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Cross-bispectra Constraints on Modified Gravity Theories from Nancy Grace Roman Space Telescope and Rubin Observatory Legacy Survey of Space and Time

One major goal of upcoming large-scale-structure surveys is to constrain dark energy and modified gravity theories. In particular, galaxy clustering and gravitational lensing convergence are probes sensitive to modifications of general relativity. While the standard analysis for these surveys typically includes power spectra or 2-point correlation functions, it is known that the bispectrum contains more information, and could offer improved constraints on parameters when combined with the power spectra. However, the use of bispectra has been limited so far to one single probe, e.g. the lensing convergence bispectrum or the galaxy bispectrum. In this paper, we extend the formalism to explore the power of cross-bispectra between different probes, and exploit their ability to break parameter degeneracies and improve constraints. We study this on a test case of lensing convergence and galaxy density auto- and cross-bispectra, for a particular sub-class of Horndeski theories parametrized by $c_M$ and $c_B$. Using the 2000 deg$^2$ notional survey of the Nancy Grace Roman Space Telescope with overlapping photometry from the Rubin Observatory Legacy Survey of Space and Time, we find that a joint power spectra and bispectra analysis with three redshift bins at $l_{\rm max} = 1000$ yields $σ_{c_M} = 1.0$ and $σ_{c_B} = 0.3$, both a factor of $\sim$1.2 better than the power spectra results; this would be further improved to $σ_{c_M} = 0.7$ and $σ_{c_B} = 0.2$ if $l_{\rm max} = 3000$ is taken. Furthermore, we find that using all possible cross-bispectra between the two probes in different tomographic bins improves upon auto-bispectra results by a factor of 1.3 in $σ_{c_M}$, 1.1 in $σ_{c_B}$ and 1.3 in $σ_{Ω_m}$. We expect that similar benefits of using cross-bispectra between probes could apply to other science cases and surveys.