Primordial non-Gaussianity constraints on dissipative inflation

Abstract: Dissipative effects appear in many early-Universe scenarios, yet their universal observational signatures and systematic confrontation with data remain largely unexplored. We employ the Open Effective Field Theory of Inflation (Open EFToI) to consistently incorporate dissipative and stochastic effects while preserving scale invariance. Dissipation enhances specific interaction channels of the Goldstone mode, generating distinctive primordial non-Gaussian signatures, beyond those generically produced by standard EFToI. In the weak-dissipation regime, this includes folded bispectrum shapes observationally more favoured than both the equilateral and orthogonal templates. Using the Modal bispectrum pipeline with the Planck CMB data, we obtain the likelihood and derive the first model-independent bounds on early-Universe dissipation. We find a marginalised upper bound on the dissipation scale $γ\leq 384\,H$ and a lower bound on the sound speed $c_s \geq 0.38$ at $95\%$ confidence level. The maximum likelihood for best-fit models reveals a degeneracy between $γ$ and $c_s$. These results open a model-independent window for probing departures from minimal inflation and discriminating between early-Universe scenarios with stochastic noise and dissipative effects.

• The paper introduces a novel application of the Open EFToI framework to integrate dissipative and stochastic effects in inflation, setting bounds on γ and cₛ.
• It employs tree-level Feynman diagrams and modal bispectrum analysis to distinguish folded and equilateral non-Gaussianity shapes linked to different dissipation regimes.
• Results indicate that too high dissipation (γ > 384H) or too low sound speed (cₛ < 0.38) is inconsistent with Planck data, refining the viable parameter space for inflation models.

Constraints on Early-Universe Dissipation from Primordial Non-Gaussianity

Formulation of Dissipative Inflation in Open EFT

The paper "Primordial non-Gaussianity constraints on dissipative inflation" (2603.13473) applies the Open Effective Field Theory of Inflation (Open EFToI) framework to parametrize dissipative and stochastic dynamics during inflation. Unlike standard single-field slow-roll inflation, dissipative channels allow primordial perturbations to couple to environmental degrees of freedom, generating both dissipative damping and stochastic noise terms. Crucially, the construction preserves adiabaticity and scale invariance, maintaining consistency with CMB power spectra while producing distinctive bispectral non-Gaussian features. The theory is built by doubling the path integral via the Schwinger–Keldysh formalism, defining the adiabatic Goldstone boson $\pi$ as the primary fluctuation—decoupled from metric perturbations under slow-roll hierarchies—whose action receives additional dissipative and noisy operators controlled by a dissipation scale $\gamma$ and sound speed $c_s$.

Phenomenology of Dissipative Bispectrum Shapes

The bispectrum from dissipative inflation is calculated via tree-level Feynman diagrams using the Open EFToI action. Dissipative operators induce enhancements in specific interaction channels, with notable regime dependence:

• Weak dissipation ($\gamma\ll H$): The bispectrum amplitude exhibits a sharp folded configuration, originating from environmental noise sourcing. This shape is observationally more favored than equilateral or orthogonal templates, as confirmed by modal correlation analysis.
• Strong dissipation ($\gamma\gg H$): The signal transitions to a predominantly equilateral configuration, as dissipation suppresses intermode correlations.
• Amplitude scaling: For operators controlled by $c_s$ alone, the amplitude $\sim c_s^{-2}$, reproducing the scaling of standard EFToI. Dissipative operators exhibit more rapid enhancement with increasing $\gamma$, up to the strong-coupling regime.

  Figure 1: The shape correlation of the Open EFToI bispectrum with standard templates demonstrates a folded-to-equilateral transition as dissipation increases; folded signals at low $\gamma$ have incomplete overlap with standard templates.

Modal Bispectrum Pipeline and Likelihood Evaluation

To confront theory with observation, the authors employ the Modal bispectrum estimator applied to Planck 2018 CMB datasets. The theoretical bispectrum is projected onto the observed CMB bispectrum via spherical harmonic transfer functions, obtaining a likelihood function for $(\gamma, c_s)$:

Figure 2: Likelihood in the $(\gamma, c_s)$ parameter plane, normalized at its maximum; likelihood is maximal for moderate $\gamma$ and $c_s$, disfavoring regions with excessive PNG amplitude.

Efficient evaluation requires a separable mode expansion, drastically reducing computational complexity from naive summation. The Bayesian posterior is then constructed assuming uniform priors across physically reasonable $(\gamma, c_s)$ ranges.

Numerical Results: Bounds and Signal-to-Noise

The marginalized posteriors yield strong constraints:

• Dissipation scale: $\gamma < 384\,H$ (95% CL)
• Sound speed: $c_s > 0.38$ (95% CL)
• The best-fit region exhibits a degeneracy between $\gamma$ and $c_s$, evident from the corner plots of the posterior distribution, indicating multiple combinations can yield comparable bispectrum shapes and amplitudes.

  Figure 3: Posterior distributions for $\gamma$ and $c_s$, with $2\sigma$ exclusion contours and numerical bounds stated.

The signal-to-noise ratio (SNR) map highlights the regions where the Open EFToI shapes match observed CMB bispectra most strongly. SNR is maximal near $\gamma\approx H$ and $c_s\approx 1$, consistent with a large negative folded component and a modest equilateral contribution. For high $\gamma$ and low $c_s$, SNR saturates at $\sim1$, indicating diminished overlap.

Figure 4: The SNR for the predicted bispectrum shape as a function of $\gamma$ and $c_s$, illustrating decreasing match with data in regimes of high dissipation and low sound speed.

Physical Interpretation and Implications

The results establish the first robust, model-independent bounds on dissipative dynamics during inflation inferred from bispectrum measurements. Crucially, the folded bispectrum signal at low $\gamma$—which cannot be mimicked by standard cold single-field models—offers a discriminant for stochastic/dissipative inflationary scenarios. The transition to equilateral dominance at high $\gamma$ mirrors expectations from strong environmental decoherence, consistent with a damping of intermode correlations and a loss of quantum coherence in primordial fluctuations.

The practical implication is that either excessive dissipation ($\gamma \gg 384\,H$) or too low sound speed ($c_s < 0.38$) is inconsistent with weakly non-Gaussian Planck measurements. These constraints refine the viable space for non-minimal inflationary and warm inflation models, and provide targets for next-generation CMB and LSS surveys, as improved noise levels and access to smaller scales promise tighter constraints and the potential to resolve folded bispectrum features more finely.

Theoretical Outlook

On the theoretical front, the Open EFToI framework provides a unified approach for describing stochastic and dissipative modifications to primordial cosmology, transcending the limitations of model-dependent analyses. The modal pipeline's ability to constrain both bispectrum shape and amplitude, coupled with precise numerical bispectrum evaluation, lays a foundation for systematic discrimination among competing early-universe scenarios. Extensions to higher-order correlators (e.g., trispectrum), parity-violating non-Gaussianity, and signatures from multifield or collider scenarios (with stochastic sources) are immediate avenues.

Conclusion

This study delivers the first stringent, model-independent constraints on dissipation and stochasticity in inflation from non-Gaussianity measurements, leveraging the Open EFToI formalism and Modal bispectrum pipeline. The primary bounds, $\gamma < 384\,H$ and $c_s > 0.38$, delimit the parameter space for viable dissipative inflation, highlight the observational relevance of folded bispectrum signals, and suggest promising directions for future cosmological probes. These advances enhance the power of non-Gaussian statistics as a probe of microphysical inflationary dynamics and the classical-quantum transition in the early universe.