Confronting holographic dark energy with the latest cosmological data: tensions and model viability

Recent results from the second data release (DR2) from the Dark Energy Spectroscopic Instrument (DESI) hint at a possible dynamical form of dark energy. This motivates a fresh look at physically motivated alternatives to the standard Lambda cold dark matter model. In this work, we test two such scenarios – holographic dark energy (HDE) and Ricci dark energy (RDE) – against a wide range of observations. The data sets include cosmic chronometers, gamma-ray bursts, three major Type Ia supernova compilations (Pantheon+SH0ES, DES-Dovekie, and Union3), the new DESI DR2 baryon acoustic oscillation (BAO) measurements, and cosmic microwave background (CMB) distance priors from Planck 2018 + ACT-DR6. Our analysis shows that the RDE model is observationally non-viable. While late-time probes suggest a good fit by favouring a low matter density ($\Omega _{m0} \approx 0.19$–0.22), the inclusion of CMB priors forces $\Omega _{m0}$ to standard values, causing a catastrophic internal tension ($\,\gt\,5\sigma$) and decisive statistical rejection. For the HDE model, we identify a clear tension among data sets. Supernova-dominated samples tend to favour a quintessence-like state ($c \,\gt\, 1.2$), while the combination of DESI BAO and CMB data strongly shifts constraints towards a phantom behaviour ($c \approx 0.69$). We confirm that neither model resolves the Hubble tension. A formal model selection analysis shows that while late-time data yield a spurious preference for dynamical models ($\Delta \text{AIC} \,\lt\, 0$), this vanishes completely when early-Universe constraints are applied. We conclude, in agreement with other analyses, that the apparent hints for new physics are likely statistical artefacts of underlying data set tensions, such as the reported $\Omega _m$ tension. The key result is the CMB-driven indication of a phantom regime for HDE, which points towards interacting holographic dark energy as a promising next step to avoid a Big Rip singularity.