
Techniques using gravitational waves or fast radio bursts to determine the universe's expansion rate.The Hubble constant measures the current rate of expansion of the universe. Traditional methods rely on the cosmic distance ladder, but new techniques use gravitational waves or fast radio bursts as 'standard sirens' or 'standard candles' to measure distances independently. These methods aim to resolve the 'Hubble tension' — a discrepancy between measurements from the early universe (cosmic microwave background) and the local universe.
The Hubble constant was first measured by Edwin Hubble in 1929. Gravitational wave-based measurements became possible in 2017 with the detection of GW170817, and fast radio bursts were proposed as cosmological probes in the 2010s.
Gravitational waves from merging neutron stars or black holes emit a known amount of energy, allowing the distance to be inferred from the signal's amplitude. Combining this with the redshift of the host galaxy gives the expansion rate. Fast radio bursts, if their dispersion measure can be calibrated to distance, offer another cosmic yardstick. These independent probes bypass the systematic uncertainties of traditional distance ladder methods.
Accurate measurement of the Hubble constant is essential for determining the age, size, and fate of the universe, and for testing models of dark energy and dark matter.
The Hubble tension currently stands at about 5 sigma significance, meaning there is a less than 1 in a million chance it is a statistical fluke.
| t_H | variable | Hubble time — time second |
| H | variable | Hubble parameter — hubble parameter per second |
| ρ_vac | variable | vacuum energy density — energy density joule per cubic metre |
| H | variable | Hubble parameter — hubble parameter per second |
| ρ_vac^0 | variable | current vacuum energy density — energy density joule per cubic metre |
| H_0 | variable | current Hubble parameter — hubble parameter per second |
| ν | variable | running coefficient |
| G | constant | Newton's constant governing gravitational strength — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \epsilon | variable | First slow-roll parameter — slow roll parameter |
| H | variable | Hubble parameter — hubble parameter per second |
| \dot{H} | variable | Time derivative of Hubble parameter — hubble parameter time derivative per second squared |
| \dot{} | operator | Derivative with respect to cosmic time — time derivative |
| \Omega | variable | Density parameter (total energy density relative to critical) — density parameter |
| h | variable | Dimensionless Hubble constant (H0/100 km/s/Mpc) — hubble constant dimensionless |
| A_s | variable | amplitude of primordial scalar perturbations — scalar perturbation amplitude |
| Γ | variable | tunneling rate (per unit volume per unit time) — tunneling rate metre per second per cubic metre |
| H | variable | Hubble parameter during inflation — hubble parameter per second |
| ∝ | operator | is proportional to — proportionality |
| q | variable | Deceleration parameter — deceleration parameter |
| a | variable | Scale factor of the universe — scale factor |
| t | variable | Cosmic time — time second |
| d/dt | operator | Computes the rate of change over time — time derivative |
| d^2/dt^2 | operator | Computes the acceleration over time — second time derivative |























