For Omega_Lambda,0>0, show that (5.100)--(5.103) are a solution of (5.96) in the presence of Lambda. Then sketch or plot a(t) for this universe, and verify that it expands forever.

H2 H 2.0 + (1 - 32m,0). ( (ko) (5.96) Q3 ...] arm ada 1-1/2 a samo (5.113 Hodt = 1+ (5.109) azarm aarm, n yields a fairly simple relation for t as a function of a during the epoch radiation and matter are significant: *r.0 40m a Hot 1+ (5.110) 3,327,0 2arm it a , (2/S2,0 Hot)' [a Arm (but before curvature or A contributes significantly to the 1 equation), the approximate result for a(t) becomes 2/3 S2m,o Hot [a >> Arm] (5.112) of radiation-matter equality, trm, can be found by setting a = Arm in 5.110: S232 =H,0.391 -H," (5.113) H2 H 2.0 + (1 - 32m,0). ( (ko) (5.96) Q3 ...] arm ada 1-1/2 a samo (5.113 Hodt = 1+ (5.109) azarm aarm, n yields a fairly simple relation for t as a function of a during the epoch radiation and matter are significant: *r.0 40m a Hot 1+ (5.110) 3,327,0 2arm it a , (2/S2,0 Hot)' [a Arm (but before curvature or A contributes significantly to the 1 equation), the approximate result for a(t) becomes 2/3 S2m,o Hot [a >> Arm] (5.112) of radiation-matter equality, trm, can be found by setting a = Arm in 5.110: S232 =H,0.391 -H," (5.113)