[Paper Review] The Impact of Non-Gaussian Primordial Tails on Cosmological Observables

William R. Coulton, Oliver H. E. Philcox+1 more|arXiv (Cornell University)|Jun 21, 2024

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates the cosmological impacts of non-Gaussian primordial perturbations with exponentially enhanced tails, using a phenomenological model that preserves Gaussian bulk statistics while modifying the tails. Through N-body simulations and CMB map generation, it shows that such tails induce scale-dependent halo bias and detectable trispectrum features, implying that scale-dependent bias alone cannot rule out single-field inflation or distinguish between primordial non-Gaussianity types without additional statistics.

ABSTRACT

Whilst current observational evidence favors a close-to-Gaussian spectrum of primordial perturbations, there exist many models of the early Universe that predict this distribution to have exponentially enhanced or suppressed tails. In this work, we generate realizations of the primordial potential with non-Gaussian tails via a phenomenological model; these are then evolved numerically to obtain maps of the cosmic microwave background (CMB) and large-scale structure (LSS). In the CMB maps, our added non-Gaussianity manifests as a localized enhancement of hot and cold spots, which would be expected to contribute to $N$-point functions up to large $N$. Such models are indirectly constrained by extit{Planck} trispectrum bounds, which restrict the changes in the temperature fluctuations to $O(10μ\mathrm{K})$. In the late-time Universe, we find that tailed cosmologies lead to a halo mass function enhanced at high masses, as expected. Furthermore, significant scale-dependent bias in the halo-halo and halo-matter power spectrum is also sourced, which arises from the squeezed limit of large $N$-point functions that are implicitly generated through the enhancement of the tails. These results underscore that a detection of scale-dependent bias alone cannot be used to rule out single field inflation, but can be used together with other statistics to probe a wide range of primordial processes.

Motivation & Objective

• To investigate how non-Gaussian primordial tails—exponentially enhanced in the distribution of the primordial potential—affect cosmological observables like the CMB and large-scale structure.
• To determine whether scale-dependent halo bias, often used to constrain local-type non-Gaussianity, can be mimicked by non-perturbative, tailed primordial distributions.
• To assess the relative constraining power of CMB trispectrum measurements versus large-scale structure bias for detecting such non-Gaussian tails.
• To develop and apply a phenomenological model of primordial non-Gaussianity with symmetric, exponential tails that preserves Gaussianity in the bulk, enabling numerical simulations.

Proposed method

• A phenomenological model is constructed where the primordial potential PDF is Gaussian in the bulk (|Φ| ≤ ασ) but has exponential tails (Φ^N) for |Φ| > ασ, allowing controlled modification of the tail behavior.
• Realizations of the primordial potential with these non-Gaussian tails are generated numerically and evolved forward in time using cosmological N-body simulations to produce halo distributions and matter power spectra.
• CMB maps are generated from the same initial conditions using linear and second-order perturbation theory, enabling analysis of non-Gaussian features in temperature fluctuations.
• The halo mass function and power spectra (halo-halo, halo-matter) are computed and compared to Gaussian baseline simulations to quantify deviations due to tail non-Gaussianity.
• Trispectrum and higher-order N-point function statistics are analyzed, particularly focusing on the squeezed limit, to identify signatures of non-perturbative non-Gaussianity.
• Constraints are estimated by comparing predicted signal levels to observational bounds: Planck trispectrum limits and forecasted detection significance for future surveys (e.g., DESI).

Figure 1: Histograms of a realization of the primordial potential for Gaussian initial conditions (blue), canonical local $f_{\mathrm{NL}}$ and $g_{\rm NL}$ non-Gaussianity (green and red), and one of the enhanced tail models considered in this work (orange), here with $N=1$ . This illustrates the q

Experimental results

Research questions

• RQ1 How do exponentially enhanced tails in the primordial potential PDF affect the cosmic microwave background (CMB) temperature fluctuations?
• RQ2 To what extent do such tailed primordial distributions alter the halo mass function and induce scale-dependent bias in large-scale structure?
• RQ3 Can the scale-dependent bias signature from tailed non-Gaussianity be distinguished from that of local-type f_NL or g_NL models?
• RQ4 What is the relative constraining power of CMB trispectrum measurements versus large-scale structure bias for detecting primordial tail non-Gaussianity?
• RQ5 Do all microphysical models with non-Gaussian tails necessarily generate squeezed N-point functions, or is this feature dependent on the model's locality?

Key findings

• The CMB maps exhibit localized enhancements of hot and cold spots due to non-Gaussian tails, which contribute to N-point functions up to large N, with trispectrum signals detectable at ~20σ by Planck if targeted.
• The halo mass function is significantly enhanced at high masses in tailed cosmologies, consistent with theoretical expectations from non-perturbative non-Gaussianity.
• Scale-dependent bias appears in both the halo-halo and halo-matter power spectra due to the squeezed limit of implicitly generated high-N-point functions, mimicking signatures of local-type non-Gaussianity.
• The scale-dependent bias feature in the halo power spectrum shows a 1/k² behavior on large scales, similar in form to local f_NL or g_NL models, but arising from a different primordial origin.
• A 1 h⁻³ Gpc³ survey with halos above 3.2×10¹³ h⁻¹ M☉ would detect the scale-dependent bias at ~5σ, implying that future large-scale structure surveys could constrain tail non-Gaussianity more tightly than the CMB.
• The results imply that detecting scale-dependent bias cannot alone rule out single-field inflation or distinguish between primordial non-Gaussianity types without complementary statistics, highlighting the need for multi-probe analyses.

Figure 2: A comparison of the trispectrum of the primordial potential for a model with $g_{\mathrm{NL}}=1.64\times 10^{6}$ and two of the enhanced tail models considered here. The squeezed trispectrum configuration, denoted by the stars, are highly similar between the tails and $g_{\mathrm{NL}}$ mod