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Primordial Physics in the Nonlinear Universe: Revealing the oscillating halo bias from cosmological collider models

This paper introduces a new simulation method to accurately model cosmological collider signatures, presenting the first measurements of oscillating halo bias in simulations and demonstrating that its mass-dependent amplitude and phase provide a robust, unique probe of primordial high-energy physics that is distinct from observational systematics.

Original authors: Dhayaa Anbajagane, Neal Dalal

Published 2026-07-29

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CC BY 4.0

Original authors: Dhayaa Anbajagane, Neal Dalal

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic ocean. When we look back in time to the very first moments after the Big Bang, we are looking at the "initial conditions" of this ocean—how the water was moving before the waves even started. Scientists believe that hidden within these initial ripples are secret messages from the tiniest particles in existence, particles so heavy and energetic that we can't create them in any lab on Earth. These messages are called "primordial non-Gaussianities." Think of them as a unique fingerprint or a specific rhythm in the water's motion that tells us what kind of "ingredients" were mixed into the universe's recipe.

For a long time, scientists have tried to read these fingerprints by looking at the Cosmic Microwave Background, which is like a baby picture of the universe. But now, they are also looking at the "Large Scale Structure"—the vast web of galaxies, clusters, and empty spaces that make up the universe today. It's like trying to understand the initial storm by looking at the shape of the waves crashing on the shore. The big question is: Can we find the specific, rhythmic patterns left behind by these high-energy particles in the way galaxies cluster together? If we can, it would be like finding a lost radio signal from the dawn of time, revealing the physics of the universe's first split-second.

This paper, titled "Primordial Physics in the Nonlinear Universe," is a detective story about finding those hidden rhythms. The authors, Dhayaa Anbajagane and Neal Dalal, are investigating a specific type of signal called a "cosmological collider." In the early universe, the rapid expansion (inflation) acted like a giant particle collider, smashing particles together. If heavy particles were present, they would have left a distinct "oscillating" pattern in the density of the universe—like a musical note that wiggles up and down in a very specific way. The challenge is that these wiggles are incredibly subtle and get messy as the universe evolves and gravity pulls matter together to form galaxies.

To solve this, the team didn't just look at the sky; they built a virtual universe. They developed a brand-new, super-precise method to simulate the initial conditions of the cosmos, one that doesn't rely on old, rigid templates but instead uses a flexible "binning" technique to capture the complex, wiggly patterns of the cosmological collider models. They then ran massive computer simulations, creating 10 different universes, each filled with billions of dark matter particles, to see how these initial wiggles would affect the formation of halos (the invisible scaffolding that holds galaxies together).

What they found is a clear, rhythmic signal in the "halo bias"—a fancy term for how much more likely heavy clumps of matter are to cluster together compared to the average. The simulations showed that these clusters don't just clump randomly; they oscillate in a pattern that matches the theoretical predictions perfectly. But here is the twist: the rhythm of the oscillation changes depending on the size of the halo. Just as a large drum produces a deeper, slower beat than a small drum, the paper found that a tenfold increase in the mass of a halo shifts the location of the oscillation by a factor of two.

Furthermore, the team discovered that the "phase" of this rhythm—the exact timing of the peaks and troughs—is sensitive to how the halo was assembled. Halos that are more concentrated (like a tightly packed crowd) show the rhythm at different scales than less concentrated ones. This "assembly bias" is a crucial detail because it means that if we want to find these signals in real observations, we have to be very careful about how we select the galaxies we study.

The authors are confident in these results because their new simulation method reproduces the input patterns with percent-level accuracy, and their theoretical models fit the simulation data almost perfectly. They also noted that while higher-frequency versions of these signals get harder to see (they get "washed out" by the size of the halos), the signal they focused on is robust. Most importantly, they argue that this specific oscillating pattern is unique. It's not something that can be easily faked by errors in our telescopes or the messy effects of gravity later in the universe's life. This makes it a very promising target for future observations, offering a potential new way to listen to the music of the early universe and uncover the physics of particles we can't yet touch.

Technical Summary: Primordial Physics in the Nonlinear Universe: Revealing the oscillating halo bias from cosmological collider models

Problem Statement
Primordial non-Gaussianities (PNGs) arising from high-energy particle physics during inflation offer a unique window into the early Universe. While the "cosmological collider" paradigm predicts that interactions between the inflaton and other heavy particles generate oscillatory signatures in the primordial bispectrum (specifically in the squeezed limit), measuring these signals in the large-scale structure (LSS) of the Universe has remained challenging. A primary bottleneck is the generation of accurate N-body simulations. Traditional methods for generating initial conditions (ICs) rely on decomposing the bispectrum kernel into a separable basis of functions. However, these basis-decomposition methods often fail to accurately represent complex, non-monotonic behaviors—such as high-frequency oscillations in the squeezed limit—leading to inaccuracies in the simulated density fields. Furthermore, there has been no simulation-focused analog for measuring how these specific collider signatures imprint on the scale-dependent halo bias, particularly regarding the effects of halo mass and assembly bias.

