The Hubble constant is an important parameter in astronomy,and recent observational evidences reveal a 5σ discrepancy in its measurements,known as the"Hubble constant crisis".In this review,we summarize several commonly used distance ladder methods for measuring the Hubble constant,including geometric distances,classical Cepheid distances,tip of red giant branch star(TRGB)distances,and type Ⅰa supernova distances.We introduce and discuss their strengths,weaknesses,potential problems,and expectations for future optimization.The most accurate geometric distances include the Gaia parallax,the eclipsing binary distance measurement of the Large Magellanic Cloud,and the water maser distance measurement of NGC 4258,with the Gaia parallax showing the most promising for further optimization.By combining these three geometric distances,the distance errors based on Cepheids and TRGBs are 0.7％and 1.1％,respectively,and they are used to calibrate type Ⅰa supernovae in the nearby galaxies.Cepheids were used to calibrate the absolute magnitude of 42 nearby type Ⅰa supernovae with an error of 0.9％,while TRGBs were used to calibrate the absolute magnitude of 18 nearby type Ⅰa supernovae with an error of 1.3％.The Hubble constant can be measured using the apparent magnitudes and redshifts of more distant type Ⅰa supernovae.The Hubble constant based on Cepheids+typeⅠa supernovae is 73kms-1Mpc-1 with an error of 1.4％,while that based on TRGB+type Ⅰa supernovae are 70 km s-1 Mpc-1 with an error of 1.7％.Additionally,we introduce several potential methods for distance measurement that can help verify commonly used distance ladders or measure the Hubble constant independently.In the next five years,with the optimization of the Gaia parallax,the accumulation of data from the James Webb Telescope,and the launch of the Chinese Space Station Telescope,astronomers are expected to resovle the current"Hubble Constant Crisis".
Hubble constantclassical Cepheidstip of red giant branch starstype Ⅰa supernovaegeometric distances
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