The determination of the luminosity function (LF) of gamma-ray bursts (GRBs) is an important role for the cosmological applications of the GRBs, which, however, is seriously hindered by some selection effects due to redshift measurements. In order to avoid these selection effects, we suggest calculating pseudo-redshifts for Swift GRBs according to the empirical L-E p relationship. Here, such a L-E p relationship is determined by reconciling the distributions of pseudo-and real redshifts of redshift-known GRBs. The values of E p taken from Butler's GRB catalog are estimated with Bayesian statistics rather than observed. Using the GRB sample with pseudo-redshifts of a relatively large number, we fit the redshift-resolved luminosity distributions of the GRBs with a broken-power-law LF. The fitting results suggest that the LF could evolve with redshift by a redshift-dependent break luminosity, e.g., L b = 1.2 × 10 51 (1 + z) 2 erg s −1 . The low-and high-luminosity indices are constrained to 0.8 and 2.0, respectively. It is found that the proportional coefficient between the GRB event rate and the star formation rate should correspondingly decrease with increasing redshifts.

In models with dark matter made of particles with keV masses, such as a sterile neutrino, small-scale density perturbations are suppressed, delaying the period at which the lowest mass galaxies are formed and therefore shifting the reionization processes to later epochs. In this study, focusing on Warm Dark Matter (WDM) with masses close to its present lower bound, i.e. around the 3 keV region, we derive constraints from galaxy luminosy functions, the ionization history and the Gunn-Peterson effect. We show that even if star formation efficiency in the simulations is adjusted to match the observed UV galaxy luminosity functions in both CDM and WDM models, the full distribution of Gunn-Peterson optical depth retains the strong signature of delayed reionization in the WDM model. However, until the star formation and stellar feedback model used in modern galaxy formation simulations is constrained better, any conclusions on the nature of dark matter derived from reionization observables remain model-dependent.

The joint observation of GW170817 and GRB 170817A indicated that short gamma-ray bursts (SGRBs) can originate from binary neutron star mergers. Moreover, some SGRBs could be detected off axis, while the SGRB jets are highly structured. Then, by assuming a universal angular distribution of the jet emission for all SGRBs, we reproduce the flux and redshift distributions of the cosmological SGRBs detected by Swift and Fermi. For self-consistency, this angular distribution is simultaneously constrained by the luminosity and event rate of GRB 170817A. As a result, it is found that the universal jet structure of SGRBs could approximately have a two-Gaussian profile. Meanwhile, the intrinsic luminosity function (LF) of the on-axis emission of the jets can be simply described by a single power law with a low-luminosity exponential cutoff. The usually discovered broken-power-law apparent LF for relatively high luminosities can naturally result from the coupling of the intrinsic LF with the angular distribution of the jet emission, as the viewing angles to the SGRBs are arbitrarily distributed.

We study the redshift evolution of the luminosity function (LF) and redshift selection effect of long gamma-ray bursts (LGRBs). The method is to fit the observed peak flux and redshift distributions, simultaneously. To account for the complex triggering algorithm of Swift, we use a flux triggering efficiency function. We find evidence supporting an evolving LF, where the break luminosity scales as L b ∝ (1 + z) τ , with τ = 3.5 +0.4 −0.2 and τ = 0.8 +0.1 −0.08 for two kind of LGRB rate models. The corresponding local GRB rates arė R(0) = 0.86 +0.11 −0.08 yr −1 Gpc −3 andṘ(0) = 0.54 +0.25 −0.07 yr −1 Gpc −3 , respectively. Furthermore, by comparing the redshift distribution between the observed one and our mocked one, we find that the redshift detection efficiency of the flux triggered GRBs decreases with redshift. Especially, a great number of GRBs miss their redshifts in the redshift range of 1 < z < 2.5, where "redshift desert" effect may be dominated. More interestingly, our results show that the "redshift desert" effect is mainly introduced by the dimmer GRBs, e.g., P < 10 −7 erg/ s/ cm 2 , but has no effect on the brighter GRBs.

Mergers of compact binaries, such as binary neutron stars (BNSs), neutron star-black hole binaries (NSBHs), and binary black holes (BBHs), are expected to be the best candidates for the sources of gravitational waves (GWs) and the leading theoretical models for short gamma-ray bursts (SGRBs). Based on the observations of SGRBs, we could derive the merger rates of these compact binaries, and study the stochastic GW backgrounds (SGWBs) or the co-detection rates of GWs associate with SGRBs (GW-SGRBs). But before that, the most important thing is to derive the GW spectrum from a single GW source. Usually, GW spectrum from a circular orbit binary is assumed. However, observations of the large spatial offsets of SGRBs from their host galaxies imply that SGRB progenitors may be formed by the dynamical processes, and will merge with residual eccentricities (e r ). The orbital eccentricity has important effect on GW spectra, and therefore on the SGWB and GW-SGRB co-detection rate. Our results show that the power spectra of the SGWBs from eccentric compact binaries are greatly suppressed at low frequencies (e.g., f 1 Hz). Especially, SGWBs from binaries with high residual eccentricities (e.g., e r 0.1 for BNSs) will hard to be detected (above the detection frequency of ∼ 100 Hz). For the co-detection rates of GW-SGRB events, they could be ∼ 1.4 times higher than the circular case within some particular ranges of e r (e.g., 0.01 e r 0.1 for BBH), but greatly reduced for high residual eccentricities (e.g., e r > 0.1 for BNSs). In general, the BBH progenitors produce 200 and 10 times higher GW-SGRB events than the BNS and NSBH progenitors, respectively. Therefore, binaries with low residual eccentricities (e.g., 0.001 e r 0.1) and high total masses will easier to be detected by aLIGO. However, only a small fraction of BBHs could be SGRB progenitors (if they can produce SGRBs), because the predicted GW-SGRB event rate (60∼100 per year) is too high compared with the recent observations, unless they merge with high residual eccentricities (e.g., e r > 0.7).