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.
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Transcribed Image Text:The Friedmann equation in a matter-dominated universe with curvature is given by
87G
-pR² – k ,
3
where R is the scale factor, p is the matter densi, and k is a positive constant.
Demonstrate that the parametric solution
4G po
4тG
Po
R(0)
(1 – cos 0)
3 k
and
t(
(e – sin 0)
3 k3/2
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.
%3D
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