Papers

What it delivers. Adds smooth component filtering (SCF) to our MWA analysis at z = 8.2. Filtering out the spectrally smooth foregrounds lowers the cylindrical bispectrum by three to four orders of magnitude and also removes the artefacts left by missing frequency channels. In the cleaner EoR window (k_⊥ ≤ 0.026 Mpc⁻¹, k_∥ > 0.135 Mpc⁻¹), the tightest limits are −(1.25 × 10⁴ mK)³ ≤ Δ³ ≤ (1.22 × 10⁴ mK)³ at k₁ = 0.281 Mpc⁻¹.

Why it matters. What remains is consistent with thermal noise rather than foreground leakage. That changes the problem: longer observations should now tighten the limits directly.

What it delivers. Develops the theory for testing gravity with the full set of redshift-space bispectrum multipoles, Bmℓ, taking degenerate higher-order scalar-tensor (DHOST) theories as the alternative to general relativity. It maps how each multipole and each triangle shape responds to changes in the second-order growth of structure.

Why it matters. The higher multipoles (ℓ = 2, 4, 6) are more sensitive than the monopole, acute triangles respond most, and several multipoles change sign when gravity departs from general relativity, a clear signature to look for. The ℓ = 6, m ≤ 4 multipoles are untouched by quadratic and tidal galaxy bias, which makes them especially robust probes.

What it delivers. The first attempt to measure the 21-cm bispectrum of the Epoch of Reionization in real data, from MWA observations at 154.2 MHz (z = 8.2). Foregrounds form a wedge in the cylindrical bispectrum, as they do in the power spectrum, but its shape is more complex because it depends on all three sides of the triangle. Outside the wedge, the best 2σ upper limits are Δ³ ≤ (1.81 × 10³ mK)³ for equilateral triangles at k₁ = 0.008 Mpc⁻¹ and Δ³ ≤ (2.04 × 10³ mK)³ for squeezed triangles at k₁ = 0.012 Mpc⁻¹.

Why it matters. It establishes the method and identifies the obstacles later analyses must overcome: the more complex bispectrum wedge, and spikes caused by periodically missing frequency channels. The limits still sit about seven orders of magnitude in Δ³ above the expected signal.

What it delivers. A fast, FFT-accelerated estimator that measures the multi-frequency angular bispectrum (MABS) and the 3D 21-cm bispectrum directly from gridded visibilities, for every triangle configuration. On simulated MWA observations (30.72 MHz of bandwidth centred on 154.25 MHz), it recovers the input bispectrum for k₁ from about 0.003 to 1.26 Mpc⁻¹ to within 20%, even with the real data's flagged channels. The differences are consistent with statistical fluctuations.

Why it matters. It makes the 21-cm bispectrum something that can actually be measured from interferometer data, and it is the measurement tool behind our MWA analysis at z = 8.2.

What it delivers. An estimator for the angular bispectrum that works directly on gridded visibilities from a single frequency channel, using FFTs to include every triangle shape and size. On simulated MWA data at 154.25 MHz, it recovers the angular bispectrum to 10–15% accuracy across 46 ≤ ℓ ≤ 1320.

Why it matters. Working with the visibilities that an interferometer actually records is the practical route to the bispectrum in radio data. This paper laid that groundwork, and AMBER then extended it across frequency.

What it delivers. A fast estimator for all the angular multipoles of the redshift-space bispectrum, Bmℓ(k₁, μ, t), including the m ≠ 0 terms that are usually left out. On a grid of N_g³ cells, FFTs cut the cost from order N_g⁶ to N_g⁴. On a test field with a known answer, it recovers all 16 non-zero multipoles up to ℓ = 6 and m = 6.

Why it matters. The m ≠ 0 multipoles can add substantial information beyond the usual m = 0 terms. The estimator is ready for galaxy surveys such as DESI, Euclid and LSST, and for future 21-cm maps.

What it delivers. Measures the bispectrum of galaxies in the SDSS DR17 main galaxy sample across triangle sizes and shapes, using a volume-limited region around z ≈ 0.09, and compares it with mock catalogues built with different galaxy bias.

Why it matters. On these scales the galaxy distribution is non-linear and strongly non-Gaussian, least for equilateral triangles and most for nearly linear ones. Mocks with a linear bias of about 1.2 match the data best, so a simple bias model works for this sample. This sets up parameter estimation with higher multipoles.

What it delivers. Uses simulations of reionization to follow the monopole and quadrupole of the 21-cm bispectrum for squeezed and stretched triangles, at k = 0.29 and 0.56 Mpc⁻¹, as the Universe becomes ionized.

Why it matters. The signs of the two moments trace the changing topology of reionization. The monopole turns negative once distinct ionized bubbles appear. Later both flip, as the picture inverts to neutral islands in an ionized Universe, and the negative quadrupole shows that those islands survive mainly in under-dense regions. The quadrupole adds information that the monopole alone cannot give.

What it delivers. A fast FFT-based estimator for the binned 3D bispectrum that separates a triangle's size (k₁) from its shape (μ, t), so the full shape dependence can be mapped. Its cost scales as N_g³ log N_g³, close to a single FFT of the grid, and it agrees with analytical predictions to within 10% across much of the shape plane, including with linear redshift-space distortions.

Why it matters. It made it practical to study the bispectrum as a function of triangle shape, and it became the starting point for the shape-dependent analyses that followed.