method

hubble constant measurement

Techniques using gravitational waves or fast radio bursts to determine the universe's expansion rate.
34 related articles · 6 formulas

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

Concept graph →

Formulas

$$t_H \approx \frac{1}{H}$$
The characteristic expansion time of the universe.
What is in the formula
t_HvariableHubble time — time second
HvariableHubble parameter — hubble parameter per second
τ_{cosm}\approx0.5(\frac{1{мэв}}{t})^2{сек} · 2606.03316v2
$$\rho_{\rm vac}(H) = \rho_{\rm vac}^0 + \frac{3\nu}{8\pi G}(H^2 - H_0^2)$$
Vacuum energy density evolves with Hubble parameter squared.
What is in the formula
ρ_vacvariablevacuum energy density — energy density joule per cubic metre
HvariableHubble parameter — hubble parameter per second
ρ_vac^0variablecurrent vacuum energy density — energy density joule per cubic metre
H_0variablecurrent Hubble parameter — hubble parameter per second
νvariablerunning coefficient
GconstantNewton's constant governing gravitational strength — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
ρ_{\rmvac}(h)\simeqρ_{\rmvac}^0+\frac{3ν_{\rmeff}}{8πg_{\rmn}}(h^2-h_0^2) · 2606.05352v2
$$\epsilon = -\frac{\dot{H}}{H^2}$$
Measures the rate of change of the Hubble parameter during inflation.
What is in the formula
\epsilonvariableFirst slow-roll parameter — slow roll parameter
HvariableHubble parameter — hubble parameter per second
\dot{H}variableTime derivative of Hubble parameter — hubble parameter time derivative per second squared
\dot{}operatorDerivative with respect to cosmic time — time derivative
ε=-\frac{\dot{h}}{h^2} · 2607.06582
$$\Omega h^{3/2}$$
Combination of density parameter and Hubble constant.
What is in the formula
\OmegavariableDensity parameter (total energy density relative to critical) — density parameter
hvariableDimensionless Hubble constant (H0/100 km/s/Mpc) — hubble constant dimensionless
ω_mh^{3/2} · 2607.24694v1
$$A_s \propto \left( \frac{\Gamma^{1/4}}{H} \right)^{-5/3}$$
The amplitude of primordial perturbations scales with the ratio of tunneling rate to Hubble parameter.
What is in the formula
A_svariableamplitude of primordial scalar perturbations — scalar perturbation amplitude
Γvariabletunneling rate (per unit volume per unit time) — tunneling rate metre per second per cubic metre
HvariableHubble parameter during inflation — hubble parameter per second
∝operatoris proportional to — proportionality
a_s=0.06(\frac{\gamma^{1/4}_*}{h_*})^{-5/3} · 2607.27193v1
$$q = - rac{ rac{ ext{d}^2 a}{ ext{d} t^2} a}{ig( rac{ ext{d} a}{ ext{d} t}ig)^2}$$
Measures acceleration of the universe's expansion.
What is in the formula
qvariableDeceleration parameter — deceleration parameter
avariableScale factor of the universe — scale factor
tvariableCosmic time — time second
d/dtoperatorComputes the rate of change over time — time derivative
d^2/dt^2operatorComputes the acceleration over time — second time derivative
q_0=-\frac{\ddot{a}a}{\dot{a}^2}\big|_{t_0} · 2605.03004v1
q_0=\frac{1}{2}ω_{m0}+\frac{1}{2}(1+3w_0)ω_{de0} · 2607.07348

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