Cosmological models and gamma-ray bursts calibrated by using Padé method

Gamma-ray bursts (GRBs) are among the most powerful sources in the universe. In the recent years, GRBs have been proposed as a complementary probe to type Ia supernovae. However, as is well known, there is a circularity problem in the use of GRBs to study cosmology. In this work, based on the Padé approximant, we propose a new cosmology-independent method to calibrate GRBs. We consider a sample consisting of 138 long Swift GRBs and obtain 79 calibrated long GRBs at high-redshift $$z>1.4$$z>1.4 (named Mayflower sample) which can be used to constrain cosmological models without the circularity problem. Then, we consider the constraints on several cosmological models with these 79 calibrated GRBs and other observational data. We show that GRBs are competent to be a complementary probe to the other well-established cosmological observations.