The wave equation and redshift in Bianchi type I spacetimes

Sammanfattning: The thesis consists of two independent parts. In the first part, we show how the solution to the scalar wave equation on 3-torus-Bianchi type I spacetimes can be written as a Fourier decomposition. We present results on the behaviour of these Fourier modes and apply them to the case of 3-torus-Kasner spacetimes. In the second part, we first consider the solution to the scalar wave equation, with special initial data, as a model for light in Bianchi type I spacetimes. We show that the obtained redshift coincides with the cosmological redshift. We also consider the Cauchy problem for Maxwell's vacuum equations, with special initial data, in order to model light in Bianchi type I spacetimes. We calculate the redshift of the solution and show that, also in this case, the obtained redshift coincides with the cosmological redshift.