⚛️ high-energy theory

Quenched Cosmological Collider Physics: Random fields & white noises

This paper demonstrates that a massive spectator field in de Sitter space coupled to a spatially quenched random source with a power-law time profile yields an exactly solvable model where disorder averaging modifies only the statistical sector of the propagator, resulting in a cosmological collider signal that factorizes into hypergeometric components with a clock frequency fixed by the heavy-field mass but an amplitude and phase controlled by the temporal profile.

Original authors: Matheus Curado Ferreira

Published 2026-09-25

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CC BY 4.0

Original authors: Matheus Curado Ferreira

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

In the earliest moments of our universe, a fraction of a second after the beginning, space itself was expanding at a furious rate. This period, known as inflation, stretched the cosmos from a microscopic speck to a vast expanse in an instant. While this rapid expansion smoothed out the universe, it also acted as a powerful amplifier for tiny quantum fluctuations. These ripples in the fabric of space eventually grew into the galaxies and stars we see today. Physicists believe that during this brief, violent epoch, heavy particles that no longer exist in our current cold universe were briefly created and then destroyed. These particles left a unique fingerprint on the distribution of matter, a signal that modern telescopes might one day detect. This potential signal is often called a "cosmological collider," a natural experiment where the high energies of the early universe allow us to probe particles far heavier than anything we can create in laboratories on Earth.

The standard view of this process assumes a perfectly uniform environment. However, a new study proposes that the early universe might have been slightly messy, filled with a random, static pattern of disorder that changed only in its overall strength as time passed. Imagine the universe as a vast, quiet lake. Usually, we think of waves on this lake as purely the result of wind or the movement of the water itself. But what if the lake bottom was covered in a fixed, random arrangement of rocks? These rocks would not move, but they would still alter how the waves travel across the surface. This is the scenario investigated by researchers at the Brazilian Center for Research in Physics. They asked what would happen to the cosmological collider signal if the heavy particles were moving through such a "rocky" environment, where the pattern of the rocks was fixed in space but the intensity of their influence faded away as the universe expanded.

The researchers found that this random environment does not change the fundamental identity of the heavy particles. The "frequency" of the signal, which tells us the mass of the particle, remains exactly the same. The heavy particles still oscillate at their characteristic rate, just as a bell still rings at the same pitch whether it is struck in a quiet room or a noisy one. However, the random environment does change how loudly the bell rings and the precise timing of the sound. The disorder acts like a filter that modifies the amplitude and phase of the signal. It can make the signal stronger or weaker, and it can shift the wave slightly forward or backward in time, but it does not change the note itself. This is a crucial distinction: the universe's memory of the particle's mass remains intact, even if the environment has scrambled the details of how that memory was recorded.

A key discovery in this work is that the timing of the disorder matters immensely. If the random influence persists forever, it leaves a permanent, static mark on the universe that creates a mathematical problem for certain types of signals. However, the researchers showed that if the disorder fades away as the universe expands, this problem disappears. When the random influence turns off, the heavy particles continue to oscillate on their own, carrying a "memory" of the chaotic stage they just passed through. This memory survives even after the force that created it is gone. The study provides a precise mathematical description of how this fading disorder shapes the final signal. It reveals that the strength of the disorder and the speed at which it fades determine the overall shape of the signal we might observe today.

The team also discovered a specific condition where the random environment can completely cancel out the original signal from the heavy particles. If the disorder is strong enough and fades at just the right rate, it can destructively interfere with the clean signal, effectively silencing the heavy particle's contribution in certain configurations. This does not mean the particle is gone; rather, the random environment has rearranged the signal so that the original pattern is suppressed, while new, mixed patterns emerge. This suggests that the signals we might detect in the future are not just a simple record of particle masses, but a complex story of how those particles interacted with a chaotic, evolving environment. The study concludes that cosmological observables can tell us not only what particles existed in the early universe but also about the specific, messy conditions in which they evolved, offering a new way to read the history of our cosmos.

Technical Summary: Quenched Cosmological Collider Physics: Random fields & white noises

Problem Statement
The paper investigates how the cosmological collider signal—oscillatory signatures in inflationary correlators generated by the exchange of massive fields—is modified when the massive spectator field is subject to a spatially quenched random environment. Unlike standard studies assuming a fixed microscopic theory and a unique quantum state, this work considers a scenario where the spatial pattern of a random source is fixed (quenched) while its overall strength evolves deterministically during inflation. The central question is whether such disorder alters the heavy-field spectrum (the "clock" frequency) or merely modifies the excitation amplitudes and phases of the collider modes.