Methodology
To address the simulation bottleneck, the authors develop a new method for generating initial conditions that foregoes global analytic or neural-network-based basis functions. Instead, they utilize a "binned estimator" approach with higher-order interpolation:

Kernel Representation: The mode-coupling kernel $K_{12}(k_1, k_2, k_3)$ is represented as a sum over bins in 3D Fourier space. The authors employ third-order (cubic) Lagrange interpolators ( $\psi$ ) to ensure smooth transitions between bins, rather than sharp Heaviside steps.
Separability: The kernel is constructed to remain separable for Fast Fourier Transform (FFT) efficiency, but without assuming a fixed global functional form. The external leg ( $k_3$ ) uses a specific kernel $\kappa_{ijl}(k_3)$ that depends on the bin choices of $k_1$ and $k_2$ , allowing for precise local fitting.
Infrared Control: To handle potential infrared (IR) divergences in the primordial power spectrum, the authors adopt the reduced bispectrum kernel formalism (Wagner & Verde 2012), which cancels divergences through linear combinations of equivalent kernels.
Simulation Setup: Using the Pkdgrav3 N-body code, the authors generate 10 realizations of simulations with a box size of $L=3$ Gpc/ $h$ and $1024^3$ particles. They focus on the "Quasi-Single Field" (QSF) oscillating model ( $SQSF_{osc}$ ), which introduces oscillations in the squeezed limit of the bispectrum: $B(k, k, q) \propto (k/q)^\Delta \cos(\omega \ln(k/q))$ .
Bias Measurement: Halo bias is measured as the ratio of the halo-matter cross-spectrum to the matter auto-spectrum ( $b(k) = P_{hm}/P_{mm}$ ) to suppress cosmic variance. Halos are selected by mass ( $M_{200c}$ ) and concentration (via $V_{max}$ ) to study assembly bias.

Key Contributions

New IC Generation Method: The paper introduces a flexible, bin-based kernel decomposition method that reproduces input bispectrum templates with percent-level accuracy, specifically overcoming the limitations of traditional basis decomposition in the squeezed limit.
First Simulations of Oscillating Bias: The authors present the first N-body measurements of oscillating halo bias induced by cosmological collider models.
Mass-Dependent Phase Shifts: They demonstrate that the phase and amplitude of the oscillating bias are strongly dependent on halo mass. A factor of ten shift in halo mass results in a factor of $\sim 2$ shift in the oscillation location ( $k_c$ ).
Assembly Bias Sensitivity: The study reveals that selection on secondary halo properties (specifically concentration via $V_{max}$ ) induces significant phase shifts in the oscillating bias, comparable in magnitude to those caused by mass selection.
Theoretical Validation: The authors show that a simple peak-background split theory (Equation 2.15), which includes a mass-dependent kernel and derivative terms, accurately models the measured oscillating bias, including the phase offsets caused by assembly bias.

Results

Oscillating Signal: The simulations confirm the presence of non-monotonic, oscillatory features in the halo bias ratio ( $b_+/b_1$ ) at $z=0$ .
Mass Dependence: As halo mass increases, the characteristic scale of the oscillation ( $k_c$ ) shifts to smaller wavenumbers (larger scales). This is attributed to the mass-dependent smoothing kernel in the theoretical prediction. The amplitude of the oscillation also increases with halo mass.
Frequency Suppression: Increasing the frequency parameter ( $\omega$ ) of the primordial bispectrum suppresses the signal amplitude in the halo bias, as the oscillations average out over the halo window function.
Assembly Bias: Splitting halos by concentration ( $\tilde{V}_{max}$ ) reveals that more concentrated halos exhibit oscillation features at smaller scales compared to less concentrated halos of the same mass. This phase shift is well-captured by adjusting the bias coefficients ( $b_\phi$ and $b_\sigma$ ) in the theoretical model.
Model Accuracy: The theoretical model fits the simulation data to high precision across all mass bins and selection criteria, validating the use of the peak-background split framework for these complex signatures.

Significance
The paper claims that the oscillating halo bias, and specifically its mass- and selection-dependent phase offsets, constitutes a unique signature of cosmological collider physics. Because these phase shifts are not easily mimicked by known observational systematics or standard gravitational evolution, they represent a more robust target for future observational constraints than amplitude-only measurements. The authors emphasize that their new simulation method enables precision tests of these models, which were previously inaccessible due to the limitations of basis-decomposition techniques. The underlying initial conditions code and simulation data are made publicly available to facilitate further research in this domain.

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