Evolution of the cosmic microwave background

We discuss the time dependence and future of the cosmic microwave background (CMB) in the context of the standard cosmological model, in which we are now entering a state of endless accelerated expansion. The mean temperature will simply decrease until it reaches the effective temperature of the de Sitter vacuum, while the dipole will oscillate as the sun orbits the Galaxy. However, the higher CMB multipoles have a richer phenomenology. The CMB anisotropy power spectrum will for the most part simply project to smaller scales, as the comoving distance to last scattering increases, and we derive a scaling relation that describes this behavior. However, there will also be a dramatic increase in the integrated Sachs-Wolfe contribution at low multipoles. We also discuss the effects of tensor modes and optical depth due to Thomson scattering. We introduce a correlation function relating the sky maps at two times and the closely related power spectrum of the difference map. We compute the evolution both analytically and numerically, and present simulated future sky maps.