Unified dark fluid with null sound speed as an alternative to phantom dark energy

TL;DR

The paper proposes a Unified Dark Fluid (UDF) with a vanishing rest-frame sound speed, $\hat{c}_s^2=0$, to reproduce the background expansion of the CPL dark-energy parametrization while avoiding phantom instabilities and NEC violations. By construction, the UDF matches the CPL background but evolves perturbations differently, implemented in CAMB with $w_{\text{UDF}}(a)$ chosen to reproduce CPL and with no anisotropic stress. Across CMB, LSS, and RSD observables, the UDF generally agrees with CPL at linear scales, yielding only percent-level differences, and non-linear analysis via spherical collapse shows structure formation remains broadly consistent with standard scenarios. Current data (Planck PR4, DESI BAO DR2, DESY5) fit the UDF nearly as well as CPL, underscoring that many cosmological probes are insensitive to the detailed dark-sector split. Forecasts for stage IV data suggest potential discrimination, but decisive evidence requires including mildly non-linear scales or additional probes, reinforcing that the dark degeneracy allows multiple viable descriptions of the dark sector without invoking phantom components.

Abstract

Recent BAO measurements from DESI, when combined with CMB and supernovae data, suggest evolving dark energy and in particular point to a possible phantom regime, with an equation of state parameter $w<-1$. We explore an alternative phenomenological way to model dark matter and dark energy based on a unified dark fluid (UDF). By construction, our model reproduces the same background expansion history as DESI's best-fit using the CPL parametrization, but assumes a vanishing rest-frame sound speed and no anisotropic stress. This simple prescription ensures a consistent and physical treatment of perturbations and, in our case, the use of a unified dark sector avoids phantom behaviour. We model CMB, LSS, and redshift-space distortion observables, and find mostly small differences with CPL, suggesting that while stage IV CMB and galaxy surveys will be able to test these models, achieving a decisive distinction between them may prove challenging on linear scales. At the non-linear level, we study spherical collapse in the UDF and show that within this framework, structure formation proceeds very similarly to standard scenarios. Using Planck, DESI BAO DR2, and DES Y5 supernovae data, we demonstrate that this simple UDF model fits current observations nearly as well as CPL, while treating perturbations consistently. Because most cosmological observations are not sensitive to how the dark sector is split, the unified framework can also approximate the phenomenology of interacting dark energy-dark matter scenarios or evolving dark matter, making it a general way to model the data, at least as long as the dark components have a vanishing sound speed, which is the most distinctive feature of our analysis. Our results highlight that a unified dark fluid with evolving equation of state and null sound speed is sufficient to pass current constraints without invoking a phantom component.

Figures (10)

• Figure 1: UDF equation of state evolution with scale factor. For comparison, we also show the dark matter and dark energy equations of state as a function of scale factor. The dark energy equation of state corresponds to the best-fit to DESI BAO DR2, Planck CMB and DESY5 supernovae obtained in the CPL parametrization.
• Figure 2: Relative difference between CMB power spectra prediction in UDF and CPL with the fiducial values stated in the text. The relative difference is mostly subpercent, apart from the ISW effect in the temperature power spectrum. Note that in the TE case, the normalization is not $C_\ell^{TE}$ but rather $\sqrt{C_\ell^{TT}C_\ell^{EE}}$.
• Figure 3: Relative difference in the matter power spectrum with the fiducial values stated in the text. The matter power spectrum is defined with respect to the baryons + UDF overdensity in the UDF case, and baryons + dark matter + dark energy in the CPL case. This definition differs from the usual convention that excludes dark energy. Consequently, the galaxy bias would be redefined when fitting galaxy power spectra.
• Figure 4: Relative difference between CMB lensing (top panel), galaxy (middle panel) and shear (low panel) power spectra with the fiducial values stated in the text. In the latter two cases, the labels indicate the mean redshift of bins we considered. Shaded areas show the 1-$\sigma$ uncertainty that is expected for an Euclid-like experiment, using equally spaced multipole bins with width $\Delta\ell=20$ or $\Delta\ell=100$.
• Figure 5: Relative difference between $(f_\textrm{eff}\sigma_8^\textrm{tot})(z)$ in UDF and $(f\sigma_8)(z)$ in CPL as a function of redshift for our fiducial cosmology.