🗎 Code for the
radiation dominated spacetime diagrams
(* ||||||||| Radiation dominated universe ||||||||| flrw.yukterez.net ||||||||| *) set = {"GlobalAdaptive", "MaxErrorIncreases"->100, Method->"GaussKronrodRule"}; (* 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 *) NIntegrate[f, {x, xmin, xmax}, Method->set, MaxRecursion->n, WorkingPrecision->wp]; wp = MachinePrecision; (* Working Precision *) im = 200; (* Image Size *) ηmax = 70; pmax = 70; (* 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 *) ρc[H_] := 3H^2/8/π/G; (* Critical Density *) kg = m = sek = 1; (* SI Units *) ΩR = 1; (* Radiation Proportion including Neutrinos *) ΩM = 0; (* Matter Proportion including Dark Matter *) ΩΛ = 0; (* Dark Energy Proportion *) ΩT = 0; (* Total Density over Critical Density *) ΩK = 1-ΩT; (* Curvature Density *) H0 = 67150 m/Mpc/sek; (* Hubble Constant *) H[a_] := H0/a^2; (* Hubble Parameter *) Η[t_] := 1/2/t; (* Hubble Parameter *) a[t_] := Sqrt[2 H0 t]; (* Scale Factor a by Time t *) т[a_] := a^2/2/H0; (* Time t by Scale Factor a *) rP[t_] := a[t] int[c/a[т], {т, 0, t}]; (* Proper Particle Horizon by t *) rp[a_] := a int[c/A^2/H[A], {A, 0, a}]; (* Proper Particle Horizon by a *) RP[t_] := int[c/a[т], {т, 0, t}]; (* Comoving Particle Horizon by t *) Rp[a_] := 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_] := a[t] int[c/a[т], {т, t, t0}]; (* Proper Light Cone by t *) rl[a0_, a_] := a int[c/A^2/H[A], {A, a, a0}]; (* Proper Light Cone by a *) RL[t0_, t_] := int[c/a[т], {т, t, t0}]; (* Comoving Light Cone by t *) Rl[a0_, a_] := int[c/A^2/H[A], {A, a, a0}]; (* Comoving Light Cone by a *) rH[t_] := c/H[a[t]]; (* Proper Hubble Radius by t *) rh[a_] := c/H[a]; (* Proper Hubble Radius by a *) RH[t_] := c/H[a[t]]/a[t]; (* Comoving Hubble Radius by t *) Rh[a_] := c/H[a]/a; (* Comoving Hubble Radius by a *) t0 = Re[t/.FindRoot[a[t]-1, {t, 10 Gyr}]]; ti = t Gyr; τi = τ Gyr; "t0"->t0/Gyr "Gyr" (* Current Time *) ã[η_] := Quiet[FindRoot[Rp[Ã]/Glyr-η, (* Scale Factor a by Conformal Time η *) {Ã, 0.00001}, WorkingPrecision->wp, MaxIterations->1000][[1, 2]]]; ā = Quiet[Interpolation[Join[{{0, 0}}, ParallelTable[{((Sin[η π/ηmax-π/2]+1) ηmax/2), ã[((Sin[η π/ηmax-π/2]+1) ηmax/2)]}, {η, ηmax/im, ηmax, ηmax/im}]]]]; Ť[η_] := Quiet[FindRoot[RP[τ Gyr]/Glyr-η, (* t by η *) {τ, 1}, WorkingPrecision->wp, MaxIterations->1000][[1, 2]]] (* ţ = Quiet[Interpolation[Join[{{0, 0}}, ParallelTable[{((Sin[η π/ηmax-π/2]+1) ηmax/2), Ť[((Sin[η π/ηmax-π/2]+1) ηmax/2)]}, {η, ηmax/im, ηmax, ηmax/im}]]]]; *) rpN = Rp[1]/Glyr; "PROPER DISTANCES, f(t)" pt = Quiet[Plot[ {rH[τi]/Glyr, rP[τi]/Glyr, rE[τi]/Glyr}, {τ, 0, pmax}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax}, {0, pmax}}, 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[ {rL[ti, τi]/Glyr, -rL[ti, τi]/Glyr}, {τ, 0, pmax}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax}, {0, pmax}}, 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, {t0/Gyr}}] plot2 = Rasterize[Grid[{{Rotate[Quiet[Plot[ Join[{0}, Table[a[τ Gyr] n^(7/2)/250, {n, 4, 55, 1}]], {τ, 0, pmax}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax}, {0, pmax}}, PlotStyle->Table[{Dashing->Large, Thickness[0.005], Gray}, {n, 1, 100}], ImageSize->im, ImagePadding->1]], 90 Degree]}}]] "COMOVING DISTANCES, f(t)" ct = Quiet[Plot[ {RH[τi]/Glyr, RP[τi]/Glyr, RE[τi]/Glyr}, {τ, 0, pmax}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax}, {0, pmax}}, 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[ {RL[ti, τi]/Glyr, -RL[ti, τi]/Glyr}, {τ, 