Hubble's Law

No, and this is the single most important subtlety of Hubble's Law. The redshift of a distant galaxy is not caused by the galaxy moving through space away from us — it is caused by space itself expanding between us and the galaxy, stretching the wavelength of the light as it travels. The "recession velocity" v is a convenient fiction: it is the velocity the galaxy would have if the redshift were caused by a Doppler shift in a static universe. In the expanding-universe picture, the galaxy is essentially at rest in its local frame — it is the space between us that is growing. This distinction matters enormously at high redshift, where v can exceed the speed of light without violating relativity, because no object is actually moving faster than c through space.

The Hubble tension is a persistent discrepancy between two independent measurements of H₀ that disagree at the 5σ level — a statistical mismatch so large that it is unlikely to be a chance fluctuation. The early-universe measurement uses the Planck satellite's map of the cosmic microwave background, fits it to the standard ΛCDM cosmological model, and infers H₀ = 67.4 ± 0.5 km/s/Mpc. The late-universe measurement uses the local distance ladder — Cepheid variable stars in the Milky Way calibrated geometrically, then Type Ia supernovae in distant galaxies calibrated by those Cepheids — and infers H₀ = 73.0 ± 1.0 km/s/Mpc. Either there is an unknown systematic in one of the measurement chains (a subtle error in the Cepheid calibration, or in the CMB modelling), or the standard cosmological model is incomplete and requires new physics. Resolving this tension is one of the highest priorities of contemporary cosmology.

For redshifts below about z = 0.1, corresponding to distances under about 400 Mpc, the linear relation v = H₀ · d is accurate to better than 5%. Beyond that, the effects of dark energy and matter on the expansion history become significant. At z = 0.5, the true distance is about 10% larger than the linear prediction; at z = 1, it is about 25% larger; at z = 6, it is more than a factor of 3 larger. To go beyond z = 0.1, cosmologists use the full Friedmann–Lemaître equation, which describes how the expansion rate H(z) evolves with redshift as a function of the matter density Ω_m, the dark energy density Ω_Λ, and the radiation density Ω_r.

Yes — in the sense of the metric expansion rate v = H₀ · d, not in the sense of proper motion through space. Galaxies beyond the Hubble radius R_H = c/H₀ ≈ 4,300 Mpc have v > c, but they are not "moving" through space at superluminal speeds. The expansion of the metric between us and them adds up to a rate that exceeds c, which is perfectly allowed in general relativity as long as no signal or object travels through space faster than c. The most distant galaxies we observe are currently receding from us at more than 3c in this metric-expansion sense, yet their light still reaches us because the Hubble radius is not a horizon — it has been growing, and light from beyond it can still make it to us through the expanding metric.

Not exactly — it is the natural timescale t_H = 1/H₀, which evaluates to about 13.97 Gyr for H₀ = 70. The actual age of the universe, from the CMB and Big Bang nucleosynthesis, is 13.797 ± 0.023 Gyr. The two numbers are close — within 1.3% — but the agreement is a coincidence of our epoch. In a universe dominated by matter alone, the age would be (2/3) · t_H ≈ 9.3 Gyr. In a universe dominated by dark energy, the age would be infinite in the limit where dark energy has been dominant forever. The real universe has a mixture: about 5% ordinary matter, 27% dark matter, and 68% dark energy, which gives an age very close to t_H by accident of when we happen to be observing.

The Hubble constant is measured by building a "cosmic distance ladder" — a chain of calibrated distance indicators that extends step by step from the solar neighbourhood to the edge of the observable universe. The base rung is geometric parallax measured by the Gaia satellite, which calibrates the distances to nearby Cepheid variable stars. Cepheids are then used to calibrate the distances to nearby Type Ia supernovae, which are bright enough to be observed in galaxies at cosmological distances. The observed supernova redshifts then give H₀ through the slope of the v–d relation. Each rung of the ladder is calibrated against the one below it, and each must be corrected for interstellar extinction, Malmquist bias, peculiar velocities, and a dozen other subtle effects. The whole chain is fragile, which is why independent cross-checks (TRGB, masers, gravitational lensing time delays, tip of the red giant branch) are so valuable — and why the current tension with the CMB measurement is so hard to resolve.

Measuring H₀ to 1% precision is one of the hardest observational challenges in astronomy, because every step of the cosmic distance ladder introduces its own errors that are difficult to quantify and control. Cepheids are affected by crowding in the host galaxies, by dust extinction, and by metallicity differences between the calibrator and target samples. Type Ia supernovae are affected by intrinsic brightness variations, by the nature of their progenitor systems, and by the peculiar velocities of their host galaxies. Each of these effects is at the 1–5% level, and their combination limits the precision of the current measurements. The next generation of surveys — the Vera Rubin Observatory (LSST), the Nancy Grace Roman Space Telescope, and the European Extremely Large Telescope — should reduce the uncertainty to the 1% level and either confirm the Hubble tension or reveal it as a systematic error.