$w_0$-probe: A new diagnostic of dark energy based on $Om$

Recent DESI data suggest that dark energy may be evolving and motivate the use of model-independent diagnostics such as $Om(z)$ and probes of the equation of state (EoS) of dark energy, $w(z)$. Traditional reconstructions of $w(z)$ rely on differentiating the expansion history, $h(z)=H(z)/H_0$, which amplifies noise and systematic uncertainties. In this work, we introduce a new diagnostic, the $w_0$-probe, which is constructed from $Om(z)$, and which enables a direct determination of the current EoS from $h(z)$ without any additional differentiation. While retaining the null-test capability of $Om(z)$ for $\Lambda$CDM, the $w_0$-probe also provides a direct estimate of $w_0$ -- the current EoS of dark energy. We demonstrate that this reconstruction of $w_0$ is robust for any smooth underlying $w(z)$. We apply this method to Gaussian-process (GP) reconstructions of $h(z)$ using current SNe Ia+BAO+CMB data. Both $Om(z)$ and the $w_0$-probe exclude $\Lambda$CDM at the $95\%$ confidence level (C.L.), with the latter favouring $w_0\simeq-0.62 \pm 0.03$ at $95\%$ C.L. To mitigate potential over-constraining from GP priors, we additionally analyze $\chi^2$-limited reconstructions with likelihoods exceeding the $95\%$ CPL threshold. The $w_0$-probe obtained from these high-likelihood samples again predominantly excludes $\Lambda$CDM and yields $w_0\in(-0.8,-0.5)$ at $z\to 0$, demonstrating the robustness of our results. The $w_0$-probe therefore provides a simple, model-independent, and robust diagnostic of the current EoS of dark energy.