Long Gamma-ray Bursts Calibrated Padé Method And Constraints On Cosmological Models

In1998, two teams studying distant Type Ia supernovae showed independent evidencethat the expansion of the Universe is accelerating, which means the beginning of a new era incosmology. There are two ideas to explain this phenomenon: Dark energy cosmology andthe modified gravity. There are several other well-established cosmological observations re-inforced an accelerating Universe, such as Baryon Acoustic Oscillations (BAO) and CosmicMicrowave Background (CMB). In recent years, Gamma-ray bursts (GRBs) have been pro-posed as a complementary probe to type Ia supernovae (SNIa). However, as is well known,there is a circularity problem in the use of GRBs to study cosmology. In this work, based onthe Padé approximant, we propose a new cosmology-independent method to calibrate GRB-s. As is well known, any function can be expanded by Padé approximation, and can avoidthe divergence problem in the higher-order terms like Taylor expansion. In this paper, weconsider a sample consisting138long GRBs and obtain79calibrated long GRBs at highredshift z>1.4(named Mayflower sample) which can be used to constrain cosmologicalmodels without the circularity problem. Then, we consider the constraints on several cosmo-logical models with these79calibrated GRBs and other observational data. We present thatGRBs are competent to be a complementary probe to the other well-established cosmologicalobservations.