Programs and Data for "Future singularities if the universe underwent Starobinsky inflation in the past", Physical Review D95, 044012 (2017)

Fortran Program for Fig. 1 written by Bradley Hicks and Paul Anderson

Note that this Fortran program uses for its ordinary differential equation solver three programs from ODEPACK which can be accessed at http://www.netlib.org/odepack/ . The programs are opkdmain.f, opkda1.f, and opkda2.f

Note also that it uses two input files called radbr.in and radbh.ad.cfg.

Data for Figure 1. m = 0.25, m = 0.5, m = 1, and m = 2. In these files there are columns for various parts of the energy density. The program prints out a file called rho.out and then for each run used that file has been renamed. For details on the columns which do not contribute to the curves in Fig. 1, see the program. The first column is the time, t. The fifth column is the energy density for the massless conformally coupled scalar field. The sixth column is the energy density for the massive conformally coupled scalar field. Note that the m = 0 curve in Fig. 1 comes from any of these files.

Below are links to the Maple programs written by John Einhorn, Andrew Lundeen, and Eric Carlson, that generated the curves for Figures 2-5 along with the data for those curves. Note that the best way to download one of the Maple programs is to right click on the link and save it.

Maple program for Figure 2, Data for Figure 2

Maple program for Figure 3, Data for Figure 2

Maple program for the left plot of Figure 4, Data for the left plot of Figure 4

Maple program for the right plot of Figure 4, Data for the right plot of Figure 4

Maple program for Figure 5, Data for Figure 5

For Figures 2 and 3 the first, third, and fifth columns are times for the second, fourth, and sixth columns respectively. The second column is the classical solution, the fourth is the solution to the order reduced equations, and the sixth is the solution to the full semiclassical backreaction equations. For the left plot in Figure 4, the first column is the time and the second is the energy density. For the right plot in Figure 4, the first column is the time and the second column is the pressure. For Figure 5, the first and third columns are the time. The second column is the pressure for the solution to the semiclassical backreaction equations and the fourth column is the pressure for the classical solution.

^M

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).