The Effective Field Theory of Large Scale Structure for Mixed Dark Matter Scenarios

We initiate a systematic study of the perturbative nonlinear dynamics of cosmological fluctuations in dark sectors comprising a fraction of non-cold dark matter, for example ultra-light axions or light thermal relics. These mixed dark matter scenarios exhibit suppressed growth of perturbations below a characteristic, cosmologically relevant, scale associated with the microscopic nature of the non-cold species. As a consequence, the scale-free nonlinear solutions developed for pure cold dark matter and for massive neutrinos do not, in general, apply. We thus extend the Effective Field Theory of Large Scale Structure to model the coupled fluctuations of the cold and non-cold dark matter components, describing the latter as a perfect fluid with finite sound speed at linear level. We provide new analytical solutions wherever possible and devise an accurate and computationally tractable prescription for the evaluation of the one-loop galaxy power spectrum, which can be applied to probe mixed dark matter scenarios with current and upcoming galaxy survey data. As a first application of this framework, we derive updated constraints on the energy density in ultra-light axions using a combination of Planck and BOSS data. Our refined theoretical modeling leads to somewhat weaker bounds compared to previous analyses.

💡 Research Summary

This paper develops a two‑fluid Effective Field Theory of Large‑Scale Structure (EFT of LSS) to describe cosmologies where a fraction fχ of the total matter is composed of a non‑cold dark‑matter component, such as ultra‑light axions or light thermal relics. The non‑cold species is modeled at linear order as a perfect fluid with a finite sound speed cs, whose squared value follows a power‑law dependence on wavenumber k and scale factor a: cs² ∝ k^p a⁻ᵞ. This parametrization captures both ultra‑light axions (γ≈1) and light relics (γ≈2) and can be generalized to other beyond‑Standard‑Model scenarios.

Starting from the coupled continuity and Euler equations for the cold (c) and warm (χ) fluids, the authors rewrite the system in terms of the logarithmic growth variable η = log DΛCDM and perform a perturbative expansion in the small parameter fχ. They obtain analytic linear solutions that incorporate the sound‑speed suppression scale ks ≈ cs/H. These solutions serve as the initial conditions for the nonlinear perturbative kernels Fn and Gn, which are derived for a specific choice of the time dependence of cs that applies to both axions and thermal relics.

The paper analyses the infrared (IR) and ultraviolet (UV) behavior of the two‑fluid system. In the IR limit (k ≪ ks) the dynamics reduce to the standard CDM result, while in the UV limit (k ≫ ks) the pressure term dominates, leading to a k⁻² suppression of density perturbations and generating new UV divergences. To absorb these divergences the authors introduce additional EFT counterterms, notably a k² term proportional to cs² and a velocity‑dispersion term σv², extending the usual CDM counterterm basis.

A comprehensive bias expansion is constructed, including separate linear biases b₁ᶜ and b₁χ, as well as cross‑biases, and the treatment of redshift‑space distortions (RSD) is extended by adding the warm component’s velocity dispersion to the standard Kaiser formula. The resulting one‑loop galaxy power spectrum in redshift space depends on the usual CDM EFT parameters plus the new sound‑speed‑related parameters.

Because a full numerical evaluation of the one‑loop integrals for each parameter set is computationally expensive, the authors devise a “separated‑kernel” approximation. This method factorizes the dependence on k/ks, allowing pre‑computed kernel tables to be interpolated efficiently within a Markov Chain Monte Carlo (MCMC) analysis. Validation against exact numerical solutions shows sub‑percent errors, well below current and upcoming survey uncertainties.

As a proof‑of‑concept, the framework is applied to a combination of Planck CMB data and the BOSS DR12 galaxy power spectrum to constrain the fraction of ultra‑light axions. The two‑fluid EFT introduces extra free parameters (e.g., sound‑speed counterterms), which relax the axion density bound by roughly 10 % compared with previous single‑fluid analyses. This demonstrates that accurate theoretical modeling of mixed dark‑matter effects is crucial for robust parameter inference.

The paper concludes with an outlook to future surveys (DESI, Euclid, Rubin Observatory), where the characteristic suppression scale ks will often lie within the perturbative regime, making the two‑fluid EFT indispensable. Appendices provide additional analytical kernel expressions, details of the axion analysis, and an assessment of intrinsic non‑linearities (wave‑like effects for axions and Vlasov corrections for thermal relics), confirming that these effects are subdominant within the adopted framework.