delta b_{ML} \approx 0.00 \pm 0.10$ ) compared to the detected signal.
Scale Dependence: The measured cross-spectrum followed the expected angular scale dependence predicted by the theoretical template.

Significance and Claims
The paper claims this is the first statistical detection of galaxies' transverse motion at cosmological distances and the first detection of the moving-lens effect.

The authors emphasize that unlike the kSZ effect, which depends on electron density and gas profiles, the moving-lens effect is purely gravitational, responding only to the mass of the halos. This provides a direct probe of halo mass and transverse velocities independent of astrophysical gas modeling.

While the current measurement is statistical (relying on the cross-correlation of millions of galaxies rather than individual detections), the authors state that this result opens a path to mapping the full three-dimensional velocity field of the Universe. By combining these transverse measurements with existing line-of-sight velocities from kSZ tomography, future surveys (such as the Simons Observatory and CMB-S4 combined with spectroscopic data from DESI) could achieve precision transverse-velocity mapping, offering a new, independent probe of cosmic structure growth and breaking degeneracies in current cosmological analyses.

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