CMB Spectral Distortion Anisotropies from Acoustic Damping with primordial non-Gaussianity

This paper develops a detailed framework for calculating CMB spectral distortion anisotropies generated by the acoustic damping of primordial perturbations in the presence of primordial non-Gaussianity (PNG). The authors use the recently developed frequency hierarchy (FH) treatment of CosmoTherm to evaluate the precise distortion source and transfer functions caused by mixing of blackbodies of different temperatures, including the coupled spectro-spatial evolution and important photon-transport effects.

Main derivation of distortion sources: The authors derive the second-order blackbody-mixing source from the Liouville and Thomson collision terms, including velocity-dependent scattering contributions. The real-space source can be written compactly as:

[

S mix(eta, r,) g [g - g,0 - g,2 - 1 over 10 2 g - 1 over 2[2 g] 0 - 1 over 10[2 g] 2]

]

in terms of the gauge-independent photon temperature variable g = + - V. The source depends not only on the magnitudes of the two dissipating modes, but also on their relative orientation and on their orientation with respect to the observable mode. This full mode-coupling geometry differs from previous treatments, which did not include these aspects consistently.

Effective anisotropic heating rates: Rather than evolving the complete second-order photon distribution, the authors use the structure of observable cross-correlations to reduce the problem to a set of effective, scale- and redshift-dependent anisotropic heating rates. These source functions are constructed from first-order photon and baryon transfer functions while retaining the primordial bispectrum and the complete mode-coupling geometry. They can then be inserted into the linear FH as external spectral-distortion sources. The authors build a transfer function database using about 6000 points in k in the range 10-4 - 10 squared, Mpc-1, computing transfer functions with max = 10 in the photon and neutrino hierarchy, including polarization effects.

Results for standard power spectrum with PNG: For a nearly scale-invariant primordial power spectrum with local-type non-Gaussianity, the anisotropies generated by propagation of the average distortion through the perturbed Universe are negligible at currently relevant sensitivities. The observable signal is instead dominated by the direct modulation of acoustic dissipation proportional to f NL. The effective monopole heating rate approaches the standard average heating rate on large scales, but develops a significant scale dependence at larger wavenumbers. Heating close to recombination is suppressed as the observable wavenumber increases, so that small-scale distortion anisotropies are sourced predominantly during the µ-era. The dipolar and quadrupolar heating sources are strongly suppressed relative to the monopole, especially at redshifts relevant for µ-distortion production.

Computed power spectra: Using the FH implementation of CosmoTherm, the authors compute the µT, µE, yT and yE cross-power spectra. The µT spectrum displays alternating regions of correlation and anti-correlation, but is damped slightly faster than the primary temperature spectrum. This enhanced damping follows from the absence of acoustic propagation in the distortion variables: in tight coupling, distortion perturbations are overdamped rather than participating in the exchange between photon monopole and dipole perturbations that supports ordinary acoustic waves. The numerical damping scale is consistent with the analytic expectation based on the modified diffusion scale of the distortion perturbations. The yT spectrum has a similar oscillatory structure to the µT signal, but is lower in amplitude and more strongly damped on small angular scales. The µE and yE spectra are further suppressed and exhibit the expected phase shift relative to the temperature correlations, with large-scale reionisation features.

Comparison to previous calculations: The refined results broadly reproduce the large-scale behavior found in previous approximate calculations. However, visible differences arise from the detailed evolution of the distortion perturbations and from the scale dependence of the source. Previous numerical results provide an accurate approximation to the µT spectrum at 400, but do not capture the additional damping at higher multipoles. For the yT spectrum, earlier approximations underestimate the signal on large angular scales and overestimate it on small angular scales.

Approximation tests: Tight-coupling transfer functions reproduce the µT and µE spectra with negligible error because their sources are generated predominantly at high redshift. The same approximation produces visible, although still moderate, changes in the yT and yE spectra, particularly at very large and very small angular scales. Restricting the anisotropic heating source to its local monopole changes the µ-distortion spectra negligibly and affects the y-distortion spectra only at the level of a few percent. Neglecting the wavenumber dependence of the source is adequate for the µT/E spectra except at few times 10 cubed, but produces appreciable changes in the small-scale yT/E signals.

