Anisotropies in the CMB

Over the last few years it has become common place to speak of the Cosmic Microwave Background (CMB) anisotropy as the premier laboratory for cosmology and early universe physics. In the titles to most talks the word \anisotropy" is often absent, it being understood that the talk will be about the anisotropy. This is an interesting phenomenon. Consider that when we speak of the CMB we could speak about 3 major properties. Firstly, the existence of the CMB is one of the pillars of the hot big bang model of cosmology. Secondly, the black body spectrum of the CMB, the most perfect black body ever measured in nature, con rms the cosmological origin of the CMB and puts extraordinarily strong constraints on early energy injection in the universe (e.g. through decaying particles, see [1]). These rst two properties show that the CMB has already delivered important cosmological information. Our current focus is the third area: the anisotropy. This fact alone indicates the high level of promise that a study of the anisotropy holds. Like much of cosmology, the CMB is a data driven subject. However, in this proceedings I focus on the theory behind the CMB anisotropies, and the current status of theoretical e orts, rather than on the CMB data. It is a blessing of this eld that numerous experimental e orts underway will make any statements about the experimental situation obsolete before they reach print (even on the web!). As an overly brief summary of the current status: the current data are in good agreement with our general paradigm and support a spatially at universe with an almost scale-invariant spectrum of adiabatic uctuations in predominantly cold dark matter. Departures from that statement in any direction t the data less well, though at present large error bars and theorist's ingenuity limit the strength of statements that can be made. The calculation of CMB anisotropies is now a highly re ned subject. While most calculations focus on the \standard" models, the theory is in fact very general. This generality also leads to complexity, but the basic physics behind the CMB is very simple. To understand CMB anisotropies it is helpful to recall several general points: