A preference for dynamical phantom dark energy using one-parameter model with Planck, DESI DR1 BAO and SN data

Baryon Acoustic Oscillation (BAO) provides a powerful tool to measure cosmic expansion and consequently the nature of the Dark Energy (DE). Recent precise BAO measurements by Dark Energy Spectroscopic Instrument data release 1 (DESI DR1), when combined with Cosmic Microwave Background (CMB) data from Planck and Supernovae of Type Ia (SN Ia), favor evolving dark energy over cosmological constant. This result is strongly related to the assumed priors on the Chevallier-Polarski-Linder (CPL) parameterization of DE. We test another parametrization which introduces two free parameters $n$ and $\alpha$, only $n$ is independent. Thus, it reduces the parameter space compared to the CPL model, which derives a more robust preference for evolving DE, if any. The model potentially produces three cosmological scenarios according to the values of its parameters. For $n=3$, the $\Lambda$CDM model is recovered, quintessence for $n<3$, and phantom for $n>3$. In the present study, we test the model on the background level, and, to our knowledge for the first time, on the linear perturbation level. Bayesian evidence analysis shows a weak preference \textbf{($\mathbf{\ln B \leq 1.8}$)} for dynamical DE in the phantom regime over the cosmological constant DE using Planck, DESI, and PantheonPlus \& SH0ES data, similarly the AIC analysis supports dynamical DE scenario for the same data. The model predicts current phantom DE $w_{de,0} = -1.073 \pm 0.032$ and $H_0=70.9\pm 1.4$ km/s/Mpc when Planck+DESI data is used, which decreases the tension with $H_0$ local measurements to $1.2\sigma$ level.