iCosmos › Hubble parameter H(z) calculator

Hubble parameter H(z) calculator

Q: What is the Hubble tension?

Values of H0 inferred from the early universe (the cosmic microwave background, assuming ΛCDM: about 67–68 km s−1 Mpc−1) disagree with local distance-ladder measurements (about 73). Change H0 above to see how much distances and ages depend on it.

The expansion rate of the universe when the light from redshift z was emitted.

The interactive calculator loads here: change the redshift and the cosmological parameters (Ω_m, Ω_Λ, Ω_r, w₀, w_a, H₀) and the result and plot update instantly.

What it is

The Hubble parameter H(z) is the expansion rate at redshift z; its value today is the Hubble constant H₀. It follows from the Friedmann equation and the densities of matter, radiation, curvature and dark energy.

All the distances and times on this site are built from integrals of 1/H(z), so H(z) is the most direct description of the expansion history.

Formula

H(z) = H₀ E(z)
E²(z) = Ω_r(1+z)⁴ + Ω_m(1+z)³ + Ω_k(1+z)² + Ω_Λ f_DE(z)
f_DE = (1+z)^3(1+w_{0+w_a)} e^{−3 w_{a} z/(1+z)} (CPL dark energy)

Worked example

In the classic model (Ω_m = 0.3, Ω_Λ = 0.7, H₀ = 70 km s⁻¹ Mpc⁻¹), H(z = 1) = 123.25 km s⁻¹ Mpc⁻¹ and H(z = 2) = 207.65 km s⁻¹ Mpc⁻¹.

The expansion started to accelerate at z = 0.671, where the deceleration parameter q changes sign; for flat ΛCDM this is (2Ω_Λ/Ω_m)^1/3 − 1.

Common questions

What is the Hubble tension?

Values of H₀ inferred from the early universe (the cosmic microwave background, assuming ΛCDM: about 67–68 km s⁻¹ Mpc⁻¹) disagree with local distance-ladder measurements (about 73). Change H₀ above to see how much distances and ages depend on it.

Is the expansion speeding up?

Today, yes. The Hubble parameter H is still decreasing with time, but slowly enough that the recession speed of any given galaxy, ȧ = aH, is increasing: the deceleration parameter q is negative. The Cosmic history section plots q(z).

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About iCosmos

iCosmos was created by Mihran Vardanyan. Mihran Vardanyan is a cosmologist who earned his DPhil in cosmology at the University of Oxford, supervised by Joseph Silk and Roberto Trotta. He developed iCosmos during his research years at Oxford Astrophysics, where his work applied Bayesian model selection to the curvature and size of the Universe.

How to cite: Vardanyan, Mihran. iCosmos V4: Cosmology Calculator. https://icosmos.co.uk/. Include your access date, model parameters and exported data when reporting calculations.