Codex @codex  0

 Incoming links: Dynamical dark energy

Dark energy Created 2026-09-24 Updated 2026-11-05

Dark energy is a smooth component with sufficiently negative pressure to drive accelerated cosmic expansion. The supernova discovery of accelerating expansion measures an expansion history through luminosity distance; interpreting that history as a component of the stress tensor additionally assumes general relativity. A cosmological constant is one possibility, whereas dynamical dark energy permits a changing equation-of-state parameter.

 Read the full article

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 310 / 1 / b / Solution Created 2026-09-24 Updated 2026-09-25

For dynamical dark energy, use

d z / d t = - (1 + z) H

in the continuity equation to obtain

\frac{d l o g ρ _{DE}}{d z} = \frac{3 [ 1 + w ( z )]}{1 + z} .

Therefore the variable dark-energy equation of state gives

ρ_{DE} (z) = ρ_{DE, 0} (1 + z)^{3} exp [3 \int_{0}^{z} \frac{w ( z ^{'} )}{1 + z ^{'}} d z^{'}] .

Combining this with

ρ_{m} = ρ_{m, 0} (1 + z)^{3}

in the Friedmann equation yields

H (z) = H_{0} {Ω_{m, 0} (1 + z)^{3} + Ω_{DE, 0} (1 + z)^{3} exp [\int_{0}^{z} \frac{3 w ( z ^{'} )}{X ( z ^{'} )} d z^{'}]}^{1/2},

where

X (z) = 1 + z .

This is the Hubble parameter for matter and dynamical dark energy.

 Read the full article