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We present a detailed report of the connection between long-duration gamma-ray bursts (GRBs) and their accompanying supernovae (SNe). The discussion presented here places emphasis on how observations, and the modelling of observations, have constrained what we know about GRB-SNe. We discuss their photometric and spectroscopic properties, their role as cosmological probes, including their measured luminosity–decline relationships, and how they can be used to measure the Hubble constant. We present a statistical summary of their bolometric properties and use this to determine the properties of the “average” GRB-SN. We discuss their geometry and consider the various physical processes that are thought to power the luminosity of GRB-SNe and whether differences exist between GRB-SNe and the SNe associated with ultra-long-duration GRBs. We discuss how observations of their environments further constrain the physical properties of their progenitor stars and give a brief overview of the current theoretical paradigms of their central engines. We then present an overview of the radioactively powered transients that have been photometrically associated with short-duration GRBs, and we conclude by discussing what additional research is needed to further our understanding of GRB-SNe, in particular the role of binary-formation channels and the connection of GRB-SNe with superluminous SNe. [ABSTRACT FROM AUTHOR]

We briefly introduce the disadvantages for Type Ia supernovae (SNe Ia) as standard candles to measure the universe, and suggest Gamma-ray bursts (GRBs) can serve as a powerful tool for probing the properties of high redshift universe. We use GRBs as distance indicators in constructing the Hubble diagram at redshifts beyond the current reach of SNe Ia observations. Since the progenitors of long GRBs (LGRBs) are confirmed to be massive stars, they are deemed as an effective approach to study the cosmic star formation rate (SFR). A detailed representation of how to measure high- SFR using GRBs is presented. Moreover, first stars can form only in structures that are suitably dense, which can be parametrized by defining the minimum dark matter halo mass . must play a crucial role in star formation. The association of LGRBs with the collapses of massive stars also indicates that the GRB data can be applied to constrain the minimum halo mass and to investigate star formation in dark matter halos. [ABSTRACT FROM AUTHOR]