We have made many simplifying assumptions in this chapter to demonstrate the strong connection to the principles and techniques developed in the preceding 27 chapters. It is possible to improve on our standard cosmological model by being more careful without introducing anything fundamentally new. (The research frontier, of course, is advancing fast and contains much we have not attempted to explain.) Consider how to implement the following corrections to standard cosmology that are mandated by observation, and then repeat the calculations with these changes, comparing with the research literature.

(a) Changing the slope of the initial cosmic noise spectrum.

(b) Including more spherical harmonics in the description of the radiation field and using the Boltzmann equation instead of a Monte Carlo simulation.

(c) Including tensor perturbations in the Robertson-Walker metric.

(d) Accounting for neutrino mass.