In this chapter we will illustrate the quantum/stringy origin of the effective field equations introduced in the previous chapter. In particular, we will show that such equations must be satisfied by the background fields through which a bosonic string is propagating, in order to implement a consistent quantization of the string motion without anomalies (i.e. without quantum breakdown of the symmetries already present at the classical level).

The main content of this chapter has no direct application in cosmology, and will not often be referred to in the rest of this book. The simple introduction presented here, even if incomplete and approximate in many respects, is nonetheless compulsory for a reader with no previous knowledge of string theory, in order to understand how the cosmological equations used throughout the book are rigidly prescribed by the theory and cannot undergo ad hoc modifications, unlike the equations of other, more conventional models of gravity based on the notions of fields and point-like sources.

The motion of a point-like particle, in fact, can be consistently quantized without imposing any constraints on the background fields with which the point is interacting. In particular, the geometry of the space-time manifold in which the particle trajectory is embedded may be generated by arbitrary sources, may be characterized by an arbitrary number of dimensions, and may be governed by dynamical equations arbitrarily prescribed (or arbitrarily modified with respect to the Einstein equations), without dramatically affecting the quantization of the point motion.