The Hubble constant is crucial to the knowledge of the universe’s nature and expansion, remaining as an active area for research in the recent decades. Cosmological microwave background observations revealed a lower value of 67–69 km-1s-1Mpc for the Hubble constant, but local data showed a higher value of 73–75 km-1s-1Mpc. This study focuses on the Hubble constant and its measurement, systematic uncertainties, observed tension, and potential modifications to the standard cosmological model. To be specific, this paper aims to address the tension between different measurement methods, which are Cepheid variables and supernovae, Baryon Acoustic Oscillations, and Gravitational waves, and understand systematic uncertainties. Results show discrepancies in Hubble constant values, indicating potential modifications to the standard cosmological model. Prospects include exploring alternative cosmological components and enhanced detection and computation methods. The study's implications lie in advancing the understanding of the expanding universe and guiding future research directions regarding to Hubble tension measurement.
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