The Power of Locality: Primordial Non-Gaussianity at the Map Level

Abstract

Primordial non-Gaussianity is a sensitive probe of the inflationary era, with a number of important theoretical targets living an order of magnitude beyond the reach of current CMB constraints. Maps of the large-scale structure of the universe, in principle, have the raw statistical power to reach these targets, but the complications of nonlinear evolution are thought to present serious, if not insurmountable, obstacles to reaching these goals. In this paper, we will argue that the challenge presented by nonlinear structure formation has been overstated. The information encoded in primordial non-Gaussianity resides in nonlocal correlations of the density field at three or more points separated by cosmological distances. In contrast, nonlinear evolution only alters the density field locally and cannot create or destroy these long-range correlations. This locality property of the late-time non-Gaussianity is obscured in Fourier space and in the standard bispectrum searches for primordial non-Gaussianity. We therefore propose to measure non-Gaussianity in the position space maps of the large-scale structure. As a proof of concept, we study the case of equilateral non-Gaussianity, for which the degeneracy with late-time nonlinearities is the most severe. We show that a map-level analysis is capable of breaking this degeneracy and thereby significantly improve the constraining power over previous estimates. Our findings suggest that "simulation-based inference" involving the forward modeling of large-scale structure maps has the potential to dramatically impact the search for primordial non-Gaussianity.

Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology

“…We interpret this robustness as a consequence of well-known stability properties of persistent homology [38]. Therefore, we anticipate that, in the presence of a parameterized model of small-scale physics such as galaxy formation, persistent homology may provide a "manifestly protected" observable along the lines of [37].…”

“…This will require the development of a new simulation suite that includes both primordial non-Gaussianity and HOD. We may also speculate as to whether the physical principles elucidated in [37] would allow for fast and cheap N-body simulation strategies that directly target accuracy at the length scales where primordial non-Gaussianity can be directly distinguished from late-time effects. At any rate, the summary statistics introduced in this work demonstrate that significant information regarding primordial non-Gaussianity can be extracted in a manifestly position-space approach.…”

“…Consider local small-scale uncertainties parameterized by the scale R * . For example, R * can be a scale at which gravitational nonlinearties (or galaxy formation) cannot be modeled by our simulation, as in [37]. Alternatively, R * could be the typical scale of redshift errors, as in the previous section.…”

“…galaxy biasing. However, as recently explained in [37], one can do significantly better by considering survey data in position space, i.e. at the map level.…”

“…at the map level. The physical argument in [37] goes as follows. Uncertainties in gravitational evolution are constrained by locality, and therefore these can affect map-level information only on scales below some R * .…”