Gravitational waves are tiny ripples in spacetime. Their first direct detection in 2015 marked a revolutionary moment in astronomy. Today, we have a thorough understanding of signals that travel far from their sources through quiet, nearly empty space, such as those emitted when black holes merge. In this case, the wave can be considered a minor disturbance on a silent background. The distinction between “background” and “wave” is clear, and the quantity measured by the detector—a tiny stretching and squeezing—is clearly determined.
In cosmology, however, things are more subtle. The focus shifts to the universe in its entirety—encompassing spacetime and everything contained within it, such as stars, black holes and galaxies. The background itself is dynamic. Small fluctuations in density and velocity gently stir spacetime everywhere, blurring the boundary with the wave.
But what exactly does a gravitational-wave detector measure when the entire universe is gently vibrating? Previously, theoretical predictions were entirely dependent on the choice of mathematical coordinates. However, the only meaningful quantity is what a real instrument records, which must be coordinate-independent.
Dr. Guillem Domènech and his team at the Institute of Theoretical Physics of Leibniz University Hannover (LUH) have now developed a precise detector-based approach. Instead of discussing the components of an abstract field, the researchers model a realistic experiment involving two freely falling test masses, or atomic clocks, linked by a light beam.
A passing gravitational wave can slightly alter the travel time of light, thereby affecting the measured time or frequency signal. The authors derive this observable in full and in a coordinate-independent manner, up to second order in cosmic fluctuations. The study is published in the journal Physical Review Letters.
“Gravitational wave detectors measure differences in the frequencies and arrival times of light beams,” says lead author Guillem Domènech. “We calculate these quantities exactly within an expanding spacetime and distinctly isolate what is genuinely measurable from effects that rely on the mathematical description. This ensures that theoretical predictions for future experiments are rigorous and reliable.”
This approach establishes a shared vocabulary for theory and experimentation. In the “quiet spacetime” limit, it reduces to the familiar measurement taken using ground-based interferometers. In a cosmological setting, however, it remains unambiguous and robust. This provides a reliable theoretical framework to guide the search for primordial gravitational waves in the universe—with direct relevance for current and future measurements, such as those using pulsar timing arrays and the space-based observatory LISA.
Publication details
Guillem Domènech et al, Observable Gravitational Wave Strain at Second Order, Physical Review Letters (2026). DOI: 10.1103/pwbs-xwrh
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Leibniz University Hannover
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Measuring gravitational waves in a humming universe with a coordinate-free approach (2026, June 4)
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