### Programs and Data for "Decay of the de Sitter vacuum", Physical Review D....

The data for Figure 1 is in eight files, each of which contains data for a given curve: File 1, File 2, File 3, File 4, File 5, File 6, File 7, File 8 See the Mathematica program for details. The data is generated in the above Mathematica program and each data file corresponds to a curve or segment of a curve in the figure. See the Mathematica file for details.

The data for Figure 2 has four columns. The first is the value of the time u, the second is the adiabatic particle number obtained using the zeroth order WKB approximation, the third is the adiabatic particle number obtained using the second order WKB approximation, and the fourth is the superadiatibatic particle number.

The data for Figure 3 is in four files, each of which contains data for a particular curve. The three main ones are T = 20,T = 40,T = 60. The fourth is not given here since it just gives the dashed curve in the figure which is the constant value of |B|^2 for a constant electric field.

The data files for the plots are: b=H, t1=20; b=H, t1=40;

First Fortran Program Used to generate data for Figures 5 - 7. Note that the program calls a subroutine odebs which comes from the book Numerical Recipes and which therefore cannot be given here. But any differential equation solver could be used to replace it.

Output from the first Fortran program is read into the second one which calculates the various quantities which are plotted in these figures.

The data files for the curves in Figure 5 are: t1=10, t1=20, t1=30, t1=40. The columns in the date files are k, |B|^2, integrand for the rate integral,integrand for the nonoscillating part of the integral for the electric current, integrand for the oscillating part of the electric current.

Data for the rates in Figure 6. The first column is T/2 in units where eE = 1. The second column is the rate in the same units. The fit to the data that was used for the plot is that the rate = 10^(-4)*(2.96936+1.0745/T)

Data for the left panel in Figure 7. The first column is the time t, the second is the nonoscillating part of the current, the third is the oscillating part of the current shown in the left panel of Figure 7, and the fourth is the total current.

Data for the right panel in Figure 7. The first column is T/2 and the second is the nonoscillating part of the current. The fit for the nonoscillating part of the current that was used is that it is equal to -0.000196001 + 0.000148282 T.

The data for Figure 8 is in 10 files each of which contains data for a segment of a curve. See the Mathematica program for details. The files are

File 1, File 2, File 3, File 4, File 5, File 6, File 7, File 8,File 9, File 10. The plot also contains a vertical line, a horizontal line, and x's where the complex turning points are.

The data for Figure 9 is in 16 files each of which contains data for a segment of a curve. See the Mathematica program for details. The files are File 1, File 2, File 3, File 4, File 5, File 6, File 10, File 11, File 12, File 13, File 14, File 15, File 16, File 17, File 18,File 19. Note that files 7, 8, 9 generated by the Mathematica program were not used in the plot and some of the files had the vertical axis shifted by one or more multiples of pi when they were plotted. The plot also contains a vertical line, a horizontal line, and x's where the complex turning points are.

The data files for the curves in the plot are: particle number using first order WKB, particle number using second order WKB, superadiabatic particle number.

Fortran Program Used to generate data for Figure 11. Note that the program calls a subroutine odeint which comes from the book Numerical Recipes and which therefore cannot be given here. But any differential equation solver could be used to replace it. Here is a quadruple precision version.

The data files for the curves in the plot are: T = 20, ,T = 40, and T=60 in terms of scaled variables.

Data for Figures 12 and 13. The first column is the value of the scale factor at which the Bogolubov coefficients were computed by matching with the flat space mode functions. The second column is the time u at which the matching occurred. The next column is the value of k, then the zeroth order frequency Sqrt[k^2/a^2+m^2], followed by |B|^2, the integrand for the integral used to compute the rate, and the integrand for the integral used to compute the energy density of the field. The third and fifth columns were plotted in Figure 12 and the third and sixth columns were plotted in Figure 13.

The type of fortran program that converts the data into the scaled version which was used for Figures 14 and 15. More than one version of this program exists but they all have the same basic structure.

Fortran program used to generate data for Figures 16 and 17. Note that this program takes data generated using the program referenced above which is used to compute the Bogolubov coefficients for the two-parameter quasi-de Sitter profile and calculates the rate of vacuum decay which is plotted in Figure 16 and the expectation value of the energy density and pressure at late times when the expansion has effectively ceased. The oscillating part of the expectation value of the pressure is plotted in Figure 17.

Data for Figure 17. The first column is the time u, the second is the nonoscillating part of the pressure, the third part is the oscillating part of the pressure which is what is plotted in Figure 17, and the fourth column is the total pressure.

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 Some of the work referenced on this page was supported in part by the National Science Foundation under grant numbers PHY-0856050, PHY-1308325, and PHY-1505875.  Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).