FLRW evolution, big crunch

(* | Evolution of a Big Crunch Universe | Simon Tyran | http://yukterez.net/f | *)
   
   set = {"GlobalAdaptive", "MaxErrorIncreases"->100};         (* Integration Rule *)
   if[F_] := If[ΩΛ<=0, Nothing, If[ΩK>0, Nothing, F]]       (* Event Horizon Check *)
   n = 100;                                                     (* Recursion Depth *)
   int[f_, {x_, xmin_, xmax_}] :=                                      (* Integral *)
   Quiet[NIntegrate[f, {x, xmin, xmax},
   Method->set, MaxRecursion->n, WorkingPrecision->wp]];
   wp = MachinePrecision;                                     (* Working Precision *)
   im = 180;                                                         (* Image Size *)
   prmax = 70; ptmax = tmax/Gyr;                             (* Regular Plot Range *)
   
   c = 299792458 m/sek;                                              (* Lightspeed *)
   G = 667384*^-16 m^3 kg^-1 sek^-2;                            (* Newton Constant *)
   Gyr = 10^7*36525*24*3600 sek;                                  (* Billion Years *)
   Glyr = Gyr*c;                                             (* Billion Lightyears *)
   Mpc = 30856775777948584200000 m;                                  (* Megaparsec *)
   kB = 13806488*^-30 kg m^2/sek^2/K;                        (* Boltzmann Constant *)
   h = 662606957*^-42 kg m^2/sek;                               (* Planck Constant *)
   ρc[H_] := 3H^2/8/π/G;                                       (* Critical Density *)
   ρR = 8π^5 kB^4 T^4/15/c^5/h^3;                             (* Radiation Density *)
   ρΛ = ρc[H0] ΩΛ;                                          (* Dark Energy Density *)
   T = 2725/1000 K;                                             (* CMB Temperature *)
   kg = m = sek = 1;                                                   (* SI Units *)
   
   ΩR = 2;                             (* Radiation Proportion including Neutrinos *)
   ΩM = 0;                              (* Matter Proportion including Dark Matter *)
   ΩΛ = 0;                                               (* Dark Energy Proportion *)
   ΩT = ΩR+ΩM+ΩΛ;                           (* Total Density over Critical Density *)
   ΩK = 1-ΩT;                                                 (* Curvature Density *)
   
   H0 = 67150 m/Mpc/sek;                                        (* Hubble Constant *)
   H[a_] := H0 Sqrt[ΩR/a^4+ΩM/a^3+ΩK/a^2+ΩΛ]                   (* Hubble Parameter *)
   Ж[t_] := (Sqrt[ΩR]+H0(t-t ΩR))/(t(2Sqrt[ΩR]+H0 (t-t ΩR)));
   
   a[t_]  := Re[Sqrt[H0 t (2Sqrt[ΩR]+H0 (t-t ΩR))]];   (* Scale Factor a by Time t *)
   т[a_]  := Re[(2H0 Sqrt[ΩR]-Sqrt[-4a^2 H0^2 (-1+ΩR)+4H0^2ΩR])/(2H0^2(ΩR-1))];
   rP[t_] := Re[a[t] int[c/a[т], {т, 0, t}]];      (* Proper Particle Horizon by t *)
   rp[a_] := Re[a int[c/A^2/H[A], {A, 0, a}]];     (* Proper Particle Horizon by a *)
   RP[t_] := Re[int[c/a[т], {т, 0, t}]];         (* Comoving Particle Horizon by t *)
   Rp[a_] := Re[int[c/A^2/H[A], {A, 0, a}]];     (* Comoving Particle Horizon by a *)
   rE[t_] := Nothing;                                 (* Proper Event Horizon by t *)
   re[a_] := Nothing;                                 (* Proper Event Horizon by a *)
   RE[t_] := Nothing;                               (* Comoving Event Horizon by t *)
   Rε[a_] := Nothing;                               (* Comoving Event Horizon by a *)
   rL[t0_, t_] := Re[a[t] int[c/a[т], {т, t, t0}]];      (* Proper Light Cone by t *)
   rl[a0_, a_] := Re[a int[c/A^2/H[A], {A, a, a0}]];     (* Proper Light Cone by a *)
   RL[t0_, t_] := Re[int[c/a[т], {т, t, t0}]];         (* Comoving Light Cone by t *)
   Rl[a0_, a_] := Re[int[c/A^2/H[A], {A, a, a0}]];     (* Comoving Light Cone by a *)
   rH[t_] := c/Abs[Ж[t]];                             (* Proper Hubble Radius by t *)
   rh[a_] := c/Abs[H[a]];                             (* Proper Hubble Radius by a *)
   RH[t_] := c/Abs[Ж[t]*a[t]];                      (* Comoving Hubble Radius by t *)
   Rh[a_] := c/Abs[H[a]*a];                         (* Comoving Hubble Radius by a *)
   
   t0 = Quiet[Re[t/.FindRoot[a[t]-Sqrt[2], {t, 10 Gyr}]]]; ti = t Gyr; τi = τ Gyr;
   "t0"->t0/Gyr "Gyr"                                              (* Current Time *)
   
   tmax = 2*t0;
   rpN = Rp[tmax/2]/Glyr;
   ηmax = RP[0.9999999 tmax]/Glyr;

Ť[η_] := Quiet[FindRoot[RP[τ Gyr]/Glyr-η,                             (* t by η *)
   {τ, ((Sin[η π/ηmax-π/2]+1)/2) ptmax}, WorkingPrecision->wp, 
   MaxIterations->1000][[1, 2]]]
   
