A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone

Abstract: Next-generation galaxy surveys will increasingly rely on the galaxy bispectrum to improve cosmological constraints, especially on primordial non-Gaussianity. A key theoretical requirement that remains to be developed is the analysis of general relativistic effects on the bispectrum, which arise from observing galaxies on the past lightcone, {as well as from relativistic corrections to the dynamics}. {As an initial step towards a fully relativistic analysis of the galaxy bispectrum, we compute for the first time the local relativistic lightcone effects on the bispectrum,} which come from Doppler and gravitational potential contributions. For the galaxy bispectrum, the problem is much more complex than for the power spectrum, since we need the lightcone corrections at second order. Mode-coupling contributions at second order mean that relativistic corrections can be non-negligible at smaller scales than in the case of the power spectrum. In a primordial Gaussian universe, we show that the local lightcone corrections for squeezed shapes at $z\sim1$ mean that the bispectrum can differ from the Newtonian prediction by $\gtrsim 10\%$ when the short modes are $k\lesssim (50\,{\rm Mpc})^{-1}$. These relativistic projection effects, if ignored in the analysis of observations, could be mistaken for primordial non-Gaussianity. For upcoming surveys which probe equality scales and beyond, {all relativistic lightcone effects and relativistic dynamical corrections should be included} for an accurate measurement of primordial non-Gaussianity.