Let the pressure term go to P = 0 in the second of the cosmological equations
where R is the size scale of the universe, Eric Weisstein's World of Astronomy is the curvature of the universe, c is the speed of light, is the cosmological constant, and G is the gravitational constant. Integrating gives
where C is a constant of integration. Now note that first of the cosmological equations
where is the density of the universe Eric Weisstein's World of Astronomy gives the constant C as
Now, plugging (4) into (2) gives
Friedmann-Lemaître Cosmological Model
