NuScalar.nb

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This notebook can be used to find the thermal history of the Universe in the \
presence of a very light and weakly coupled neutrinophilic scalar. Relevant \
equations and details can be found in Escudero 2001.04466. \
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The code works as follows: 

1) Evaluate the Basic Modules Section. 
2) Evaluate the Neutrinophilic Scalar Section. It takes ~40 secs per example \
evaluation.

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.\
\>", "Text",
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Hubble Parameter and total Energy and Pressure of the Universe\
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Func\[Phi]Mless[\[CapitalGamma]eff_,m\[Phi]_,Tminrat_]: \
\[LineSeparator]Computes the themodynamic evolution assuming m\[Phi] = 0 up \
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Func\[Phi]Thermo[\[CapitalGamma]eff_,m\[Phi]_]:\nComputes the themodynamic \
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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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        Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& }, 
     AxesOrigin -> {7.428034415120802, -3.0557610918180265`}, 
     FrameTicks -> {{Quiet[
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        Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[
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        Charting`ScaledFrameTicks[{Log, Exp}]}}, GridLines -> {None, None}, 
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        Scaled[0.02]}, {
        Scaled[0.05], 
        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
     DisplayFunction -> Identity, 
     Method -> {
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       "ClippingRange" -> {{{7.428034655335118, 
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     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
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     AxesOrigin -> {7.428034415120802, 0}, 
     CoordinatesToolOptions -> {"DisplayFunction" -> ({
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         Exp[
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         Exp[
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     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
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     Method -> {
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     PlotRange -> {{7.428034415120802, 
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     PlotRangeClipping -> True, PlotRangePadding -> {{
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        Scaled[0.02]}, {
        Scaled[0.02], 
        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
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       "\"\[LeftBracketingBar]\\!\\(\\*FractionBox[\\(T\[Nu]\\), \\(T\[Gamma]\
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       "\"\[LeftBracketingBar]\\!\\(\\*FractionBox[\\(T\[Phi]\\), \
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
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                    AbsoluteThickness[1.6], 
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                    ImagePadding -> Automatic, 
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                    GrayLevel[0]]], 
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                    GrayLevel[0]]], 
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                    Opacity[1.], 
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                    ImagePadding -> Automatic, 
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                 AutoDelete -> False, 
                 GridBoxDividers -> {
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             GridBoxItemSize -> {
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                    StyleBox[
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                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
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                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
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                    AbsoluteCurrentValue[Magnification]}]], 
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                    RowBox[{"0", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
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                    FrontEnd`Private`$ColorSelectorInitialColor = 
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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 -> {
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     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}, 
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        Scaled[0.02]}, {
        Scaled[0.05], 
        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
     DisplayFunction -> Identity, 
     Method -> {
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     DisplayFunction -> Identity, AspectRatio -> 
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     AxesLabel -> {
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     AxesOrigin -> {0, -5.379403156495451}, 
     CoordinatesToolOptions -> {"DisplayFunction" -> ({
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         Exp[
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     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
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     Method -> {
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        Scaled[0.02]}, {
        Scaled[0.02], 
        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
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                    GrayLevel[0]]], 
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                    Dashing[{0, Small}]], {}}}, AspectRatio -> Full, 
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                    ImagePadding -> Automatic, 
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                    Opacity[1.], 
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                 GridBoxDividers -> {
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             GridBoxItemSize -> {
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        Annotation[#, "Charting`Private`Tag$1947024#3"]& ]}}, {}, {}}, {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 -> {7.428034415120802, -4.859788804246675}, 
     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" -> {{{7.428034655335118, 
        19.198535652653945`}, {-14.140867068529136`, -2.54109558113583}}, {{
        7.428034655335118, 
        19.198535652653945`}, {-4.859788804246675, -2.54109558113583}}}}, 
     DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
       FormBox["\"t(s)\"", TraditionalForm], None}, 
     AxesOrigin -> {7.428034415120802, -4.859788804246675}, 
     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 -> {{7.428034415120802, 
      19.19853589286826}, {-4.859788804246675, -2.54109558113583}}, 
     PlotRangeClipping -> True, PlotRangePadding -> {{
        Scaled[0.02], 
        Scaled[0.02]}, {
        Scaled[0.02], 
        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
    FormBox[
     TemplateBox[{
      "\"\\!\\(\\*FractionBox[\\(\[Rho]\[Phi]\\), SuperscriptBox[\\(T\[Gamma]\
\\), \\(4\\)]]\\)|max\"", 
       "\"\\!\\(\\*FractionBox[\\(\[Rho]\[Phi]\\), \
SuperscriptBox[\\(T\[Gamma]\\), \\(4\\)]]\\)\"", 
       "\"\\!\\(\\*FractionBox[\\(\[Rho]\[Nu]\\), SuperscriptBox[\\(T\[Gamma]\
\\), \\(4\\)]]\\)\""}, "LineLegend", DisplayFunction -> (FormBox[
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         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0], 
                    Dashing[{0, Small}]], {
                    LineBox[{{0, 10}, {40, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0], 
                    Dashing[{0, Small}]], {}}}, 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], 
                    Dashing[{Small, Small}], 
                    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], 
                    Dashing[{Small, Small}], 
                    RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {
                    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]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {40, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, 
                 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[{
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                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
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                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "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`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
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                    RGBColor[0, 1, 0], Editable -> False, Selectable -> 
                    False], ",", 
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                    RowBox[{"{", 
                    RowBox[{"0", ",", "Small"}], "}"}], "]"}]}], "]"}], ",", 
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                 RowBox[{
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                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   RowBox[{"Dashing", "[", 
                    RowBox[{"{", 
                    RowBox[{"Small", ",", "Small"}], "}"}], "]"}], ",", 
                   InterpretationBox[
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                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    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 -> 
                    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$, All, Expression]; 
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                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
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