Methodology
The author employs a linear, exactly solvable model in de Sitter space. The setup involves a massive spectator field $\sigma$ coupled linearly to a spatially quenched random source $h(\mathbf{x})$ with a deterministic power-law time profile:
$h(\mathbf{x}, \eta) = (-H\eta)^p h(\mathbf{x})$
where $p$ is a real parameter. The case $p=0$ corresponds to a persistent source, while $p>0$ describes a source that decays toward the future boundary.

The analysis proceeds through three main technical frameworks:

Exact Retarded Response: For a fixed realization of the disorder, the field equation reduces to an inhomogeneous Bessel equation. The exact retarded solution is derived in terms of Lommel functions $S_{\rho, \nu}$ , separating the particular (forced) solution from the homogeneous massive tails.
Schwinger–Keldysh Formalism: The disorder average is performed within the in-in formalism. By rotating to the Keldysh basis (average/difference fields), the author demonstrates that the Gaussian disorder average generates a rank-one noise kernel in time. This modifies the statistical propagator ( $F$ ) by an additive term proportional to the product of retarded responses, $f(k)R_{k,p}(\eta)R_{k,p}(\eta')$ , while leaving the spectral function ( $\rho$ ) and the retarded/advanced propagators unchanged.
Cosmological Collider Seeds: The disorder-corrected propagator is inserted into cosmological collider exchange diagrams. The author derives the exact factorized seed for the trispectrum and bispectrum, utilizing Mellin–Barnes representations and hypergeometric functions to evaluate the time integrals. They analyze the soft limits (bispectrum) and folded limits (trispectrum) to identify the phenomenological signatures.

Key Contributions and Results

Spectral Invariance: A primary result is that the linear Gaussian disorder does not shift the poles of the massive retarded propagator. The heavy-field scaling dimensions ( $\nu = \pm i\mu$ ) and the associated oscillatory frequency $\mu$ remain fixed. The disorder only modifies the amplitudes, phases, and the relative weighting of the forced response versus the homogeneous massive signal.
Exact Factorization: The disorder-averaged cosmological collider seed factorizes exactly. It consists of a product of two one-variable functions, each containing three distinct sectors:
1. An analytic forced response (associated with the source).
2. Two non-analytic homogeneous branches (carrying the collider signal $u^{\pm i\mu}$ ).
Role of the Temporal Profile ( $p$ ): The parameter $p$ $p$ controls the infrared behavior of the solution:
- Persistent Limit ( $p=0$ ): The forced response approaches a static constant ( $1/m^2$ ) at late times. While harmless for the trispectrum seed ( $\ell=0$ ), this static term generates a local late-time logarithmic divergence in the bispectrum sector ( $\ell=-2$ ).
- Decaying Sources ( $p>0$ ): The forced response vanishes at the future boundary. For $p>0$ , the Schwinger–Keldysh endpoint integrals become finite, resolving the logarithmic divergence found in the persistent case.
Crossover at $p=3/2$ : For spatial white noise, the value $p=3/2$ is distinguished. At this point, the explicit dependence on the exchanged momentum scale $s$ in the disorder seed vanishes. The disorder contribution interferes destructively with the clean de Sitter collider branch. Specifically, the coefficient of the collider oscillation is rescaled by a factor $(1 - \pi f_0 / \mu^2)$ , allowing for complete cancellation of the leading oscillatory branch at a critical disorder strength $f_{0, \text{crit}} = \mu^2/\pi$ .
Soft Limit Behavior: In the squeezed limit of the bispectrum, the temporal profile determines the power-law envelope. For $p > 3/2$ , the non-analytic massive clock contribution ( $\sim x^{7/2-2p}$ ) becomes parametrically dominant over the analytic forced contribution ( $\sim x^{2-p}$ ). For $p < 3/2$ , the analytic forced sector dominates. Crucially, while $p$ changes the envelope and phase, it leaves the logarithmic frequency $\mu$ fixed.

Significance and Claims
The paper claims to provide the first study combining a spatially quenched random source, an exactly solvable time-weighted retarded response in de Sitter space, and its insertion into cosmological collider exchanges.

The author emphasizes that their results offer a clear separation between the particle content of the theory (the mass and spin of the exchanged field, which determine the frequency of the clock) and the environmental history (the temporal profile of the disorder, which determines how the clock is excited). The disorder acts as a "memory" of the disordered stage: even after the forcing decays, the homogeneous massive modes excited during that period survive and imprint a modified signal on late-time correlators.

The work suggests that cosmological collider observables may encode not only the spectrum of fields present during inflation but also information about the stochastic environment in which those fields evolved. The author notes that their construction is a first step, suggesting future extensions to multiplicative disorder (random mass), which could potentially alter the heavy-field spectrum itself, and to Euclidean formulations via replica methods.

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