The statistical properties of the soft gamma repeater SGR J1550-5418 are investigated carefully. We find that the cumulative distributions of fluence, peak flux and duration can be well fitted by a bent power law, while the cumulative distribution of waiting time follows a simple power law. In particular, the probability density functions of fluctuations of fluence, peak flux, and duration have a sharp peak and fat tails, which can be well fitted by a q-Gaussian function. The q values keep approximately steady for different scale intervals, indicating a scale-invariant structure of soft gamma repeaters. Those results support that the origin of soft gamma repeaters is crustquakes of neutron stars with extremely strong magnetic fields.

In some quantum gravity theories, a foamy structure of space-time may lead to Lorentz invariance violation (LIV). As the most energetic explosions in the Universe, gamma-ray bursts (GRBs) provide an effect way to probe quantum gravity effects. In this paper, we use the continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale M QG . Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to low energy ones. Based on the fact that the LIV-induced time delay cannot be longer than the duration of a GRB, we present the most conservative estimate of the quantum gravity energy scales from 20 short GRBs. The strictest constraint, M QG > 5.05×10 14 GeV in the linearly corrected case, is from GRB 140622A. Our constraint on M QG , although not as tight as previous results, is the safest and most reliable so far.

Axion monodromy is a generic phenomenon in string compactifications. We investigate the production of gravitational-wave background from axion monodromy inflation during preheating. By performing lattice simulations using pseudospectral methods, we find that significant single-peak stochastic gravitational-wave backgrounds are generated during preheating for asymptotic linear |φ| and φ 2/3 potentials in axion monodromy inflation and cuspy potentials. This may allow us to explore string compactifications through gravitational waves.

The statistical properties of the repeating fast radio burst FRB 121102 are investigated. We find that the cumulative distributions of fluence, flux density, total energy and waiting time can be well fitted by the bent power law. In addition, the probability density functions of fluctuations of fluence, flux density and total energy well follow the Tsallis q-Gaussian distribution. The q values keep steady around q ∼ 2 for different scale intervals, indicating a scale-invariant structure of the bursts. The statistical properties of FRB 121102 are very similar to that of the soft gamma repeater SGR J1550-5418. The underlying physical implications need to be further investigated.

We constrain three cosmological models, i.e. the concordance cold dark matter plus a cosmological constant (ΛCDM) model, Power-law (PL) model, and R h = ct model using the available local probes, which includes the JLA compilation of type-Ia supernovae (SNe Ia), the direct measurement of Hubble constant (H(z)), and the baryon acoustic oscillations (BAO). For ΛCDM model, we consider two different cases, i.e. zero and non-zero spatial curvature. We find that by using the JLA alone, it is indistinguishable between ΛCDM and PL models, but the R h = ct model is strongly disfavored. If we combine JLA+H(z), the ΛCDM model is strongly favored against the other two models. The combination of all the three datasets also supports ΛCDM as the best model. We also use the low-redshift (z < 0.2) data to constrain the deceleration parameter using cosmography method, and find that only the ΛCDM model is consistent with cosmography. However, there is no strong evidence to distinguish between flat and non-flat ΛCDM models by using the local data alone.

We study the statistical properties of the soft gamma repeater SGR 1935+2154. We find that the cumulative distributions of duration, waiting time, fluence and flux can be well fitted by bent power law. In addition, the probability density functions of fluctuations of duration, waiting time, fluence and flux well follow the Tsallis q-Gaussian distribution. The q values keep steady for different temporal scale intervals, indicating a scale-invariant structure of the bursts. Those features are very similar to the property of the repeating fast radio burst FRB 121102, indicating the underlying association between the origins of soft gamma repeaters and repeating fast radio bursts.

Einstein's equivalence principle (EEP) can be tested by the time delay between photons with different energies passing through a gravitational field. As one of the most energetic explosions in the Universe, gamma-ray bursts (GRBs) provide an effective tool to test the accuracy of EEP. In this paper, we use the continuous spectra of 20 short GRBs detected by the Swift/BAT to test the validity of EEP. Taking the duration of GRBs as the upper limit of the time delay induced by EEP violation (assuming that the high energy photons arrive later than the low energy photons), the difference of the parameterized post-Newtonian parameter is constrained with high accuracy. The strictest constraint, |γ(150 keV) − γ(15 keV)| < 5.59 × 10 −10 from GRB 150101B, is about 1 ∼ 2 orders of magnitude tighter than previous constraints. Moreover, our result is more statistically significant than previous results because we use the continuous spectra instead of isolated photons.

We test the cosmological principle by fitting a dipolar modulation of distance modulus and searching for an evolution of this modulation with respect to cosmological redshift. Based on a redshift tomographic method, we divide the Joint Light-curve Analysis compilation of supernovae of type Ia into different redshift bins, and employ a Markov-Chain Monte-Carlo method to infer the anisotropic amplitude and direction in each redshift bin. However, we do not find any significant deviations from the cosmological principle, and the anisotropic amplitude is stringently constrained to be less than a few thousandths at 95% confidence level.