N[(1.491710580279889`*^59)×(Sqrt[(1/3)(((10^67.7)/(((1.491710580279889`*^59))^3))+(((1.491710580279889`*^59)(10^67.7))/(((1.491710580279889`*^59))^4))+1.1139911652492607`*^-120)])]

Error Analysis

s1=NDSolve[{-((2a[t]a''[t])/((a'[t])^2))==1+(((a[t])^2)/((a'[t])^2))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))+(1/3)(((1.491710580279889`*^59)(10^67.7))/((a[t])^4))),-(1/2) ((a[t])^2) (6 a'[t] h'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^3)+h[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^2)+60516 ((10^(-124.8))))+2 h''[t]))==0,-(1/2) ((a[t])^2) (6 a'[t] A'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^3)+A[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^2)+60516 ((10^(-124.8))))+2 A''[t]))==0,h[1]==1,h'[1]==0,A[1]==1,A'[1]==0,a[1]==1.491710580279889`*^59,a'[1]==14966.218638223512`},{h,A,a},{t,1,(10^62)},NormFunction->1,MaxSteps->∞]

s10=NDSolve[{-((2a[t]a''[t])/((a'[t])^2))==1+(((a[t])^2)/((a'[t])^2))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))+(1/3)(((1.491710580279889`*^59)(10^67.7))/((a[t])^4))),-(1/2) ((a[t])^2) (6 a'[t] h'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^3)+h[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^2)+60516 ((10^(-124.8))))+2 h''[t]))==0,-(1/2) ((a[t])^2) (6 a'[t] A'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^3)+A[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^2)+60516 ((10^(-124.8))))+2 A''[t]))==0,h[1]==1,h'[1]==0,A[1]==1,A'[1]==0,a[1]==1.491710580279889`*^59,a'[1]==14966.218638223512`,WhenEvent[((5.326898482179484`*^62)/(a[t]))-1==0,"StopIntegration"]},{h,A,a},{t,1,(10^62)},NormFunction->1,MaxSteps->∞]

sinf=NDSolve[{-((2a[t]a''[t])/((a'[t])^2))==1+(((a[t])^2)/((a'[t])^2))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))+(1/3)(((1.491710580279889`*^59)(10^67.7))/((a[t])^4))),-(1/2) ((a[t])^2) (6 a'[t] h'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^3)+h[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^2)+60516 ((10^(-124.8))))+2 h''[t]))==0,-(1/2) ((a[t])^2) (6 a'[t] A'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^3)+A[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^2)+60516 ((10^(-124.8))))+2 A''[t]))==0,h[1]==1,h'[1]==0,A[1]==1,A'[1]==0,a[1]==1.491710580279889`*^59,a'[1]==14966.218638223512`},{h,A,a},{t,1,(10^62)},NormFunction->∞,MaxSteps->∞]

sinf0=NDSolve[{-((2a[t]a''[t])/((a'[t])^2))==1+(((a[t])^2)/((a'[t])^2))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))+(1/3)(((1.491710580279889`*^59)(10^67.7))/((a[t])^4))),-(1/2) ((a[t])^2) (6 a'[t] h'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^3)+h[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^2)+60516 ((10^(-124.8))))+2 h''[t]))==0,-(1/2) ((a[t])^2) (6 a'[t] A'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^3)+A[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^2)+60516 ((10^(-124.8))))+2 A''[t]))==0,h[1]==1,h'[1]==0,A[1]==1,A'[1]==0,a[1]==1.491710580279889`*^59,a'[1]==14966.218638223512`,WhenEvent[((5.326898482179484`*^62)/(a[t]))-1==0,"StopIntegration"]},{h,A,a},{t,1,(10^62)},NormFunction->∞,MaxSteps->∞]

ωHiggs=GraphicsGrid[{{ωHiggs1=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}}/.s1],{t,1,(10^62)},PlotRange->{{1,-10},{-1.025,-0.8}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, Higgs])=((Subscript[P, Higgs])/(Subscript[ρ, Higgs]))",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.5,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, Higgs])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],ωHiggs2=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}}/.s1],{t,1,(10^62)},PlotRange->{{1,-2},{-1.025,-0.8}},AxesOrigin->{-2,-1.025},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, Higgs])=((Subscript[P, Higgs])/(Subscript[ρ, Higgs]))",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.5,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, Higgs])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]}},AspectRatio->(1/GoldenRatio),Frame->False,ImageSize->{1500,750/GoldenRatio}]

