Non-Gaussianity in the distribution of inflationary perturbations, measurable in statistics of the cosmic microwave background (CMB) and large scale structure fluctuations, can be used to probe non-trivial initial quantum states for these perturbatio
ns. The bispectrum shapes predicted for generic non-Bunch-Davies initial states are non-factorizable (non-separable) and are highly oscillatory functions of the three constituent wavenumbers. This can make the computation of CMB bispectra, in particular, computationally intractable. To efficiently compare with CMB data one needs to construct a separable template that has a significant similarity with the actual shape in momentum space. In this paper we consider a variety of inflationary scenarios, with different non-standard initial conditions, and how best to construct viable template matches. In addition to implementing commonly used separable polynomial and Fourier bases, we introduce a basis of localized piecewise spline functions. The spline basis is naturally nearly orthogonal, making it easy to implement and to extend to many modes. We show that, in comparison to existing techniques, the spline basis can provide better fits to the true bispectrum, as measured by the cosine between shapes, for sectors of the theory space of general initial states. As such, it offers a useful approach to investigate non-trivial features generated by fundamental properties of the inflationary Universe.
[Abridged] We consider how galaxy clustering data, from Mpc to Gpc scales, from upcoming large scale structure surveys, such as Euclid and DESI, can provide discriminating information about the bispectrum shape arising from a variety of inflationary
scenarios. Through exploring in detail the weighting of shape properties in the calculation of the halo bias and halo mass function we show how they probe a broad range of configurations, beyond those in the squeezed limit, that can help distinguish between shapes with similar large scale bias behaviors. We assess the impact, on constraints for a diverse set of non-Gaussian shapes, of galaxy clustering information in the mildly non-linear regime, and surveys that span multiple redshifts and employ different galactic tracers of the dark matter distribution. Fisher forecasts are presented for a Euclid-like spectroscopic survey of H$alpha$-selected emission line galaxies (ELGs) using recent revisions of the expected H$alpha$ luminosity function, and a DESI-like survey, of luminous red galaxies (LRGs) and [O-II] doublet-selected ELGs, in combination with Planck-like CMB temperature and polarization data. While ELG samples provide better probes of shapes that are divergent in the squeezed limit, LRG constraints, centered below $z<1$, yield stronger constraints on shapes with scale-independent large-scale halo biases, such as the equilateral template. The ELG and LRG samples provide complementary degeneracy directions for distinguishing between different shapes. If the Gaussian galaxy bias is constrained to better than a percent level, such as can be determined from the galaxy bispectrum or weak lensing, then the LSS and CMB data could provide complementary constraints that will enable differentiation of bispectra with distinct theoretical origins but with similar large scale, squeezed-limit properties.
A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming CMB and large-scale structure surveys raises a natural question: if a detection given a particular
template is made, what does this truly tell us about the underlying theory? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad template classes, satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.
