Week 1: freeze out - adam-coogan/GRAPPA_Student_Seminar_2019 GitHub Wiki

In week 1, you will be producing scripts for calculating the thermal freeze-out of Dark Matter particles.

Outputs

  • Assume freeze-out takes place instantaneously. This is the approximation Gamma(T_fo) ~ H(T_fo) discussed in lecture.
    • Plot the present-day abundance of hot dark matter (where T_fo >> m) for different masses and cross sections. How does it scale with these variables?
    • Do the same for cold dark matter (T_fo << m).
  • In reality, freeze-out does not happen instantaneously. Write a solver for the cold dark matter relic abundance that takes this into account. (See eg Steigman et al 2012.)
    • Create a plot for a few different DM masses and cross sections demonstrating the freeze-out process, showing the quantity Y=n/s as a function of the temperature the temperature variable x=m/T.
    • Show the value of x_fo=m/T_fo estimated from instantaneous freeze-out on this plot.

Suggestions

  • Write functions to calculate the Hubble constant and g_{*S} as a function of temperature.
  • Write functions to calculate the equilibrium number density of particles as a function of temperature (for the relativistic and non-relativistic cases).

References