The spatial gauge-dependence of single-field inflationary bispectra

In single-field inflationary models the bispectra are usually given in $\zeta$-gauge, because its temporal part leads to super-horizon conservation of fluctuations. However, this property is independent choice {\it spatial} gauge, so letter we explore freedom. We compute variation under most general spatial gauge transformation that globally defined and privileges no point, direction or scale. squeezed configuration then obtain a generalization classic $\zeta$-gauge consistency relations, which also derive through `large diffeomorphism' approach for all four bispectra. At leading order long wave-number only affects case where mode scalar. The first effect shift tilt factor, one can significantly reduce amplitude contribution. Secondly, there now an extra term depending on triangle shape, same as solid inflation, due fact 3-metric has scalar anisotropy generic gauge. next-to-leading variation, conformal relations preserved.