ωHiggs=GraphicsGrid[{{ωHiggs3=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}}/.sinf],{t,1,(10^62)},PlotRange->{{1,-10},{-1.025,-0.8}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, Higgs])=((Subscript[P, Higgs])/(Subscript[ρ, Higgs]))",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.5,0.9}], {1, 0.8}}],PlotStyle->{{Red,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, Higgs])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],ωHiggs4=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}}/.sinf],{t,1,(10^62)},PlotRange->{{1,-2},{-1.025,-0.8}},AxesOrigin->{-2,-1.025},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, Higgs])=((Subscript[P, Higgs])/(Subscript[ρ, Higgs]))",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.5,0.9}], {1, 0.8}}],PlotStyle->{{Red,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, Higgs])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]}},AspectRatio->(1/GoldenRatio),Frame->False,ImageSize->{1500,750/GoldenRatio}]

Show[ωHiggs1,ωHiggs3]

Show[ωHiggs2,ωHiggs4]

ωHiggsmaxmin=GraphicsGrid[{{ωHiggsdiff1=ParametricPlot[Evaluate[{{{(1/2)(First[(((5.326898482179484`*^62)/(a[t]))-1)/.s1]+First[(((5.326898482179484`*^62)/(a[t]))-1)/.sinf])},{First[(((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))))/.s1]-First[(((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))))/.sinf]}}}],{t,1,(10^62)},PlotRange->{{1,-10},All},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, (Subscript[Higgs, MAX])])- (Subscript[ω, (Subscript[Higgs, MIN])])",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.6,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, (Subscript[Higgs, MAX])])- (Subscript[ω, (Subscript[Higgs, MIN])])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],ωHiggsdiff2=ParametricPlot[Evaluate[{{{(1/2)(First[(((5.326898482179484`*^62)/(a[t]))-1)/.s1]+First[(((5.326898482179484`*^62)/(a[t]))-1)/.sinf])},{First[(((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))))/.s1]-First[(((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))))/.sinf]}}}],{t,1,(10^62)},PlotRange->{{1,-2},All},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, (Subscript[Higgs, MAX])])- (Subscript[ω, (Subscript[Higgs, MIN])])",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.6,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, (Subscript[Higgs, MAX])])- (Subscript[ω, (Subscript[Higgs, MIN])])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]}},AspectRatio->(1/GoldenRatio),Frame->False,ImageSize->{1500,750/GoldenRatio}]

Export["omegaHiggsMAX-omegaHiggsMIN.pdf",ωHiggsmaxmin];
SystemOpen[DirectoryName[AbsoluteFileName["omegaHiggsMAX-omegaHiggsMIN.pdf"]]];

ωHiggsdiff=ParametricPlot[Evaluate[{{{(1/2)(First[(((5.326898482179484`*^62)/(a[t]))-1)/.s1]+First[(((5.326898482179484`*^62)/(a[t]))-1)/.sinf])},{First[(((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))))/.s1]-First[(((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))))/.sinf]}}}],{t,1,(10^62)},PlotRange->{{1,-2},All},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, (Subscript[Higgs, MAX])])-(Subscript[ω, (Subscript[Higgs, MIN])])",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.6,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, (Subscript[Higgs, MAX])])-(Subscript[ω, (Subscript[Higgs, MIN])])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]

Export["omegaHiggsMAX-omegaHiggsMIN.pdf",ωHiggsdiff]

SystemOpen[DirectoryName[AbsoluteFileName["omegaHiggsMAX-omegaHiggsMIN.pdf"]]]

1.5358315144272005`*^60
1.5358305349170835`*^60

Evaluate[{{{(1/2)(First[(((5.326898482179484`*^62)/(a[t]))-1)/.s1]+First[(((5.326898482179484`*^62)/(a[t]))-1)/.sinf])},{First[(((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))))/.s1]-First[(((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))))/.sinf]}}}]

{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}/.{t->1.5358315144272005`*^60}/.s1

-0.8580171149039496+1

0.1419828850960504

{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}/.{t->1.5358305349170835`*^60}/.sinf

-0.8580171797712483+1

0.14198282022875175

{{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}/.{t->1.5358315144272005`*^60}/.s1}[[1]][[1]][[1]]-{{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}/.{t->1.5358305349170835`*^60}/.sinf}[[1]][[1]][[1]]

((0.1419828850960504+0.14198282022875175)/2)

