Speeding Up The Detectability Of The Harmonic-Space Galaxy Bispectrum

We present a method that allows us for the first time to estimate the signal-to-noise ratio (SNR) of the harmonic-space galaxy bispectrum induced by gravity, a complementary probe to already well established Fourier-space clustering analyses. We show how to do it considering only similar to 1000 triangle configurations in multipole space, corresponding to a computational speedup of a factor Script O(10(2))-O(10(3)), depending on the redshift bin, when including mildly non-linear scales. Assuming observational specifications consistent with forthcoming spectroscopic and photometric galaxy surveys like the Euclid satellite and the Square Kilometre Array (phase 1), we show: that given a single redshift bin, spectroscopic surveys outperform photometric surveys; and that-due to shot-noise and redshift bin width balance-bins at redshifts z similar to 1 bring higher cumulative SNR than bins at lower redshifts z similar to 0.5. Our results for the largest cumulative SNR similar to 15 suggest that the harmonic-space bispectrum is detectable within narrow (Delta z similar to 0.01) spectroscopic redshift bins even when including only mildly non-linear scales. Tomographic reconstructions and inclusion of highly non-linear scales will further boost detectability with upcoming galaxy surveys. In addition, we discuss how, using the Karhunen-Loeve transform, a detection analysis only requires a 1 x 1 covariance matrix for a single redshift bin.