The recent results from the first-year baryon acoustic oscillations (BAO) data released by the Dark Energy Spectroscopic Instrument (DESI), combined with cosmic microwave background (CMB) and Type Ia supernova (SN) data, have shown a detection of significant deviation from a cosmological constant for dark energy. In this work, we utilize the latest DESI BAO data in combination with the SN data from the full 5 yr observations of the Dark Energy Survey and the CMB data from the Planck satellite to explore potential interactions between dark energy and dark matter. We consider four typical forms of the interaction term Q. Our findings suggest that interacting dark energy (IDE) models with Q ∝ ρ _de support the presence of an interaction where dark energy decays into dark matter. Specifically, the deviation from ΛCDM for the IDE model with Q = β H ₀ ρ _de reaches the 3σ level. These models yield a lower value of Akaike information criterion than the ΛCDM model, indicating a preference for these IDE models based on the current observational data. For IDE models with Q ∝ ρ _c, the existence of interaction depends on the form of the proportionality coefficient Γ. The IDE model with Q = β H ρ _c yields β = 0.0003 ± 0.0011, which essentially does not support the presence of the interaction. In general, whether the observational data support the existence of interaction is closely related to the model. Our analysis helps to elucidate which type of IDE model can better explain the current observational data.

New insights from the Dark Energy Spectroscopic Instrument (DESI) 2024 baryon acoustic oscillations (BAO) data, in conjunction with cosmic microwave background (CMB) and Type Ia supernova (SN) data, suggest that dark energy may not be a cosmological constant. In this work, we investigate the cosmological implications of holographic dark energy (HDE) and interacting holographic dark energy (IHDE) models, utilizing CMB, DESI BAO, and SN data. By considering the combined DESI BAO and SN data, we determine that in the IHDE model, the parameter $$c > 1$$ c > 1 and the dark-energy equation of state w does not cross $$-1$$ - 1 at the $$1\sigma $$ 1 σ confidence level, whereas in the HDE model, it marginally falls below this threshold. Upon incorporating CMB data, we observe that in the HDE model, the parameter $$c < 1$$ c < 1 and w crosses $$-1$$ - 1 at a level beyond $$10\sigma $$ 10 σ . Conversely, for the IHDE model, the likelihood of w crossing $$-1$$ - 1 is considerably diminished, implying that the introduction of interaction within the HDE model could potentially resolve or mitigate the cosmic big rip conundrum. Furthermore, our analysis reveals that the HDE and IHDE models are statistically as viable as the $$\Lambda $$ Λ CDM model when assessing Bayesian evidence with DESI BAO data combined with SN data. However, when CMB data are added, the HDE and IHDE models are significantly less favored than the $$\Lambda $$ Λ CDM model. Our findings advocate for further exploration of the HDE and IHDE models using forthcoming, more precise late-universe observations.

Gravitational wave (GW) standard siren observations provide a rather useful tool to explore the evolution of the Universe. In this work, we wish to investigate whether dark sirens with neutron star (NS) deformation from third-generation GW detectors could help probe the interaction between dark energy and dark matter. We simulate the GW dark sirens of four detection strategies based on 3 yr observation and consider four phenomenological interacting dark energy (IDE) models to perform cosmological analysis. We find that GW dark sirens could provide tight constraints on Ω_m and H ₀ in the four IDE models but do not perform well in constraining the dimensionless coupling parameter β in models of the interaction proportional to the energy density of cold dark matter. Nevertheless, the parameter degeneracy orientations of cosmic microwave background (CMB) and GW are almost orthogonal, and thus, the combination of them could effectively break cosmological parameter degeneracies, with the constraint errors of β being 0.00068–0.018. In addition, we choose three typical equations of state (EoSs) of an NS, i.e., SLy, MPA1, and MS1, to investigate the effect of an NS’s EoS on cosmological analysis. The stiffer EoS could give tighter constraints than the softer EoS. Nonetheless, the combination of CMB and GW dark sirens (using different EoSs of an NS) shows basically the same constraint results of cosmological parameters. We conclude that the dark sirens from 3G GW detectors would play a crucial role in helping probe the interaction between dark energy and dark matter, and the CMB+GW results are basically not affected by the EoS of an NS.