   "PROPER DISTANCES, f(t)"
   
   pt = Quiet[Plot[Evaluate[
   {rH[τi]/Glyr, rP[τi]/Glyr, Nothing}],
   {τ, 0, ptmax}, Frame->True, AspectRatio->prmax/ptmax,
   FrameTicks->None, PlotRange->{{0, ptmax}, {0, prmax}},
   PlotStyle->{{Thickness[0.005]},
   {Darker[Green], Thickness[0.005]}, {Purple, Thickness[0.005]}},
   ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1,
   GridLines->{{}, {}}]];
   
   plot1[t_] := Rasterize[Grid[{{Rotate[Quiet[Show[Plot[Evaluate[
   {rL[ti, τi]/Glyr, -rL[ti, τi]/Glyr}],
   {τ, 0, ptmax}, Frame->True, AspectRatio->prmax/ptmax,
   FrameTicks->None, PlotRange->{{0, ptmax}, {0, prmax}},
   PlotStyle->{{Orange, Thickness[0.005]}, {{Orange, Thickness[0.005]}, Dashed}},
   ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1,
   GridLines->{{}, {}}], pt]], 90 Degree]}}]];
   
   Do[Print[plot1[t]], {t, {ptmax/2}}]
   
   plot2 = Rasterize[Grid[{{Rotate[Quiet[Plot[Evaluate[
   Join[{0}, Table[a[τ Gyr] n^(7/2)/250, {n, 1, 55, 1}]]],
   {τ, 0, ptmax}, Frame->True, AspectRatio->prmax/ptmax,
   FrameTicks->None, PlotRange->{{0, ptmax}, {0, prmax}},
   PlotStyle->Table[{Dashing->Large, Thickness[0.005],
   Gray}, {n, 1, 100}], ImageSize->im, ImagePadding->1]], 90 Degree]}}]]
   
   "COMOVING DISTANCES, f(t)"
   
   ct = Quiet[Plot[Evaluate[
   {rH[τi]/(a[τi]Glyr), rP[τi]/(a[τi]Glyr), Nothing}],
   {τ, 0, ptmax}, Frame->True, AspectRatio->prmax/ptmax,
   FrameTicks->None, PlotRange->{{0, ptmax}, {0, prmax}},
   PlotStyle->{{Thickness[0.005]},
   {Darker[Green], Thickness[0.005]}, {Purple, Thickness[0.005]}},
   ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1,
   GridLines->{{}, {}}]];
   
   plot3[t_] := Rasterize[Grid[{{Rotate[Quiet[Show[Plot[Evaluate[
   {rL[ti, τi]/(a[τi]Glyr), -rL[ti, τi]/(a[τi]Glyr)}],
   {τ, 0, ptmax}, Frame->True, AspectRatio->prmax/ptmax,
   FrameTicks->None, PlotRange->{{0, ptmax}, {0, prmax}},
   PlotStyle->{{Orange, Thickness[0.005]}, {{Orange, Thickness[0.005]}, Dashed}},
   ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1,
   GridLines->{{}, {}}], ct]], 90 Degree]}}]];
   
   Do[Print[plot3[t]], {t, {ptmax/2}}]
   
   plot4 = Rasterize[Grid[{{Rotate[Quiet[Plot[Evaluate[
   Join[{0}, Table[n, {n, 10, 100, 10}]]],
   {τ, 0, ptmax}, Frame->True, AspectRatio->prmax/ptmax,
   FrameTicks->None, PlotRange->{{0, ptmax}, {0, prmax}},
   PlotStyle->Table[{Dashing->Large, Thickness[0.005],
   Gray}, {n, 1, 100}], ImageSize->im, ImagePadding->1]], 90 Degree]}}]]
   
   "COMOVING DISTANCES, f(η)"
   
   cη = Quiet[Plot[Evaluate[{RH[Ť[Ct] Gyr]/Glyr, Ct}],
   {Ct, 0, ηmax}, Frame->True, AspectRatio->prmax/ηmax,
   FrameTicks->None, PlotRange->{{0, ηmax}, {0, prmax}},
   PlotStyle->{{Thickness[0.005]}, {Darker[Green], Thickness[0.005]}},
   ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1,
   GridLines->{{}, {}}]];
   
   plot9[η_] := Rasterize[Grid[{{Rotate[Quiet[Show[Plot[Evaluate[
   {η-Ct, Ct-η}], {Ct, 0, ηmax},
   Frame->True, AspectRatio->prmax/ηmax,
   FrameTicks->None, PlotRange->{{0, ηmax}, {0, prmax}},
   PlotStyle->{{Orange, Thickness[0.005]}, {{Orange, Thickness[0.005]}, Dashed}},
   ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1,
   GridLines->{{}, {}}], cη]], 90 Degree]}}]];
   
   Do[Print[plot9[η]], {η, {rpN}}]
   
   plot10 = Rasterize[Grid[{{Rotate[Quiet[Plot[Evaluate[
   Join[{0}, Table[n, {n, 10, 100, 10}]]],
   {Ct, 0, ηmax}, Frame->True, AspectRatio->prmax/ηmax,
   FrameTicks->None, PlotRange->{{0, ηmax}, {0, prmax}},
   PlotStyle->Table[{Dashing->Large, Thickness[0.005],
   Gray}, {n, 1, 100}], ImageSize->im, ImagePadding->1]], 90 Degree]}}]]