The cosmological constant
Show that a nonzero (infinite!) vacuum energy density of a quantum field redefines the cosmological constant in Einstein’s equations.
Discuss how the solution describing the evolution of a homogeneous and isotropic Universe changes depending on the contributions of fermion and boson fields to the vacuum energy.
Study the literature on modern experimental measurements of the cosmological constant in the model of a homogeneous and isotropic Universe. State what properties a system must have to explain the observed accelerated expansion of the Universe.
Consider the simplest supersymmetric model, the Wess–Zumino model [1], which contains one complex scalar \(\phi\) and one Majorana fermion \(\psi\). Obtain the mean vacuum energy density. Does supersymmetry solve the cosmological constant problem?
References
1 Wess, Julius, Zumino, Bruno, Supergauge transformations in four dimensions, Nucl. Phys. B 70 39–50 (1974) https://doi.org/10.1016/0550-3213(74)90355-1