0.14198285266240107

0.14198285266240107-0.1419828850960504

0.14198285266240107-0.14198282022875175

NumberForm[N[((0.1419828850960504+0.14198282022875175)/2),20],20]

s=NDSolve[{-((2a[t]a''[t])/((a'[t])^2))==1+(((a[t])^2)/((a'[t])^2))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))+(1/3)(((1.491710580279889`*^59)(10^67.7))/((a[t])^4))),-(1/2) ((a[t])^2) (6 a'[t] h'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^3)+h[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^2)+60516 ((10^(-124.8))))+2 h''[t]))==0,-(1/2) ((a[t])^2) (6 a'[t] A'[t]+a[t] (2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((A[t])^3)+A[t] (0.` +2.3952470578630415`*^-121 (E^((1/8) (((((A[t])^2)+((h[t])^2)))^2))) ((h[t])^2)+60516 ((10^(-124.8))))+2 A''[t]))==0,h[1]==1,h'[1]==0,A[1]==1,A'[1]==0,a[1]==1.491710580279889`*^59,a'[1]==14966.218638223512`},{h,A,a},{t,1,(10^62)},MaxSteps->∞]

{field1=Plot[Evaluate[{h[t],A[t]}/.s],{t,1,7×(10^61)},PlotRange->Full,PlotStyle->{Thick,Blue},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],Frame->True,FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["\!\(\*FractionBox[\(t\), \(\(\\ \\ \)\*SubscriptBox[\(t\), \(o\)]\)]\)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},ImageSize->Medium],field2=Plot[Evaluate[{h[t],A[t]}/.s],{t,1,7×(10^61)},PlotRange->{{1,7×(10^61)},{-0.5*(10^(-2)),2×(10^(-2))}},PlotStyle->{Thick,Blue},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],Frame->True,FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["\!\(\*FractionBox[\(t\), \(\(\\ \\ \)\*SubscriptBox[\(t\), \(o\)]\)]\)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},ImageSize->Medium],field3=Plot[Evaluate[{h[t],A[t]}/.s],{t,1,7×(10^61)},PlotRange->Automatic,PlotStyle->{Thick,Blue},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],Frame->True,FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["\!\(\*FractionBox[\(t\), \(\(\\ \\ \)\*SubscriptBox[\(t\), \(o\)]\)]\)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},ImageSize->Medium]}

{Field2=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{h[t]}}/.s],{t,1,(10^62)},PlotRange->{{1,-3},{-0.05,1.05}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},AxesOrigin->{3,-0.05},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Large],Field4=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{h[t]}}/.s],{t,1,(10^62)},PlotRange->{{1,0.8},{-0.2*(10^(-1)),0.9*(10^(-1))}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.7}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Large]}

Fields=GraphicsGrid[{{Field1=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{h[t]}}/.s],{t,1,(10^62)},PlotRange->{{1.5,-10},{-0.05,1.05}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},AxesOrigin->{3751,-0.05},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.3,0.15}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],Field3=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{h[t]}}/.s],{t,1,(10^62)},PlotRange->{{1,-1},{-0.05,1}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.3,0.15}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[η, 2]) / (Subscript[χ, 2])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]}},AspectRatio->(1/GoldenRatio),Frame->False,ImageSize->{1500,750/GoldenRatio}]

Export["Fields-Z.eps",Fields]

{scaleparameter=Plot[Evaluate[{a[t]}/.s],{t,1,(10^62)},PlotRange->{{1,3*(10^60)},{(10^60),1.2*(10^63)}},PlotStyle->{Thick,Blue},AxesOrigin->{0,5.593914676049584`*^62},PlotLegends->Placed[{Table[Text[Style["Scale factor a(t)",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],Frame->True,FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["\!\(\*FractionBox[\(t\), \(\(\\ \\ \)\*SubscriptBox[\(t\), \(o\)]\)]\)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["a(t)",FontSize->p]],{p,{22}}][[1]]},ImageSize->Large],scaleparameterZ=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{a[t]}}/.s],{t,1,(10^62)},PlotRange->{{1,-1},{(10^59),2*(10^63)}},AxesOrigin->{1,(10^59)},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["Scale factor",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Scale factor",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Large]}