0, pmax}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax}, {0, pmax}}, 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, {t0/Gyr}}] plot4 = Rasterize[Grid[{{Rotate[Quiet[Plot[ Join[{0}, Table[n, {n, 10, 100, 10}]], {τ, 0, pmax}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax}, {0, pmax}}, PlotStyle->Table[{Dashing->Large, Thickness[0.005], Gray}, {n, 1, 100}], ImageSize->im, ImagePadding->1]], 90 Degree]}}]] "PROPER DISTANCES, f(a)" pa = Quiet[Plot[ {rh[α]/Glyr, rp[α]/Glyr, re[α]/Glyr}, {α, 0, pmax Gyr/t0}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax Gyr/t0}, {0, pmax}}, PlotStyle->{{Thickness[0.005]}, {Darker[Green], Thickness[0.005]}, {Purple, Thickness[0.005]}}, ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1, GridLines->{{}, {}}]]; plot5[å_] := Rasterize[Grid[{{Rotate[Quiet[Show[Plot[ {rl[å, α]/Glyr, -rl[å, α]/Glyr}, {α, 0, pmax Gyr/t0}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax Gyr/t0}, {0, pmax}}, PlotStyle->{{Orange, Thickness[0.005]}, {{Orange, Thickness[0.005]}, Dashed}}, ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1, GridLines->{{}, {}}], pa]], 90 Degree]}}]]; Do[Print[plot5[å]], {å, {1}}] plot6 = Rasterize[Grid[{{Rotate[Quiet[Plot[ Join[{0}, Table[α n^(7/2)/250, {n, 4, 55, 1}]], {α, 0, pmax Gyr/t0}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax Gyr/t0}, {0, pmax}}, PlotStyle->Table[{Dashing->Large, Thickness[0.005], Gray}, {n, 1, 100}], ImageSize->im, ImagePadding->1]], 90 Degree]}}]] "COMOVING DISTANCES, f(a)" ca = Quiet[Plot[ {Rh[α]/Glyr, Rp[α]/Glyr, Rε[α]/Glyr}, {α, 0, pmax Gyr/t0}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax Gyr/t0}, {0, pmax}}, PlotStyle->{{Thickness[0.005]}, {Darker[Green], Thickness[0.005]}, {Purple, Thickness[0.005]}}, ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1, GridLines->{{}, {}}]]; plot7[å_] := Rasterize[Grid[{{Rotate[Quiet[Show[Plot[ {Rl[å, α]/Glyr, -Rl[å, α]/Glyr}, {α, 0, pmax Gyr/t0}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax Gyr/t0}, {0, pmax}}, PlotStyle->{{Orange, Thickness[0.005]}, {{Orange, Thickness[0.005]}, Dashed}}, ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1, GridLines->{{}, {}}], ca]], 90 Degree]}}]]; Do[Print[plot7[å]], {å, {1}}] plot8 = Rasterize[Grid[{{Rotate[Quiet[Plot[ Join[{0}, Table[n, {n, 10, 100, 10}]], {α, 0, pmax Gyr/t0}, Frame->True, AspectRatio->pmax/pmax, FrameTicks->None, PlotRange->{{0, pmax Gyr/t0}, {0, pmax}}, PlotStyle->Table[{Dashing->Large, Thickness[0.005], Gray}, {n, 1, 100}], ImageSize->im, ImagePadding->1]], 90 Degree]}}]] "CONFORMAL DIAGRAM, f(η)" cη = Quiet[Plot[ {Rh[ā[Ct]]/Glyr, Ct, Rε[ā[Ct]]/Glyr}, {Ct, 0, ηmax}, Frame->True, AspectRatio->pmax/ηmax, FrameTicks->None, PlotRange->{{0, ηmax}, {0, pmax}}, PlotStyle->{{Thickness[0.005]}, {Darker[Green], Thickness[0.005]}, {Purple, Thickness[0.005]}}, ImageSize->im, Filling->Top, FillingStyle->Opacity[0.1], ImagePadding->1, GridLines->{{}, {}}]]; plot9[η_] := Rasterize[Grid[{{Rotate[Quiet[Show[Plot[ {η-Ct, Ct-η}, {Ct, 0, ηmax}, Frame->True, AspectRatio->pmax/ηmax, FrameTicks->None, PlotRange->{{0, ηmax}, {0, pmax}}, 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[ Join[{0}, Table[n, {n, 10, 100, 10}]], {Ct, 0, ηmax}, Frame->True, AspectRatio->pmax/ηmax, FrameTicks->None, PlotRange->{{0, ηmax}, {0, pmax}}, PlotStyle->Table[{Dashing->Large, Thickness[0.005], Gray}, {n, 1, 100}], ImageSize->im, ImagePadding->1]], 90 Degree]}}]] s[text_] := Style[text, FontFamily->"Lucida Console", FontSize->36]