Breaking dark degeneracies in $k$-essence models with redshift-space distortions

Abstract

Dynamical dark energy models are often difficult to constrain with background observations alone due to parameter degeneracies. This is especially true when the dark energy sector evolves through an effective pressureless matter phase, leading to degeneracies between the model parameters and the matter density parameter. In this work, we show that redshift-space distortion (RSD) measurements help break this degeneracy when combined with expansion history probes including Pantheon$^{+}$ supernovae and DESI DR2 BAO measurements. We demonstrate this in the ghost and dilatonic ghost condensate $k$-essence models, restricting the observational analysis to physically admissible solutions by imposing the absence of ghosts and gradient instabilities. Given the small scalar sound speeds in these models, we also explicitly check the validity of the quasi-static approximation used in the growth analysis. Our results show that combining growth-rate data with stability requirements and standard background observations provides a fast and efficient way to constrain potentially degenerate dark sector models. Lastly, we discuss the matter clustering constraints on these models in light of the recent $S_8$ discrepancies.