The evolution of methods for determining the Hubble constant

With the failure of the idea of the static universe, and the discovery of the expansion of the universe by Hubble, the Hubble constant became of great importance in cosmology. Given the key role of this constant in determining many important parameters, including the age, acceleration, and density of the universe, the precise determination of its numerical value is becoming increasingly important. The numerical determination of the Hubble constant (H0) has had a history of ups and downs, and in the last century, it has been the subject of much scientific research, as many prominent people have addressed it with advanced methods and in new papers. Most methods of determining the numerical value of the Hubble constant are done by distance measurement. The important distance methods include: the methods of Cepheid variables, Type Ia supernovae, the Tully-Fisher relation, surface brightness fluctuation, the tip of the red giant branch, the Sunyaev–Zeldovich effect, Mega Maser, and Baryon acoustic oscillations. To derive the Hubble constant value using distance methods, galaxies are used whose special velocities (the rate of local and catastrophic motion) are observable due to their great distance, compared to the speed of their neighbors (the rate of expansion of the universe). In this case, the distance and velocity of the galaxy can be calculated using Hubble's law to determine the value of the Hubble constant. The important non-distance methods are time-delayed gravitational lensing, gravitational waves, and methods based on learning machines. In addition to these methods, there is also a method based on the cosmic microwave background radiation, in which the Hubble constant is determined universally, regardless of distance. What is certain is that the results of these studies show the evolutionary course of determination of the Hubble constant over the past decades, as well as the obvious changes in its numerical value.Here, while briefly describing the different methods of determining the Hubble constant, the numerical results presented over the past decades are finally summarized in a table in a comparative form.The summarized data in the table are classified based on the method of obtaining the Hubble constant, the maximum distance observed, the most recent numerical value obtained, and their accuracy. Although the use of the new data has resulted in numerical values in the range of 67 to 75 (in Km s-1/Mpc) for the Hubble constant, the same amount of dispersion is also significant for a "constant". The Hubble constant value derived from the latest data in the Type Ia supernova method is about 67 Km s-1/Mpc, whereas with the Tully-Fisher relation, a value of about 75 Km s-1/Mpc has been reported for this constant. Perhaps this dispersion can be attributed to whether the objects under consideration for the determination of the Hubble constant are local or cosmic; but, we still can't say for sure. The different reported values for the Hubble constant based on different methods and models which is now known as a “tension” (the Hubble tension) makes cosmologists propose alternative models and new physics for solving the problem.