Weak gravitational lensing effects on cosmological parameters and dark energy from gamma-ray bursts

Context. Gamma-ray bursts (GRBs) are attractive objects for constraining the nature of dark energy in a way complementary to other cosmological probes, especially at high redshifts. However, the apparent magnitude of distant GRBs can be distorted by the gravitational lensing from the density fluctuations along the line of sight . Aims. We investigate the gravitational lensing effect on the cosmological parameters and dark energy equation of state from GRBs. Methods. We first calibrated the GRB luminosity relations without ass uming any cosmological models. The luminosity distances of low-redshift GRBs were calibrated with the cosmography method using a latest type Ia supernova (SNe Ia) sample. The luminosity distances of high-redshift GRBs were derived by assuming that the luminosity relations do not evolve with redshift. Then we investigated the non-Gaussian nature of the magnification probability distribution funct ions and the magnification bias of the gravitational lensing . Results. We find that the gravitational lensing has non-negligible e ffects on the determination of cosmological parameters and dark energy. The gravitational lensing shifts the best-fit constraints o n cosmological parameters and dark energy. Because high-redshift GRBs are more

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