Gravity as an effective theory

Using as inspiration the well known chiral effective lagrangian describing the interactions of pions at low energies, in these lectures we review the quantization procedure of Einstein gravity in the spirit of effective field theories. As has been emphasized by several authors, quantum corrections to observables in gravity are, by naive power counting, very small. While some quantities are not predictable (they require local counterterms of higher dimensionality) others, non local, are. A notable example is the calculation of quantum corrections to Newton's law. Albeit tiny these corrections are of considerable theoretical importance, perhaps providing information on the ultaviolet properties of gravity. We then try to search for a situation where these non local corrections may be observable in a cosmological context in the early universe. Having seen that gravity admits an effective treatment similar to the one of pions, we pursue this analogy and propose a two-dimensional toy modelwhere a dynamical zwei-bein is generated from a theory without any metric at all.