(* This computes plots for the Electric field part of the perturbations of de Sitter paper.  We begin with the mode functions. *)

f0 = Exp[-I*u^2/4]*Hypergeometric1F1[1/4+I*lambda/2,1/2,I*u^2/2]

f1 = u*Exp[-I*u^2/4]*Hypergeometric1F1[3/4+I*lambda/2,3/2,I*u^2/2]

(* Emil uses the factor of 1/(4 lambda)^(1/4) *)
upsreal = 1/(4*lambda)^(1/4)*f0

N[upsreal/.{u->1,lambda->5}]

Plot[Re[upsreal/.{lambda->5}],{u,-10,10}]

upsimag = 1/(4*lambda)^(1/4)*Sqrt[lambda]*f1

Plot[upsimag/. {lambda ->1},{u,-10,10}]

ups = upsreal-I*upsimag

ups2 = ups^2

upsabs2 = Abs[ups]^2

Plot[upsabs2/. {lambda ->5},{u,-10,10}]

AbsUps= upsreal^2 + upsimag^2;

Plot[AbsUps/. {lambda ->5},{u,-10,10}]

Plot[u*(upsabs2/.{lambda->5}),{u,-100,100}]

Plot[u*(upsabs2/.{lambda->1}),{u,-20,20}]

Plot[u*((upsabs2-1/Sqrt[u^2+4 lambda])/.{lambda->0.1}),{u,-20,20}]

t1 = u*(upsabs2/.{lambda->1});

delta = 1/100

Table1 = Table[{N[-20+j*delta],N[t1/.{u->(-20+j*delta)}]},{j,0,4000}];

Table1[[4001,1]]

t2 = u*(upsabs2/.{lambda->5});

Table2 = Table[{N[-20+j*delta],N[t2/.{u->(-20+j*delta)}]},{j,0,4000}];

t3 = u*upsimag^2;

Export["C:\\Users\\anderson\\Research\\de Sitter States\\uupsabs2_lam_1.dat",Table1]

Export["C:\\Users\\anderson\\Research\\de Sitter States\\uupsabs2_lam_5.dat",Table2]

t3 = u*(Re[ups2/.{lambda->1}]);

Table3 = Table[{N[-10+j*delta],Re[N[t3/.{u->(-10+j*delta)}]]},{j,0,2000}];

Table3[[1,2]]

Export["C:\\Users\\anderson\\Research\\de Sitter States\\uupsre2_lam_1.dat",Table3]

t4 = u*(Re[ups2/.{lambda->1/10}]);

Table4 = Table[{N[-10+j*delta],Re[N[t4/.{u->(-10+j*delta)}]]},{j,0,2000}];

Export["C:\\Users\\anderson\\Research\\de Sitter States\\uupsre2_lam_0p1.dat",Table4]

t5 = u*(Im[ups2/.{lambda->1}]);

Table5 = Table[{N[-10+j*delta],Re[N[t5/.{u->(-10+j*delta)}]]},{j,0,2000}];

Table5[[1,2]]

Export["C:\\Users\\anderson\\Research\\de Sitter States\\uupsim2_lam_1.dat",Table5]

t6 = u*(Im[ups2/.{lambda->1/10}]);

Table6 = Table[{N[-10+j*delta],Re[N[t6/.{u->(-10+j*delta)}]]},{j,0,2000}];

Export["C:\\Users\\anderson\\Research\\de Sitter States\\uupsim2_lam_0p1.dat",Table6]

N[-Exp[-Pi*0.1]]

Table6a = Table[{N[-10+j*delta],-0.7304026910486456},{j,0,2000}];

N[-Exp[-Pi]]

Table5a = Table[{N[-10+j*delta],-0.04321391826377226},{j,0,2000}];

Export["C:\\Users\\anderson\\Research\\de Sitter States\\table5a.dat",Table5a]

Export["C:\\Users\\anderson\\Research\\de Sitter States\\table6a.dat",Table6a]