Constraints from CMB lensing tomography with projected bispectra

We measure the angular power spectrum and bispectrum of the projected overdensity of photometric DESI luminous red galaxies, and its cross-correlation with maps of the Cosmic Microwave Background lensing convergence from Planck. This analysis is enabled by the use of the “filtered-squared bispectrum” approach, introduced in previous work, which we generalise here to the case of cross-correlations between multiple fields. The projected galaxy bispectrum is detected at very high significance (above <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>30</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> in all redshift bins), and the galaxy-galaxy-convergence bispectrum is detected above <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>5</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> in the three highest-redshift bins. We find that the bispectrum is reasonably well described over a broad range of scales by a tree-level prediction using the linear galaxy bias measured from the power spectrum. We carry out the first cosmological analysis combining projected power spectra and bispectra under a relatively simple model, and show that the galaxy bispectrum can be used in combination with the power spectrum to place a constraint on the amplitude of matter fluctuations, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> , an on the non-relativistic matter fraction <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> . We find that data combinations involving the galaxy bispectrum recover constraints on these parameters that are in good agreement with those found from the traditional “2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>×</mml:mo> </mml:math> 2-point” combination of galaxy-galaxy and galaxy-convergence power spectra, across all redshift bins.