Searching for Folded Primordial Non-Gaussianity with Galaxy Surveys
Large-scale structure provides a powerful probe of inflationary physics through primordial non-Gaussianity (PNG): the galaxy power spectrum depends on local PNG through scale-dependent bias, while the galaxy bispectrum depends sensitively on both equilateral and orthogonal PNG. In this paper, we study whether galaxy surveys can also probe folded PNG, whose shape is enhanced near $k_1+k_2-k_3\rightarrow0$. We consider three inflationary models with folded PNG, including excited initial states, imaginary speeds of sound, and dissipative inflation. These models fall into two classes: cutoff-regulated cases in which the folded-enhanced region has a power-law width, and dissipation-regulated cases in which the enhanced region is exponentially narrow. We develop a numerical pipeline for computing the corresponding PNG contributions to the redshift-space galaxy power spectrum multipoles and bispectrum monopole within the EFTofLSS. Using Fisher forecasts, we show that most of the constraining power on folded PNG comes from the galaxy bispectrum. For the cutoff-regulated models, nuisance parameter marginalization causes only a mild loss of information at large folded enhancement, but finite Fourier-space binning degrades constraints once the folded region becomes narrower than the bin width. For the dissipation-regulated models, the exponentially narrow folded enhancement is hard to resolve and the observable signal instead comes from the broader support of the template, leading to weaker binning dependence but larger overlap with the equilateral template. Our results show that folded PNG is a distinctive and promising target for galaxy bispectrum analyses, and the detectability depends on the width and morphology of the folded enhancement. The numerical pipeline developed in this work is general and can be used to study a wide class of non-separable primordial bispectra.