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Z4co: add Z4c_vars.wl
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lwJi committed Jul 1, 2024
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(* ::Package:: *)

(* Z4c_vars.wl *)

(* (c) Liwei Ji, 07/2024 *)

(***********************)

(* Evolution Variables *)

(***********************)

DefTensors[{chi[], PrintAs -> "\[Chi]"}, {gamt[-i, -j], Symmetric[{-i,
-j}], PrintAs -> "\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, {exKh[],
PrintAs -> "\!\(\*OverscriptBox[\(K\), \(^\)]\)"}, {exAt[-i, -j], Symmetric[
{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(A\), \(~\)]\)"}, {trGt[i],
PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, {Theta[
], PrintAs -> "\[CapitalTheta]"}, {alpha[], PrintAs -> "\[Alpha]"}, {beta[
i], PrintAs -> "\[Beta]"}];

(*************************)

(* Other Input Variables *)

(*************************)

DefTensors[{dchi[-k], PrintAs -> "\[PartialD]\[Chi]"}, {dgamt[-k, -i, -
j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"
}, {dexKh[-k], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(K\), \(^\)]\)"
}, {dexAt[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(A\), \(~\)]\)"
}, {dtrGt[-k, i], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"
}, {dTheta[-k], PrintAs -> "\[PartialD]\[CapitalTheta]"}, {dalpha[-k],
PrintAs -> "\[PartialD]\[Alpha]"}, {dbeta[-k, i], PrintAs -> "\[PartialD]\[Beta]"
}];

DefTensors[{ddchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Chi]"
}, {ddgamt[-l, -m, -i, -j], GenSet[Cycles[{1, 2}], Cycles[{3, 4}]], PrintAs
-> "\[PartialD]\[PartialD]\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"},
{ddalpha[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Alpha]"
}, {ddbeta[-i, -j, k], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Beta]"
}];

DefTensors[{eTtt[], PrintAs -> "\!\(\*SubscriptBox[\(T\), \(tt\)]\)"},
{eTt[-i], PrintAs -> "\!\(\*SubscriptBox[\(T\), \(t\)]\)"}, {eT[-i, -j],
PrintAs -> "T"}];

(**************************)

(* Intermediate Variables *)

(**************************)

DefTensors[{invgamt[i, j], Symmetric[{i, j}], PrintAs -> "\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"
}, {invgam[i, j], Symmetric[{i, j}], PrintAs -> "\[Gamma]"}, {gam[-i, -
j], Symmetric[{-i, -j}], PrintAs -> "\[Gamma]"}, {GtDDD[-k, -i, -j], Symmetric[
{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"
}, {GtDDU[-k, -i, j], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"
}, {Gt[k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"
}, {trGtd[i], PrintAs -> "(\!\(\*SubscriptBox[OverscriptBox[\(\[CapitalGamma]\), \(~\)], \(d\)]\))"
}, {exAtUU[i, j], Symmetric[{i, j}], PrintAs -> "\!\(\*OverscriptBox[\(A\), \(~\)]\)"
}];

DefTensors[{tDtDchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(D\), \(~\)]\)\!\(\*OverscriptBox[\(D\), \(~\)]\)\[Chi]"
}, {DDalpha[-i, -j], Symmetric[{-i, -j}], PrintAs -> "DD\[Alpha]"}];

DefTensors[{Rtchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[OverscriptBox[\(R\), \(~\)], \(\[Chi]\)]\)"
}, {Rt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(R\), \(~\)]\)"
}, {R[-i, -j], Symmetric[{-i, -j}]}, {trR[], PrintAs -> "R"}];

(* Matter *)

DefTensors[{rho[], PrintAs -> "\[Rho]"}, {Sm[-i], PrintAs -> "S"}, {Ss[
-i, -j], Symmetric[{-i, -j}], PrintAs -> "S"}, {trSs[], PrintAs -> "S"}
];

(* Constraints *)

DefTensors[{dexAtUU[-k, i, j], Symmetric[{i, j}], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(A\), \(~\)]\)"
}];

DefTensors[{ZtC[i], PrintAs -> "\!\(\*OverscriptBox[\(Z\), \(~\)]\)"},
{HC[], PrintAs -> "H"}, {MtC[i], PrintAs -> "\!\(\*OverscriptBox[\(M\), \(~\)]\)"
}];

(************)

(* Constant *)

(************)

DefConstantSymbol[cpi, PrintAs -> "\[Pi]"];

DefConstantSymbol[ckappa1, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(1\)]\)"
];

DefConstantSymbol[ckappa2, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(2\)]\)"
];

DefConstantSymbol[cmuL, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(L\)]\)"
];

DefConstantSymbol[cmuS, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(S\)]\)"
];

DefConstantSymbol[ceta, PrintAs -> "\[Eta]"];

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