{ω=Plot[Evaluate[{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}/.s],{t,1,(10^62)},PlotRange->All,PlotStyle->{Thick,Blue},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, Higgs])",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],Frame->True,FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["\!\(\*FractionBox[\(t\), \(\(\\ \\ \)\*SubscriptBox[\(t\), \(o\)]\)]\)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["(Subscript[ω, Higgs])",FontSize->p]],{p,{22}}][[1]]},ImageSize->Large],ωeff=Plot[Evaluate[{(1/(3(((((a'[t])/(a[t]))))^2)))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))+((1.491710580279889`*^59((10^67.7)))/(3((a[t])^4))))}/.s],{t,1,(10^62)},AxesOrigin->{1,-(1/3)},PlotRange->{{1,4*(10^60)},{-1.1,0.2}},PlotStyle->{Thick,Blue},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, eff])",FontSize->p]],{p,{22}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],Frame->True,FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["\!\(\*FractionBox[\(t\), \(\(\\ \\ \)\*SubscriptBox[\(t\), \(o\)]\)]\)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["(Subscript[ω, eff])",FontSize->p]],{p,{22}}][[1]]},ImageSize->Large]}

ωHiggs=GraphicsGrid[{{ωHiggs1=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}}/.s],{t,1,(10^62)},PlotRange->{{1,-10},{-1.025,-0.8}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, Higgs])=((Subscript[P, Higgs])/(Subscript[ρ, Higgs]))",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.5,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, Higgs])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],ωHiggs2=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))/((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}}/.s],{t,1,(10^62)},PlotRange->{{1,-2},{-1.025,-0.8}},AxesOrigin->{-2,-1.025},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, Higgs])=((Subscript[P, Higgs])/(Subscript[ρ, Higgs]))",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.5,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, Higgs])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]}},AspectRatio->(1/GoldenRatio),Frame->False,ImageSize->{1500,750/GoldenRatio}]

Export["omegaHiggs-Z.eps",ωHiggs]

ωeff=GraphicsGrid[{{ωeff1=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{(1/(3(((((a'[t])/(a[t]))))^2)))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))+((1.491710580279889`*^59((10^67.7)))/(3((a[t])^4))))}}/.s],{t,1,(10^62)},PlotRange->{{1,-3571},{-1.025,0.5}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, eff])=(Subscript[Ω, M])(Subscript[ω, M])+(Subscript[Ω, RM])(Subscript[ω, RM])+(Subscript[Ω, Higgs])(Subscript[ω, Higgs])",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, eff])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],ωeff2=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{(1/(3(((((a'[t])/(a[t]))))^2)))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)-(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))+((1.491710580279889`*^59((10^67.7)))/(3((a[t])^4))))}}/.s],{t,1,(10^62)},PlotRange->{{1,-2},{-1.025,0}},AxesOrigin->{1,-(1/3)},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["(Subscript[ω, eff])=(Subscript[Ω, M])(Subscript[ω, M])+(Subscript[Ω, RM])(Subscript[ω, RM])+(Subscript[Ω, Higgs])(Subscript[ω, Higgs])",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.9}], {1, 0.8}}],PlotStyle->{{Blue,Thick}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["(Subscript[ω, eff])",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]}},AspectRatio->(1/GoldenRatio),Frame->False,ImageSize->{1500,750/GoldenRatio}]

Export["omegaeff-Z.eps",ωeff]

{ρ=Plot[Evaluate[{(1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))),((10^67.7)/((a[t])^3)),((1.491710580279889`*^59((10^67.7)))/((a[t])^4)),3(((((a'[t])/(a[t]))))^2)}/.s],{t,0,4×(10^60)},PlotRange->{{1,4×(10^60)},{(10^(-123)),2*(10^(-120))}},PlotStyle->{{Thick,Black,Dashing[Tiny]},{Thick,Green,Dashing[Small]},{Thick, Red,Dashing[Medium]},{Thick,Blue,Dashing[Large]},{Thick,Magenta},{Thick,Pink},{Orange,Dashed}},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) and (Subscript[χ, 2]) energy density",FontSize->p]],{p,{18}}][[1]],Table[Text[Style["Non-Relativistic Matter",FontSize->p]],{p,{18}}][[1]],Table[Text[Style["Relativistic Matter",FontSize->p]],{p,{18}}][[1]],Table[Text[Style["Critical energy density",FontSize->p]],{p,{18}}][[1]]},{Scaled[{1,0.8}], {1, 0.8}}],Frame->True,FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["\!\(\*FractionBox[\(t\), \(\(\\ \\ \)\*SubscriptBox[\(t\), \(o\)]\)]\)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{22}}][[1]]},ImageSize->Large],Ω=Plot[Evaluate[{(1/(3(((((a'[t])/(a[t]))))^2)))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))),(1/(3(((((a'[t])/(a[t]))))^2)))(((10^67.7)/((a[t])^3))),(1/(3(((((a'[t])/(a[t]))))^2)))(((1.491710580279889`*^59*(10^67.7))/((a[t])^4)))}/.s],{t,1,2.5*(10^60)},AxesOrigin->{0,0},PlotStyle->{{Thick,Black,Dashing[Small]},{Thick,Green,Dashing[Medium]},{Thick,Red,Dashing[Large]},{Blue,Thick}},Frame->True,FrameStyle->Directive[15],PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) and (Subscript[χ, 2]) Relic Energy Density",FontSize->p]],{p,{18}}][[1]],Table[Text[Style["Non-Relativistic Matter Relic Denstiy",FontSize->p]],{p,{18}}][[1]],Table[Text[Style["Relativistic Matter Relic Density",FontSize->p]],{p,{18}}][[1]]},{Scaled[{1,0.5}], {1, 0.5}}],FrameLabel->{Table[Text[Style["\!\(\*FractionBox[\(t\), \(\(\\ \\ \)\*SubscriptBox[\(t\), \(o\)]\)]\)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Relic energy density",FontSize->p]],{p,{22}}][[1]]},ImageSize->Large]}

