Manipulate[Plot[((Ω/(1-Ω))^(1/2)*Sinh[3/2*(1-Ω)^(1/2)*t])^(2/3),{t,0,1}, AxesLabel-> {t,a}],{Ω,0,1}]
(*Omega_m=0.3*)

Plot[((o/(1-o))^(1/2)*Sinh[3/2*(1-o)^(1/2)*t])^(2/3),{t,0,1}, AxesLabel-> {t,a}]
(*Omega_m=0.6*)

Plot[((o/(1-o))^(1/2)*Sinh[3/2*(1-o)^(1/2)*t])^(2/3),{t,0,1}, AxesLabel-> {t,a}](*Omega_m=0.15*)

Plot[3/2*(1-m)^(-1/2)*ArcSinh[((1-m)/m)^(1/2)],{m,0,1},AxesOrigin->{0,0},AxesLabel-> {Omega_m,t}]
(*Omega_m Vs  T*)