ИСТИНА

The ongoing discrepancy between local and early-universe measurements of the Hubble constant, known as the "Hubble tension," represents one of the most significant challenges in modern cosmology. Measurements based on the local distance ladder—using Cepheid-calibrated Type Ia supernovae by SH0ES team consistently yield a higher value of the Hubble constant (H₀ ≈ 73–75 km/s/Mpc) than those inferred from observations of the Cosmic Microwave Background (CMB) by Planck under the ΛCDM model (H₀ ≈ 67–68 km/s/Mpc). This tension, now exceeding 5σ, has prompted widespread theoretical and observational scrutiny. On the other hand the studies by CCHP team using the same SNIa standarf candles calibrated using other local distance indicators such as TRGB and JAGB (J-band Asymptotic-Giant-Branch) have converged to H₀ ≈ 70 km/s/Mpc invalidating the tension and heralding the \"Local Hubble Tension\" instead, meaning we have yet to understand the reasons behind this local 70 vs 73 km/s/Mpc discrepancy This review synthesizes recent state-of-the-art distance measurements using both TRGB, JAGB and Cepheids trying to explain this Local Hubble tension. We assess advancements in local measurements with new JWST data, including improvements in Cepheid photometry, parallax calibration with Gaia, alternative distance indicators such as Tip of the Red Giant Branch (TRGB) and their implications for systematic uncertainties. We also provide the first estimates of the Cepheid selection bias and the methodological uncertainties of SNIa host distance moduli, giving a first Local H0 estimate done outside of CCHP/SH0ES groups. These recent developments in the field should paint a more detailed picture of current rate of the expansion of the Universe which has paramount Cosmological importance.