densities=GraphicsGrid[{{ρcrit=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{3(((((a'[t])/(a[t]))))^2)}}/.s],{t,1,(10^62)},PlotRange->Full,AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["Critical Energy density",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.9}], {1, 0.8}}],PlotStyle->{{Thick,Black,Dashing[Tiny]}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],ρHiggs=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{(1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))}}/.s],{t,1,(10^62)},PlotRange->Full,AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["Higgs Energy density",FontSize->p]],{p,{28}}][[1]]},{Scaled[{0.9,0.9}], {1, 0.8}}],PlotStyle->{{Thick,Green,Dashing[Small]}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Large]},{ρmatter=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((10^67.7)/((a[t])^3))}}/.s],{t,1,(10^62)},PlotRange->Full,AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["NR matter energy density",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.9}], {1, 0.8}}],PlotStyle->{{Thick, Red,Dashing[Medium]}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Large],ρradiation=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((1.491710580279889`*^59((10^67.7)))/((a[t])^4))}}/.s],{t,1,(10^62)},PlotRange->Full,AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["R matter energy density",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.9}], {1, 0.8}}],PlotStyle->{{Thick,Blue,Dashing[Large]}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Large]}},AspectRatio->(1/GoldenRatio),Frame->False,ImageSize->{1500,1500/GoldenRatio}]

Export["densities-Z.eps",densities]

densities1=GraphicsGrid[{{ρcrit1=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{3(((((a'[t])/(a[t]))))^2)}}/.s],{t,6.015*(10^59),9*(10^60)},PlotRange->{{1,-1},{4*(10^(-120)),4*(10^(-121))}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["Critical Energy density",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],PlotStyle->{{Thick,Black,Dashing[Tiny]}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],ρHiggs1=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{(1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8))))}}/.s],{t,6.015*(10^59),9*(10^60)},PlotRange->{{1,-1},{4*(10^(-121)),1.15*(10^(-120))}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["Higgs Energy density",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],PlotStyle->{{Thick,Green,Dashing[Small]}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]},ρmatter1={ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((10^67.7)/((a[t])^3))}}/.s],{t,6.015*(10^59),3.5*(10^60)},PlotRange->{{1,-1},{(10^(-122)),3.5*(10^(-120))}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["Matter Energy density",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],PlotStyle->{{Thick, Red,Dashing[Medium]}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full],ρradiation1=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{((1.491710580279889`*^59((10^67.7)))/((a[t])^4))}}/.s],{t,6.015*(10^59),3.5*(10^60)},PlotRange->{{1,-1},{2*(10^(-126)),2*(10^(-123))}},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotLegends->Placed[{Table[Text[Style["Radiation Energy density",FontSize->p]],{p,{28}}][[1]]},{Scaled[{1,0.65}], {1, 0.8}}],PlotStyle->{{Thick,Blue,Dashing[Large]}},FrameStyle->Directive[22],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{28}}][[1]],Table[Text[Style["Energy density",FontSize->p]],{p,{28}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]}},AspectRatio->(1/GoldenRatio),ImageSize->{1500,1500/GoldenRatio}]

Export["densities1-Z_1.eps",densities1]

RDHiggs=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{(1/(3(((((a'[t])/(a[t]))))^2)))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}}/.s],{t,1×(10^59),1*(10^62)},PlotRange->All,AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotStyle->{{Thick,Black,Dashing[Small]}},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) and (Subscript[χ, 2]) Relic Density",FontSize->p]],{p,{18}}][[1]]},{Scaled[{0.4,0.65}], {1, 0.5}}],FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Relic density",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]

