Gamma-ray bursts (GRBs) are the most luminous explosions in and can be detectable out to the edge of the universe. They have long been thought to be able to extend the Hubble diagram to very high redshifts. Several correlations between temporal or spectral properties and GRB luminosities have been proposed to make GRBs cosmological tools. However, those correlations cannot be properly standardized. In this paper, we select a long-GRB sample with X-ray plateau phases produced by electromagnetic dipole emissions from central newborn magnetars. A tight correlation is found between the plateau luminosity and the end time of the plateau in the X-ray afterglows out to the redshift z = 5.91. We standardize these long-GRB X-ray light curves to a universal behavior through this correlation, with a luminosity dispersion of 0.5 dex. The derived distance–redshift relation of GRBs is in agreement with the standard ΛCDM model both at low and high redshifts. The evidence for an accelerating universe from this GRB sample is 3σ, which is the highest statistical significance from GRBs to date.

Gamma-ray bursts (GRBs), as a possible probe to extend the Hubble diagram to high redshifts, have attracted much attention recently. In this paper, we select two samples of GRBs that have a plateau phase in X-ray afterglow. One is short GRBs with plateau phases dominated by magnetic dipole (MD) radiations. The other is long GRBs with gravitational-wave (GW) dominated plateau phases. These GRBs can be well standardized using the correlation between the plateau luminosity L0 and the end time of plateau tb. The so-called circularity problem is mitigated by using the observational Hubble parameter data and Gaussian process method. The calibrated L0 – tb correlations are also used to constrain ΛCDM and w(z) = w0 models. Combining the MD-LGRBs sample from Wang et al. (2021) and the MD-SGRBs sample, we find $\Omega _{m} = 0.33_{-0.09}^{+0.06}$ and ΩΛ = $1.06_{-0.34}^{+0.15}$ excluding systematic uncertainties in the nonflat ΛCDM model. Adding type Ia supernovae from Pantheon sample, the best-fitting results are w0 = $-1.11_{-0.15}^{+0.11}$ and Ωm = $0.34_{-0.04}^{+0.05}$ in the w = w0 model. These results are in agreement with the ΛCDM model. Our result supports that selection of GRBs from the same physical mechanism is crucial for cosmological purposes.

The ΛCDM model provides a good fit to most astronomical observations but harbors large areas of phenomenology and ignorance. With the improvements in the precision and number of observations, discrepancies between key cosmological parameters of this model have emerged. Among them, the most notable tension is the 4σ to 6σ deviation between the Hubble constant (H0) estimations measured by the local distance ladder and the cosmic microwave background (CMB) measurement. In this review, we revisit the H0 tension based on the latest research and sort out evidence from solutions to this tension that might imply new physics beyond the ΛCDM model. The evidence leans more towards modifying the late-time universe.

In this paper, we investigate the cosmic anisotropy from the SN-Q sample, consisting of the Pantheon sample and quasars, by employing the hemisphere comparison (HC) method and the dipole fitting (DF) method. Compared to the Pantheon sample, the new sample has a larger redshift range, a more homogeneous distribution, and a larger sample size. For the HC method, we find that the maximum anisotropy level is ALmax = 0.142 ± 0.026 in the direction (l, b) = (316.08°−129.48+27.41, 4.53°−64.06+26.29). The magnitude of anisotropy is A = (−8.46−5.51+4.34) × 10−4 and the corresponding preferred direction points toward (l, b) = (29.31°−30.54+30.59, 71.40°−9.72+9.79) for the quasar sample from the DF method. The combined SN and quasar sample is consistent with the isotropy hypothesis. The distribution of the dataset might impact the preferred direction from the dipole results. The result is weakly dependent on the redshift from the redshift tomography analysis. There is no evidence of cosmic anisotropy in the SN-Q sample. Though some results obtained from the quasar sample are not consistent with the standard cosmological model, we still do not find any distinct evidence of cosmic anisotropy in the SN-Q sample.

Gamma-ray bursts (GRBs) are the most explosive phenomena and can be used to study the expansion of Universe. In this paper, we compile a long GRB sample for the Eiso-Ep correlation from Swift and Fermi observations. The sample contains 221 long GRBs with redshifts from 0.03 to 8.20. From the analysis of data in different redshift intervals, we find no statistically significant evidence for the redshift evolution of this correlation. Then we calibrate the correlation in six sub-samples and use the calibrated one to constrain cosmological parameters. Employing a piece-wise approach, we study the redshift evolution of dark energy equation of state (EOS), and find that the EOS tends to be oscillating at low redshift, but consistent with −1 at high redshift. It hints a dynamical dark energy at 2σ confidence level at low redshift.