Enhanced small-scale power model: For illustration, the authors consider a model with enhanced small-scale curvature power (Model I: (k) = A p (k/k p) n p-1 e-k/k c with A p = 4 times 10-7, k p = 10 squared, Mpc-1, n p = 3, k c = 10 cubed, Mpc-1). In this case, the average µ-distortion can approach the COBE/FIRAS limit, and the propagation of this distorted average spectrum through the perturbed Universe produces an additional anisotropic signal that is no longer negligible. The propagation contribution and the signal generated directly by anisotropic dissipation exhibit differing angular dependences. The propagation signal scales with the amplitude A p of the enhanced small-scale power, while the anisotropic-dissipation signal scales as A p f NL. These differing angular structures and parameter scalings imply that measurements of the distortion monopole and the distortion anisotropies can jointly constrain the amplitude of the small-scale power spectrum and the primordial non-Gaussianity, rather than only their product.

Conclusions: The newly developed FH of CosmoTherm now makes it possible to exploit the full spectro-spatial information carried by distortion anisotropies in scenarios with PNG. It provides a systematic way to distinguish distortions generated at different epochs, include all relevant photon-transport effects, and connect the observed correlations to the scale dependence and configuration dependence of primordial fluctuations. The results pave the path for studying PNG in new regimes using existing and upcoming high precision CMB anisotropy data to measure primordial distortion correlations.

Improvements to AI systems based on this paper:

1. Physics-informed generative models for CMB spectral distortion maps: Train a diffusion or GAN-based model that generates full-sky µ- and y-distortion maps conditioned on primordial non-Gaussianity parameters (e.g., f NL, A p, n p, k c). The model can embed the derived source term S mix and the mode-coupling geometry as inductive biases, enabling rapid simulation of distortion anisotropies without running full CosmoTherm hierarchies.

2. Neural emulators for anisotropic heating rates: Build a neural network that takes as input wavenumber k, redshift z, and cosmological parameters, and outputs the effective monopole, dipole, and quadrupole heating rates (including their scale dependence and suppression near recombination). This emulator can replace the 6000-point transfer function database, accelerating parameter estimation by orders of magnitude.

3. Automatic differentiation of spectral distortion power spectra: Implement a differentiable forward model for µT, µE, yT, and yE cross-power spectra using the FH framework. This allows gradient-based Bayesian inference (e.g., Hamiltonian Monte Carlo) to jointly constrain f NL and small-scale power amplitude from future CMB observations (e.g., PIXIE, Voyage 2050), avoiding expensive MCMC likelihood evaluations.

4. Uncertainty-aware interpolation for transfer functions: Use a Gaussian process or normalizing flow to interpolate the photon and neutrino transfer functions across the 10-4 - 10 squared, Mpc-1 range, providing smooth derivatives and calibrated uncertainties. This improves the accuracy of the source functions at intermediate scales where the current grid may be sparse.

5. Reinforcement learning for optimal survey design: Train an RL agent to propose observational strategies (frequency channels, sky coverage, integration time) that maximize the signal-to-noise of µT and yT correlations, given the predicted angular damping and reionisation features. The agent can use the paper's finding that small-scale distortion anisotropies are sourced predominantly during the µ-era to prioritize high-frequency, low-noise measurements.

6. Symbolic regression for compact source approximations: Apply symbolic regression to the computed anisotropic heating rates to discover closed-form approximations that capture the scale dependence and orientation effects. This could yield analytic formulas for the dipole and quadrupole sources, enabling faster semi-analytic codes for parameter scans.

7. Hybrid physics-ML classifier for PNG detection: Develop a classifier that distinguishes local-type PNG from other bispectrum shapes (e.g., equilateral, orthogonal) using the angular structure of µT and yT spectra. The classifier can be trained on the paper's predicted mode-coupling signatures (e.g., alternating correlation/anti-correlation regions, enhanced damping) and then applied to real CMB data to flag candidate detections.

8. Active learning for transfer function database refinement: Use active learning to iteratively add new k points where the emulator's prediction error is highest, reducing the required number of transfer function evaluations from 6000 to a few hundred while maintaining accuracy—crucial for exploring non-standard cosmologies (e.g., running spectral index, oscillatory features).

9. Interpretable feature extraction for distortion anisotropies: Train an autoencoder on the computed µT and yT spectra to extract physically meaningful latent variables (e.g., effective damping scale, monopole heating amplitude, reionisation contribution). This can help identify degeneracies between f NL and small-scale power amplitude, as highlighted by the differing angular scalings in the paper.

10. Fast likelihood-free inference for joint constraints: Implement a simulation-based inference (SBI) pipeline (e.g., neural posterior estimation) that uses the FH-based forward model to directly estimate posteriors on f NL, A p, and n p from mock distortion anisotropy maps. The pipeline can exploit the paper's result that propagation and anisotropic-dissipation signals scale differently, breaking degeneracies that would otherwise require high-resolution maps.