Statistical and time analyses of gamma-ray bursts

If Gamma-Ray Bursts (GRBs) are cosmological in origin, different signatures are expected to be found in the available BATSE catalog and time series. Cross-correlation with extragalactic objects and gravitational lensing by intervening objects are some examples of these particular features.; A new statistical method to perform 2D angular cross-correlations between GRB positions and different catalogs of extragalactic objects has been implemented. For the best located 74 3B GRBs, a 2.5-{dollar}sigma{dollar} level association with rich, nearby Abell clusters is found. If all the cluster are taken into account, a 3.5-{dollar}sigma{dollar} association is found for the best located 27 2B bursts. Another 2.5-{dollar}sigma{dollar} excess is found between soft GRBs and the whole Abell catalog. On the other hand, excesses of the order of {dollar}{lcub}sim{rcub}3.5{lcub}-{rcub}4{dollar}-{dollar}sigma{dollar} are found between the best located 10 to 380 bursts and the nearest, intrinsically brightest radio quiet quasars. However, the correlations appears to be due to statistical fluctuation and the excesses are only suggestive of a physical association.; A fully automated search among 1,235 4B bursts has been carried out to search for statistical similarities in the GRB time series. No two GRBs are found to be identical to within the statistical limits of the data, regardless of their position on the sky. GRBs that appear statistically similar in one energy channel are either dissimilar in other energy channels or too dim for a significant statistical comparison. One consequence of the search for statistical similarities is that no gravitational lensing of GRBs by foreground galaxies have been found. Given this null result, and assuming no GRB rate density or luminosity evolution, and that QSO images are distorted by the same galaxy field, a conservative upper limit to the redshift is derived, {dollar}zsb{lcub}max{rcub}sim 4.22,{dollar} for an Einstein-de Sitter universe at a 2-{dollar}sigma{dollar} confidence level. The gravitational lensing rates have been computed for different Friedman-Robertson-Walker universes and GRB number density models. For a monoluminous population of GRBs with uniform comoving rate density, an {dollar}(Omegasb{lcub}M{rcub},Omegasb{lcub}Lambda{rcub})=(0,1){dollar} universe has been rejected, whereas, if the GRB number density is given either by the star formation rate or by the delayed star formation rate, (0,0.9) and (0,1) universes are ruled out at {dollar}{lcub}>{rcub}95.4%{dollar} confidence level.; The cosmological abundance of dark compact objects (COs) in the universe has been studied by means of gravitational lensing of GRBs. An {dollar}Omega = 0.15{dollar} nearly filled with COs with {dollar}Msb{lcub}CO{rcub}sim 10sp{lcub}6.5{rcub}Msbodot{dollar} has been ruled out at {dollar}{lcub}sim{rcub}90.0{lcub}-{rcub}92.0%{dollar} confidence level, given that no lensing by such masses has been found. A comparison of peak counts for 60 bright bursts simultaneously detected by BATSE and Ulysses was performed, and no evident discrepancies in the amplitudes have been detected. Although nearly no lenses are expected in the sample, an Einstein-de Sitter universe with {dollar}Msb{lcub}co{rcub}sim 10sp{lcub}-12.5{rcub}{lcub}-{rcub}10sp{lcub}-9.0{rcub}Msbodot{dollar} and {dollar}Omegasb{lcub}co{rcub}ge 0.9{dollar} has been weakly ruled out. Since BATSE has not detected spectral lines, which might be created by gravitational lensing events by COs with masses between {dollar}10sp{lcub}-16{rcub}Msbodot{dollar} and 10{dollar}sp{lcub}-13{rcub}Msbodot{dollar}, very loose constraints have been imposed on the CO density, rejecting {dollar}Omegasb{lcub}co{rcub}ge 0.2{dollar} if {dollar}zsb{lcub}max{rcub}sim 1{dollar}, or {dollar}Omegasb{lcub}co{rcub}ge 0.1{dollar} if {dollar}zsb{lcub}max{rcub}sim 2.{dollar}...