"Geschlossenes Universum mit ΩR>1"
sol=Quiet[FullSimplify[DSolve[{((a'[t])/(a[t]))==H0 (Sqrt[((ΩR)/((a[t])^4))+((1-ΩR)/((a[t])^2))]) , a[0]==a0},a[t],t],ΩR>1&&t>0]]

FullSimplify[(Sqrt[(a0^2)+H0 t (2 (Sqrt[(a0^2)+ΩR-(a0^2) ΩR])+H0 (t-t ΩR))]),a0==0&&ΩR>1&&H0>0]

a[t_]:=(Sqrt[H0 t (2 (Sqrt[ΩR])+H0 (t-t ΩR))])
H[t_]:=a'[t]/a[t]

"Skalenfaktor"
"a[t]"->FullSimplify[a[t]]
"a'[t]"->FullSimplify[a'[t]]
"a''[t]"->FullSimplify[a''[t]]
"a'''[t]"->FullSimplify[a'''[t]]
"Hubbleparameter"
"H[t]"->FullSimplify[H[t]]
"H'[t]"->FullSimplify[H'[t]]
"H''[t]"->FullSimplify[H''[t]]
"H'''[t]"->FullSimplify[H'''[t]]

"Beispiel"
ΩR=11/10;H0=1;
T=2(FindMaximum[a[t],{t,1}, WorkingPrecision->32][[2,1,2]]);
Plot[a[t],{t,0,T}, Frame->True, AspectRatio->1/2, GridLines->{{T/2},{}},ImagePadding->{{60, 2}, {20, 2}}]
Plot[a'[t],{t,0,T}, Frame->True, AspectRatio->1/2, GridLines->{{T/2},{}},ImagePadding->{{60, 2}, {20, 2}}]
Plot[a''[t],{t,0,T}, Frame->True, AspectRatio->1/2, GridLines->{{T/2},{}},ImagePadding->{{60, 2}, {20, 2}}]
Plot[a'''[t],{t,0,T}, Frame->True, AspectRatio->1/2, GridLines->{{T/2},{}},ImagePadding->{{60, 2}, {20, 2}}]
Plot[H[t],{t,0,T}, Frame->True, AspectRatio->1/2, GridLines->{{T/2},{}},ImagePadding->{{60, 2}, {20, 2}}]
Plot[H'[t],{t,0,T}, Frame->True, AspectRatio->1/2, GridLines->{{T/2},{}},ImagePadding->{{60, 2}, {20, 2}}]
Plot[H''[t],{t,0,T}, Frame->True, AspectRatio->1/2, GridLines->{{T/2},{}},ImagePadding->{{60, 2}, {20, 2}}]
Plot[H'''[t],{t,0,T}, Frame->True, AspectRatio->1/2, GridLines->{{T/2},{}},ImagePadding->{{60, 2}, {20, 2}}]