
Matched circles on the surface of last scattering are searched for.Matched filtering is a signal processing technique used to detect a known pattern (the 'signal') buried in noisy data. In cosmology, it is applied to search for 'matched circles' in the cosmic microwave background (CMB) — patterns that would appear if the universe had a non-trivial topology, such as a torus or a multiply-connected shape. The idea is that if the universe is finite and small enough, the same region of the early universe would be visible from different directions, leaving circles of similar temperature fluctuations on the sky.
The concept of matched filtering originated in radar and communications theory in the 1940s, and was adapted to cosmology in the 1990s by researchers like Neil Cornish and colleagues to test cosmic topology.
The method works by correlating the data with a template of the expected signal. If the template matches a feature in the data, the correlation produces a peak; if not, the result is just noise. For matched circles, the algorithm searches for pairs of circles on the CMB sky with similar temperature patterns, using a filter that maximizes the signal-to-noise ratio. This requires careful handling of the noise properties of the CMB maps.
Beyond cosmology, matched filtering is used in gravitational wave detection (e.g., LIGO) to identify the faint chirp of merging black holes, and in radar and sonar systems.
The first direct detection of gravitational waves in 2015 relied on matched filtering, where the predicted waveform of a black hole merger was matched against the noisy detector data to find the signal.



