Dark Energy Density Calculator
Dark Energy Density Calculator computes density, fractional density at redshift, plots evolution.
Dark Energy Density Overview
Dark energy density remains constant for a cosmological constant, while critical density evolves with redshift:
Critical Density:
\\[ \rho_{\text{crit}}(z) = \frac{3 H(z)^2}{8 \pi G} \\] \\[ H(z) = H_0 \sqrt{\Omega_m (1+z)^3 + \Omega_\Lambda} \\]Dark Energy Density:
\\[ \rho_\Lambda = \rho_{\Lambda,0} = \Omega_{\Lambda,0} \rho_{\text{crit},0} \\]Fractional Density:
\\[ \Omega_\Lambda(z) = \frac{\rho_\Lambda}{\rho_{\text{crit}}(z)} \\]Where:
- \\(\rho_{\text{crit}}(z)\\): Critical density at redshift \\(z\\) (kg/m³)
- \\(H(z)\\): Hubble parameter at redshift \\(z\\) (km/s/Mpc)
- \\(H_0\\): Present-day Hubble constant (\\(\approx 70 \, \text{km/s/Mpc}\\))
- \\(\Omega_m\\): Present-day matter density parameter (\\(\approx 0.3\\))
- \\(\Omega_\Lambda\\): Present-day dark energy density parameter (\\(\approx 0.7\\))
- \\(\rho_\Lambda\\): Dark energy density (kg/m³, constant)
- \\(G\\): Gravitational constant (\\(6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\\))
Example Calculation
Example: \\(z = 0\\), \\(H_0 = 70 \, \text{km/s/Mpc}\\), \\(\Omega_m = 0.3\\)
\\[
\rho_{\text{crit},0} = \frac{3 \cdot (70 \cdot 3.24078 \times 10^{-20})^2}{8 \pi \cdot 6.67430 \times 10^{-11}} \approx 8.55 \times 10^{-27} \, \text{kg/m}^3
\\]
\\[
\rho_\Lambda = 0.7 \cdot 8.55 \times 10^{-27} \approx 5.99 \times 10^{-27} \, \text{kg/m}^3
\\]
\\[
\Omega_\Lambda(0) = \frac{5.99 \times 10^{-27}}{8.55 \times 10^{-27}} \approx 0.7
\\]