Fast radio bursts (FRBs) are a mysterious astrophysical phenomenon of bright pulses emitted at radio frequencies, and they are expected to be frequently detected in the future. The dispersion measures of FRBs are related to cosmological parameters, thus FRBs have the potential to be developed into a new cosmological probe if their data can be largely accumulated in the future. In this work, we study the capability of future FRB data to improve cosmological parameter estimation in two dynamical dark energy models. We find that the simulated FRB data can break the parameter degeneracies inherent in the current cosmic microwave background (CMB) data. Therefore, the combination of CMB and FRB data can significantly improve the constraints on the Hubble constant and dark energy parameters, compared to those using CMB or FRB alone. If 10,000 FRB events with known redshifts are detected in the future, they would perform better than the baryon acoustic oscillation (BAO) data in breaking the parameter degeneracies inherent in the CMB data. We also find that the combination of FRB and gravitational-wave (GW) standard siren data provides an independent low-redshift probe to verify the results from the CMB and BAO data. For the data combination of CMB, GW, and FRB, it is found that the main contribution to the constraints comes from the CMB and GW data, but the inclusion of the FRB data still can evidently improve the constraint on the baryon density.

We forecast constraints on cosmological parameters in the interacting dark energy models using the mock data generated for neutral hydrogen intensity mapping (IM) experiments. In this work, we only consider the interacting dark energy models with energy transfer rate Q = β H ρ _c and take BINGO, FAST, SKA1-MID, and Tianlai as typical examples of the 21 cm IM experiments. We find that the Tianlai cylinder array will play an important role in constraining the interacting dark energy model. Assuming perfect foreground removal and calibration and using the Tianlai-alone data, we obtain σ(H ₀) = 0.19 km s⁻¹ Mpc⁻¹, σ(Ω _m ) = 0.0033, and σ(σ ₈) = 0.0033 in the IΛCDM model, which are much better than the results of Planck+optical BAO (i.e., optical galaxy surveys). However, the Tianlai-alone data cannot provide a very tight constraint on the coupling parameter β compared with Planck+optical BAO, while the Planck+Tianlai data can give a rather tight constraint of σ(β) = 0.00023 due to the parameter degeneracies being well broken by the data combination. In the IwCDM model, we obtain σ(β) = 0.00079 and σ(w) = 0.013 from Planck+Tianlai. In addition, we also make a detailed comparison among BINGO, FAST, SKA1-MID, and Tianlai in constraining the interacting dark energy models. We show that future 21 cm IM experiments will provide a useful tool for exploring the nature of dark energy and play a significant role in measuring the coupling between dark energy and dark matter.

In the context of the discrepancies between the early and late universe, we emphasize the importance of independent measurements of the cosmic curvature in the late universe. We present an investigation of the model-independent measurement of the cosmic curvature parameter ${\mathrm{\Omega }}_k$ in the late universe with the latest Hubble parameter $H(z)$ measurements and type Ia supernovae (SNe Ia) data. For that, we use two reconstruction methods, the Gaussian process (GP) and artificial neural network (ANN) methods, to achieve the distance construction from $H(z)$ data. Our analysis reveals that the GP method provides the most precise constraint on ${\mathrm{\Omega }}_k$, with a constraint precision of $\xi ({\mathrm{\Omega }}_k)=0.13$, surpassing recent estimations using similar methods. The GP method consistently indicates a preference for a flat universe at the $2\sigma$ confidence level. Moreover, we find that the choice of reconstruction method influences the estimation of ${\mathrm{\Omega }}_k$. The ANN reconstruction method exhibits higher sensitivity to the addition of BAO $H(z)$ data, resulting in comparable constraint precision to the GP method. A discrepancy exists between the best-fit values obtained by these two reconstruction methods, indicating their dependence on the reconstruction approach. However, we anticipate that with the improvement of sample size and precision of observational $H(z)$ data, the estimation of ${\mathrm{\Omega }}_k$ using this approach will become more robust and reliable.

In recent years, a crisis in the standard cosmology has been caused by inconsistencies in the measurements of some key cosmological parameters, the Hubble constant H ₀ and cosmic curvature parameter Ω _K , for example. It is necessary to remeasure them with the cosmological model-independent methods. In this paper, based on the distance sum rule, we present such a way to constrain H ₀ and Ω _K simultaneously in the late universe from strong gravitational lensing time-delay (SGLTD) data and gravitational wave (GW) standard siren data simulated from the future observation of the Einstein Telescope (ET). Based on the data for six currently observed SGLTDs, we find that the constraint precision of H ₀ from the combined 100 GW events can be comparable with the measurement from the SH0ES collaboration. As the number of GW events increases to 700, the constraint precision of H ₀ will exceed that of the Planck 2018 results. Considering 1000 GW events as the conservative estimation of ET in the 10 yr observation, we obtain H ₀ = 73.69 ± 0.36 km s⁻¹ Mpc⁻¹ with a 0.5% uncertainty and Ω K = 0.076 − 0.087 + 0.068 . In addition, we simulate 55 strong gravitational lensing (SGL) systems with a 6.6% uncertainty for the measurement of time-delay distance. By combining with 1000 GWs, we infer that H ₀ = 73.65 ± 0.35 km s⁻¹ Mpc⁻¹ and Ω _K = 0.008 ± 0.048. Our results suggest that this approach can play an important role in exploring cosmological tensions.

With the measurement of the electromagnetic (EM) counterpart, a gravitational wave (GW) event could be treated as a standard siren. As a novel cosmological probe, GW standard sirens will bring significant implications for cosmology. In this paper, by considering the coincident detections of GW and associated γ ray burst (GRB), we find that only about 400 GW bright standard sirens from binary neutron star mergers could be detected in a 10-year observation of the Einstein Telescope and the THESEUS satellite mission. Based on this mock sample, we investigate the implications of GW standard sirens on the interaction between dark energy and dark matter. In our analysis, four viable interacting dark energy (IDE) models, with interaction forms Q = 3βHρ _de and Q = Q = 3βHρ _c, are considered. Compared with the traditional EM observational data such as CMB, BAO, and SN Ia, the combination of both GW and EM observations could effectively break the degeneracies between different cosmological parameters and provide more stringent cosmological fits. We find that the GW data could play a more important role for determining the interaction in the models with Q = 3βHρ _c, compared with the models with Q = 3βHρ _de. We also show that constraining IDE models with mock GW data based on different fiducial H ₀ values yield different results, indicating that accurate determination of H ₀ is significant for exploring the interaction between dark energy and dark matter.