The Friedmann equation in a matter-dominated universe with curvature is given by 87G -pR² –k where R is the scale factor, p is the matter densiy, and k is a positive constant. Demonstrate that the parametric solution 4xG po (1 – cos 0) 3 k 47G po R(0) = and t %3D 3 3/2 (0 - sin 0) solves this equation, where 0 is a variable that runs from 0 to 27 and the present-day scale factor is set to Ro = 1.

The Friedmann equation in a matter-dominated universe with curvature is given by 87G -pR² –k where R is the scale factor, p is the matter densiy, and k is a positive constant. Demonstrate that the parametric solution 4xG po (1 – cos 0) 3 k 47G po R(0) = and t %3D 3 3/2 (0 - sin 0) solves this equation, where 0 is a variable that runs from 0 to 27 and the present-day scale factor is set to Ro = 1.