"Geschlossenes Universum mit ΩM>1"

Η[a_]:=H0 (Sqrt[((ΩM)/(a^3))+((1-ΩM)/(a^2))]);

sol=Quiet[FullSimplify[DSolve[{((a'[t])/(a[t]))==Η[a[t]] , a[0]==a0},a[t],t],ΩM>1&&t>0]]

f[x_]:=((ΩM Log[-(Sqrt[1-ΩM]) (Sqrt[x])+(Sqrt[ΩM+x-ΩM x])] (Sqrt[ΩM+x-ΩM x])+(Sqrt[1-ΩM]) (Sqrt[x]) (ΩM+x-ΩM x))/((((1-ΩM))^(3/2)) (x^(3/2)) (Sqrt[((ΩM+x-ΩM x)/(x^3))])))
x[t_]:=((-(Sqrt[a0 (1-ΩM)]) (-ΩM+a0 (-1+ΩM) (1+H0 t (Sqrt[((a0+ΩM-a0 ΩM)/(a0^3))])))+ΩM (Sqrt[a0+ΩM-a0 ΩM]) Log[-(Sqrt[a0 (1-ΩM)])+(Sqrt[a0+ΩM-a0 ΩM])])/((a0^(3/2)) (((1-ΩM))^(3/2)) (Sqrt[((a0+ΩM-a0 ΩM)/(a0^3))])))

a[t_]:=InverseFunction[f[#1]&][x[t]]

"Beispiel"
ΩM=11/10;H0=1;a0=1*^-16; 
T=2(FindMaximum[a[t],{t,0.1}, WorkingPrecision->32][[2,1,2]]); 
τ:=If[t<T/2,t,T-t]; if[x_]:=If[t<T/2,x,-x];

sol=Quiet[NDSolve[{((ă'[t])/(ă[t]))==Η[ă[t]],ă[0]==a0},ă,{t,0,T/2},MaxSteps->∞,WorkingPrecision->32]];
Å[t_]:=Evaluate[(ă[t]/.sol)[[1]]];
ā[t_]:=If[t<T/2,Å[t],Å[T-t]];
H[t_]:=ā'[t]/ā[t]

Plot[N[ā[τ]],{t,0,T}]
Plot[if[N[ā'[τ]]],{t,0,T}]
Plot[N[ā''[τ]],{t,0,T}]
Plot[if[N[ā'''[τ]]],{t,0,T}]
Plot[if[N[H[τ]]],{t,0,T}]
Plot[N[H'[τ]],{t,0,T}]
Plot[if[N[H''[τ]]],{t,0,T}]
Plot[N[H'''[τ]],{t,0,T}]