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Sound mode and scale-dependent growth in two-fluid dynamical dark energy

Frans van Die* and Vincent Desjacques†

  • Physics Department, Technion, Haifa 3200003, Israel

  • *Contact author: frans.van@campus.technion.ac.il
  • †Contact author: dvince@physics.technion.ac.il
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Phys. Rev. D 114, 023509 – Published 6 July, 2026

DOI: https://doi.org/10.1103/r8y8-bcqw

Abstract

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 ΛCDM. Using a Fisher forecast for a multitracer 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∼10  h−3 Gpc3 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 cs2∼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 cs2∼10−5. Larger sound speeds cs2>10−2 could be probed with optimal weighting schemes that reduce shot noise and increase the effective bias.

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Phys. Rev. D 114, 023509– Published 6 July, 2026
  • Received 9 March 2026
  • Accepted 9 June 2026
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