2.1 × 10⁻⁹—that’s the minuscule amplitude of the primordial density ripples frozen into the cosmic microwave background. These nearly scale-invariant perturbations were born during inflation—a brief burst of exponential expansion of the universe driven by gravity, predicted by Alan Guth and Andrei Linde. If massive scalar partner fields existed back then, they would have left imprints in the fine structure of those fluctuations—non-Gaussian correlations. The hunt for such ‘fingerprints’ is the cosmological collider program, dreamed up by Juan Maldacena and extended by many theorists. The Standard Model of particle physics has no answers for dark matter or the mass hierarchy; the cosmological collider offers a unique window into the energy scales of Grand Unification. Until now, most data analyses assumed weak coupling between fields—an assumption that recent work has shown is hard to reconcile with theory. This paper is the first to tackle a realistic strong-mixing scenario, using real Planck data.
The authors started from the most general effective Lagrangian coupling two scalar fields: a Goldstone boson π (tied to the inflaton) and a massive field σ. The Lagrangian packs up to seven independent cubic interaction operators that shape the bispectrum of the curvature perturbation ζ. To compute the bispectra, they used a two‑pronged strategy: an analytical cosmological bootstrap (valid at weak coupling) and the numerical code CosmoFlow, which tracks the real‑time evolution of correlation functions without assuming small mixing. In total they computed over 40 000 bispectrum templates across a grid of sound speeds c_π and c_σ, mass m, and mixing ρ. The theoretical shapes were pitted against the Planck PR4 bispectrum (171 bins) using Bayesian inference; the cubic couplings were analytically marginalized, slashing sampling time to mere milliseconds per step.
No statistically significant non‑Gaussian signal popped out for any parameter set. The best χ² improvement over the no‑exchange model (ρ = 0) was 5,3 after adding five free parameters—fully consistent with a random fluctuation. Bayesian evidence ratios Z/$Z_{null}$ never exceeded unity, and the AIC and BIC criteria also disfavor the more complex model. In the weak‑mixing regime (ρ ≪ H), constraints on the coupling amplitudes ρ² and ρΔρ are orders of magnitude weaker than the theoretical perturbativity bounds, making this region practically invisible to Planck—except for the very lightest masses (m ≲ 1.5H). In the strong‑mixing regime (ρ ≳ H), the data limit ρ/H to ≲ 170 (for a uniform prior) or ≲ 50 (for a logarithmic prior). Constraints on the cubic parameters Δρ, α, and μ are also far from saturating their theoretical limits, yet they lie deep in the non‑perturbative domain. The characteristic collider oscillations, whose frequency is set by the effective mass $m_{eff}$ = √(m²+ρ²), are exponentially damped at large ρ and drown in the noise. Varying all seven parameters jointly smears out the already faint signals. So Planck sees no compelling evidence for multi‑field inflation with scalar exchange.
For the first time, this work lays down consistent limits on realistic multi‑field inflation models without the weak‑coupling crutch. It proves that current CMB data can already probe regimes once thought out of reach. The absence of a signal shrinks the parameter space for theories motivated by, say, superstring constructions teeming with moduli fields. A critical insight: the popular weak‑mixing approximation is unfit for Planck data, because every perturbatively allowed ρ gives a bispectrum contribution that’s negligible. This forces a rethink of earlier cosmological‑collider observational studies.
Next‑generation experiments—CMB‑S4, Simons Observatory, and large galaxy surveys—will sharpen non‑Gaussianity sensitivity by only a factor of 2–5. That may still miss faint exchange signals, especially in the strong‑mixing regime where oscillations are suppressed. A real breakthrough could come from 21‑cm maps of the cosmic dark ages, which probe a vastly larger number of modes. Meanwhile, the method developed here, jointly handling the quadratic and cubic sectors of the Lagrangian, will be turned on more exotic inflationary scenarios: exchange of higher‑spin particles, non‑perturbative gauge sectors, and dissipative models.
The results matter for particle physics and cosmology because they constrain interactions at Grand Unification energy scales. They also push forward the development of new numerical tools for predicting inflationary observables.
The authors plan to extend the analysis to models with chemical potentials and partially massless fields, and to fold in CMB trispectrum and polarization data.
The search for inflaton partner particles is closely tied to the mass hierarchy problem and the completeness of the Standard Model: if inflation were multi‑field, it could explain the tiny Higgs mass via mechanisms like the relaxion. The null signal so far gives no experimental support to such ideas.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors for the first time analyzed the strong mixing scenario of two scalar fields in inflation using Planck PR4 data. They constructed a general Lagrangian, computed bispectra analytically and numerically (with the CosmoFlow code), and through Bayesian analysis found no significant non-Gaussianities.
Where its strength is
The strength of the work lies in moving from idealized weak mixing to physically motivated strong mixing, which allowed obtaining robust constraints on the parameters. The method of analytic marginalization of cubic couplings makes the analysis efficient and suitable for future data.
Where it could go next
Worth trying
Nearby works in our archive
The closest work in the archive sits at 0.70 by meaning — the usual level for our corpus.
Computing 40 000 bispectra for 171 triangle configurations took more than 4 million calls to CosmoFlow and about 100 000 processor‑hours — equivalent to running a hefty computer nonstop for 11 years. Yet each model evaluation, after interpolation, takes just milliseconds.