Tensions between measurements of the Hubble constant from the early and late Universe

Abstract Hubble constant (H0) is one of the most important parameters in cosmology. There are mainly two ways to determine the value of Hubble constant, which measure the properties of early universe and the late universe, namely cosmic microwave background radiation (CMB) and Type Ia supernovae (SNe Ia). Those who had used these two methods to measure the Hubble constant won the Nobel Prize in Physics respectively, in 1978 and 2011. This article introduces the principle of accelerating universe and the methods to measure the Hubble constant. We analyze each method and discuss the uncertainties of them. In addition, we investigate possible reasons for Hubble constant discrepancy based on previous studies. We discuss about the conclusion and prospects of Hubble constant measurement.