Sound Mode and Scale-Dependent Growth in Two-Fluid Dynamical Dark Energy

We investigate the effects of dynamical dark energy (DDE) on the growth of cosmic structure using a two-fluid model. This framework allows the dark energy equation of state to smoothly cross the phantom divide, in agreement with recent DESI results. In this effective description, DDE supports propagating perturbations that behave like sound waves. These perturbations induce a scale dependence in the growth of matter fluctuations and in halo bias, which can be exploited to test the dynamical nature of dark energy at the level of its fluctuations. For cluster-sized halos, the amplitude of the scale-dependent halo bias is comparable to that produced by massless neutrinos in $Λ$CDM. Using a Fisher forecast for a multi-tracer analysis of the power spectrum (P) and bispectrum (B) of galaxy number counts, we find that bispectrum information is essential to detect the scale dependence induced by the DDE sound mode. For a survey of volume $V\sim 10, h^{-3}{\rm Gpc}^3$ at redshift $z=0.5 - 1$, a two-tracer P+B analysis could detect this scale dependence if the sound speeds of the dark energy fluids are in the range $c_s^2\sim 10^{-2} - 10^{-4}$. Lower sound speeds cause halos to experience a gravitational drag force through the excitations of sound waves. This effect impacts measurements of the growth rate inferred from cluster-sized halos at the 10% level if one of the fluids has a very low sound speed $c_s^2\sim 10^{-5}$. Larger sound speeds $c_s^2 > 10^{-2}$ could be probed with optimal weighting schemes that reduce shot noise and increase the effective bias.

💡 Research Summary

This paper investigates how dynamical dark energy (DDE) that supports propagating perturbations—so‑called sound modes—affects the growth of cosmic structure. The authors adopt an effective two‑fluid description of DDE, wherein each fluid has a constant equation‑of‑state parameter (w_{\pm}) and a propagation (sound) speed (\hat c_{\pm}). By splitting the dark‑energy sector into two components, the model can smoothly cross the phantom divide ((w=-1)) without encountering the singularities that plague single‑field quintom constructions.

The theoretical framework shows that the sound speed introduces a characteristic Jeans‑like scale (k_{\pm}=H/\hat c_{\pm}). On scales comparable to or larger than this sound horizon, pressure gradients in the dark‑energy fluids become important, modifying the Poisson equation and the linear growth equation for matter perturbations (\delta_m). Consequently, the linear growth rate (f(k,z)) acquires a scale dependence, which propagates into a scale‑dependent halo bias (b(k,z)). For cluster‑mass halos ((M\gtrsim10^{14}M_{\odot})), the induced bias variation is of order a few percent, comparable to the effect of massless neutrinos in a standard ΛCDM cosmology.

A particularly striking result is that if one of the fluids has an extremely low sound speed ((\hat c^2\sim10^{-5})), the dark‑energy medium behaves like a viscous fluid, exerting a dynamical‑friction drag on massive halos. This drag reduces the inferred growth rate from redshift‑space‑distortion measurements by roughly 10 %, representing a potentially significant systematic bias for future surveys.

To assess observational prospects, the authors perform a Fisher‑matrix forecast for a multi‑tracer analysis that combines the galaxy power spectrum (P) and bispectrum (B). Assuming a survey volume of (V\sim10,h^{-3}{\rm Gpc}^3) spanning redshifts (0.5<z<1), they find that the bispectrum is essential: P‑only analyses cannot distinguish the DDE sound‑mode signal from noise, whereas a joint P+B analysis can achieve a 3σ detection for sound‑speed values in the range (\hat c^2\approx10^{-2})–(10^{-4}). Moreover, optimal weighting schemes that suppress shot noise extend the detectable region to (\hat c^2>10^{-2}).

The paper concludes that scale‑dependent growth and bias provide a novel, largely model‑independent probe of the internal degrees of freedom of dark energy. The two‑fluid effective description serves as a proof‑of‑concept, demonstrating that upcoming large‑scale structure surveys (DESI, Euclid, LSST) could test the existence of dark‑energy sound modes and, if present, constrain their propagation speeds. The authors also highlight the need for more sophisticated non‑linear modeling and N‑body simulations to fully capture the interplay between sound‑mode dynamics and halo formation, especially in the low‑sound‑speed regime where dynamical friction becomes important.