Neff_SM.nb

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This notebook can be used to find the thermal history of the Universe in the \
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This code is based on Escudero 1812.05605 and 2001.04466. \
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The code works as follows:

1) Evaluate the Basic Modules Section. 
2) Evaluate the Standard Model Section. It takes ~\.1d20 s per example \
evaluation.
3) Evaluate the Standard Model with neutrino chemical potentials Section. It \
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Note that everything is in MeV Units but the rates, the Hubble parameter and \
time which are in seconds.\
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This Section loads the main common Modules: 
\t1) Thermodynamic Formulae 
\t2) Finite Temperature QED corrections
\t3) SM \[Nu]-\[Nu] and \[Nu]-e Interaction Rates
\t4) Constants and Parameters
\t
These modules are loaded from BasicModules.m. One can alternatively copy the \
content of BasicModules.nb here and load it locally.\
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       Charting`ScaledTicks[{Log, Exp}]}, GridLines -> {None, None}, 
     FrameTicks -> {{
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        Charting`ScaledFrameTicks[{Log, Exp}]}, {
        Charting`ScaledTicks[{Log, Exp}], 
        Charting`ScaledFrameTicks[{Log, Exp}]}}, DisplayFunction -> Identity, 
     Method -> {
      "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
       AbsolutePointSize[6], "ScalingFunctions" -> None}, DisplayFunction -> 
     Identity, DisplayFunction -> Identity, Ticks -> {Quiet[
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     AxesOrigin -> {-4.605170185988091, 0.}, FrameTicks -> {{Quiet[
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        Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[
         Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
        Charting`ScaledFrameTicks[{Log, Exp}]}}, GridLines -> {None, None}, 
     DisplayFunction -> Identity, PlotRangePadding -> {{
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        Scaled[0.02]}, {
        Scaled[0.05], 
        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
     DisplayFunction -> Identity, 
     Method -> {
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       AbsolutePointSize[6], "ScalingFunctions" -> None, 
       "ClippingRange" -> {{{-4.605170045013494, 2.3025849520194486`}, {
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     DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
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     AxesOrigin -> {0, 0}, CoordinatesToolOptions -> {"DisplayFunction" -> ({
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          Part[#, 1]], 
         Exp[
          Part[#, 2]]}& ), "CopiedValueFunction" -> ({
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          Part[#, 1]], 
         Exp[
          Part[#, 2]]}& )}, DisplayFunction :> Identity, 
     Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
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     Method -> {
      "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
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        Scaled[0.02]}, {
        Scaled[0.02], 
        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
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     TemplateBox[{
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       "\"\\!\\(\\*FractionBox[\\(T\[Gamma]\\), \\(T\[Nu]\[Mu]\\)]\\)\""}, 
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         StyleBox[
          PaneBox[
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               TagBox[
                GridBox[{{
                   GraphicsBox[{{
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
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                    EdgeForm[
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
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                    Dashing[{Small, Small}]], {
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1], 
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                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}}, 
                 GridBoxAlignment -> {
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                 AutoDelete -> False, 
                 GridBoxDividers -> {
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                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
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             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
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             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
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           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
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             RowBox[{
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                 RowBox[{
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                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
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                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
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                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
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                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
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                    FrontEnd`Private`$ColorSelectorInitialColor = 
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                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
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                    FrontEndResource["RGBColorValueSelector"], {
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                    "ClosingActions" -> {
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          "]]}, 
        Annotation[#, "Charting`Private`Tag$589601#2"]& ]}}, {}, {}}, {Ticks -> {
       Charting`ScaledTicks[{Log, Exp}], 
       Charting`ScaledTicks[{Log, Exp}]}, GridLines -> {None, None}, 
     FrameTicks -> {{
        Charting`ScaledTicks[{Log, Exp}], 
        Charting`ScaledFrameTicks[{Log, Exp}]}, {
        Charting`ScaledTicks[{Log, Exp}], 
        Charting`ScaledFrameTicks[{Log, Exp}]}}, DisplayFunction -> Identity, 
     Method -> {
      "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
       AbsolutePointSize[6], "ScalingFunctions" -> None}, DisplayFunction -> 
     Identity, DisplayFunction -> Identity, Ticks -> {Quiet[
        Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Quiet[
        Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& }, 
     AxesOrigin -> {-4.605170185988091, 0.}, FrameTicks -> {{Quiet[
         Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
        Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[
         Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
        Charting`ScaledFrameTicks[{Log, Exp}]}}, GridLines -> {None, None}, 
     DisplayFunction -> Identity, PlotRangePadding -> {{
        Scaled[0.02], 
        Scaled[0.02]}, {
        Scaled[0.05], 
        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
     DisplayFunction -> Identity, 
     Method -> {
      "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
       AbsolutePointSize[6], "ScalingFunctions" -> None, 
       "ClippingRange" -> {{{-4.605170045013494, 2.3025849520194486`}, {
        3.2111126820031084`*^-7, 0.33399644671996614`}}, {{-4.605170045013494,
         2.3025849520194486`}, {3.2111126820031084`*^-7, 
        0.33399644671996614`}}}}, DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
       FormBox["\"T\[Gamma](MeV)\"", TraditionalForm], None}, 
     AxesOrigin -> {0, 0}, CoordinatesToolOptions -> {"DisplayFunction" -> ({
         Exp[
          Part[#, 1]], 
         Exp[
          Part[#, 2]]}& ), "CopiedValueFunction" -> ({
         Exp[
          Part[#, 1]], 
         Exp[
          Part[#, 2]]}& )}, DisplayFunction :> Identity, 
     Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], 
     Method -> {
      "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
       AbsolutePointSize[6], "ScalingFunctions" -> None}, PlotRange -> 
     NCache[{{-4.605170185988091, 
         Log[10]}, {0., 0.33399644671996614`}}, {{-4.605170185988091, 
       2.302585092994046}, {0., 0.33399644671996614`}}], PlotRangeClipping -> 
     True, PlotRangePadding -> {{
        Scaled[0.02], 
        Scaled[0.02]}, {
        Scaled[0.02], 
        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
    FormBox[
     TemplateBox[{
      "\"\\!\\(\\*FractionBox[\\(T\[Gamma]\\), \\(T\[Nu]e\\)]\\)\"", 
       "\"\\!\\(\\*FractionBox[\\(T\[Gamma]\\), \\(T\[Nu]\[Mu]\\)]\\)\""}, 
      "LineLegend", DisplayFunction -> (FormBox[
        StyleBox[
         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {
                    LineBox[{{0, 10}, {40, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1], 
                    Dashing[{Small, Small}]], {
                    LineBox[{{0, 10}, {40, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1], 
                    Dashing[{Small, Small}]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}}, 
                 GridBoxAlignment -> {
                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                 AutoDelete -> False, 
                 GridBoxDividers -> {
                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
            "Grid"], Alignment -> Left, AppearanceElements -> None, 
           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
         False], TraditionalForm]& ), 
      InterpretationFunction :> (RowBox[{"LineLegend", "[", 
         RowBox[{
           RowBox[{"{", 
             RowBox[{
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"Opacity", "[", "1.`", "]"}], ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"Opacity", "[", "1.`", "]"}], ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 0, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 0, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 0, 1], Editable -> False, Selectable -> 
                    False], ",", 
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