t := 1
logQlb[a_] := -a^2/2 + Log[a] - Log[1 + a^2] - Log[Sqrt[2*[Pi]]]
logQub[a_] := -a^2/2 - Log[a] - Log[Sqrt[2*[Pi]]]
ratefn[t_] := t^2/2
Plot[{-n*ratefn[t], logQlb[t*Sqrt[n]], logQub[t*Sqrt[n]]}, {n, 1,
  100}, PlotLegends -> {"Large Deviations (Cramer) estimate",
   "Exact (lower bound) via Q fn", "Exact (upper bound) via Q fn"},
 AxesLabel -> {"n", "Log[P[Sn>=t]]"}]