RDM=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{(1/(3(((((a'[t])/(a[t]))))^2)))(((10^67.7)/((a[t])^3)))}}/.s],{t,1×(10^59),1*(10^62)},PlotRange->All,AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotStyle->{{Thick,Green,Dashing[Medium]}},PlotLegends->Placed[{Table[Text[Style["Matter Relic Denstiy",FontSize->p]],{p,{18}}][[1]]},{Scaled[{0.38,0.6}], {1, 0.5}}],FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Relic density",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]

RDRM=ParametricPlot[Evaluate[{{((5.326898482179484`*^62)/(a[t]))-1},{(1/(3(((((a'[t])/(a[t]))))^2)))(((1.491710580279889`*^59*(10^67.7))/((a[t])^4)))}}/.s],{t,1×(10^59),1*(10^62)},PlotRange->All,AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotStyle->{{Thick,Red,Dashing[Large]}},PlotLegends->Placed[{Table[Text[Style["Radiation Relic Density",FontSize->p]],{p,{18}}][[1]]},{Scaled[{0.4,0.55}], {1, 0.5}}],FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["Redshift - Z",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Relic density",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]

RDHiggsMRM=Show[RDHiggs,RDM,RDRM]

Export["relicdensity-Z.eps",RDHiggsMRM]

RDHiggs1=ParametricPlot[Evaluate[{{Log[((5.326898482179484`*^62)/(a[t]))]},{(1/(3(((((a'[t])/(a[t]))))^2)))((1/2) ((A'[t])^2)+(1/2) ((h'[t])^2)+(2.3952470578630415`*^-121+2.3952470578630415`*^-121 (E^((((A[t])^4)/8)+(1/4) ((A[t])^2) ((h[t])^2)+(((h[t])^4)/8)))+15129 ((A[t])^2) ((10^(-124.8)))+15129 ((h[t])^2) ((10^(-124.8)))))}}/.s],{t,1,1*(10^62)},PlotRange->{{8.1806,-8.1806},{-0.1,1.1}},AxesOrigin->{7.75,-0.2},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotStyle->{{Thick,Black,Dashing[Small]}},PlotLegends->Placed[{Table[Text[Style["(Subscript[η, 2]) and (Subscript[χ, 2]) Relic Density",FontSize->p]],{p,{18}}][[1]]},{Scaled[{1,0.5}], {1, 0.5}}],FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["ln((Subscript[a, 0])/a)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Relic density",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]

RDM1=ParametricPlot[Evaluate[{{Log[((5.326898482179484`*^62)/(a[t]))]},{(1/(3(((((a'[t])/(a[t]))))^2)))(((10^67.7)/((a[t])^3)))}}/.s],{t,1,1*(10^62)},PlotRange->{{8.1806,-8.1806},{-0.1,1.1}},AxesOrigin->{7.75,-0.2},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotStyle->{{Thick,Green,Dashing[Medium]}},PlotLegends->Placed[{Table[Text[Style["Matter Relic Denstiy",FontSize->p]],{p,{18}}][[1]]},{Scaled[{1,0.5}], {1, 0.5}}],FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["ln((Subscript[a, 0])/a)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Relic density",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]

RDRM1=ParametricPlot[Evaluate[{{Log[((5.326898482179484`*^62)/(a[t]))]},{(1/(3(((((a'[t])/(a[t]))))^2)))(((1.491710580279889`*^59*(10^67.7))/((a[t])^4)))}}/.s],{t,1,1*(10^62)},PlotRange->{{8.1806,-8.1806},{-0.1,1.1}},AxesOrigin->{7.75,-0.2},AspectRatio->(1/GoldenRatio),ScalingFunctions->{"Reverse",None},PlotStyle->{{Thick,Red,Dashing[Large]}},PlotLegends->Placed[{Table[Text[Style["Radiation Relic Density",FontSize->p]],{p,{18}}][[1]]},{Scaled[{1,0.5}], {1, 0.5}}],FrameStyle->Directive[15],FrameLabel->{Table[Text[Style["ln((Subscript[a, 0])/a)",FontSize->p]],{p,{22}}][[1]],Table[Text[Style["Relic density",FontSize->p]],{p,{22}}][[1]]},Frame->True,FrameTicks->All,ImageSize->Full]

RDHiggsMRM1=Show[RDHiggs1,RDM1,RDRM1]

Export["relicdensity-Z_1.eps",RDHiggsMRM1]