Week 1: freeze out
Adam Coogan edited this page Jun 4, 2019
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In week 1, you will be producing scripts for calculating the thermal freeze-out of Dark Matter particles.
- 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.
- 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).
- Profumo 2012 sec 2.2
- Steigman et al 2012 sec II-C
- Lisanti 2015 sec 2
- Gondolo & Gelmini 1991