Cosmological Horizon Calculator
Cosmological Horizon Calculator finds particle or event horizon distance in a flat universe, with a plot.
Formulas Used in Cosmological Horizon Calculator
The calculator computes the particle or event horizon distance in a flat \\(\Lambda\\)CDM universe:
Particle Horizon:
\\[ d_p = \frac{c}{H_0} \int_0^\infty \frac{dz}{\sqrt{\Omega_m (1+z)^3 + \Omega_\Lambda}} \\]Event Horizon:
\\[ d_e = \frac{c}{H_0} \int_0^\infty \frac{dz}{\sqrt{\Omega_m (1+z)^3 + \Omega_\Lambda}} \\]Where:
- \\(d_p\\): Particle horizon distance (Mpc)
- \\(d_e\\): Event horizon distance (Mpc)
- \\(c\\): Speed of light (\\(2.99792458 \times 10^8 \, \text{m/s}\\))
- \\(H_0\\): Hubble constant (km/s/Mpc)
- \\(\Omega_m\\): Matter density parameter
- \\(\Omega_\Lambda\\): Dark energy density parameter (\\(\Omega_\Lambda = 1 – \Omega_m\\) for flat universe)
- \\(z\\): Redshift
Example Calculation
Example: Particle Horizon (\\(H_0 = 70 \, \text{km/s/Mpc}, \Omega_m = 0.3, \Omega_\Lambda = 0.7\\))
\\[
d_p \approx \frac{2.99792458 \times 10^8}{70 \times 10^3} \int_0^{1000} \frac{dz}{\sqrt{0.3 (1+z)^3 + 0.7}} \approx 14400 \, \text{Mpc} \approx 47 \, \text{Gly}
\\]