Universe age

This program calculates the age of the universe by integrating Friedmann equation.

The following parameters are fixed.

• H₀ = 72 km/s/Mpc
• Ω_R = 0
• a₀ = 1

Parameter cases

• (Ω_M, Ω_K, Ω_Λ) = (1, 0, 0)
• (Ω_M, Ω_K, Ω_Λ) = (0.3, 0.7, 0)
• (Ω_M, Ω_K, Ω_Λ) = (2, -1, 0)
• (Ω_M, Ω_K, Ω_Λ) = (3, -2, 0)

Requirements

Fortran compiler is required. By using gnuplot, you can output graph for a vs t.

brew install gfortran
brew install gnuplot

Compile and Run

gfortran universe.f90
./a.out
gnuplot < gnu

Results

(ΩM, ΩK, ΩΛ)	Age
(1, 0, 0)	9.07 Gyr
(0.3, 0.7, 0)	11.00 Gyr
(2, -1, 0)	13.11 Gyr
(3, -2, 0)	6.98 Gyr