String cosmology

String cosmology is a relatively new field that tries to apply equations of string theory to solve the questions of early cosmology. A related area of study is brane cosmology. This approach can be dated back to a paper by Gabriele Veneziano that shows how an inflationary cosmological model can be obtained from string theory, thus opening the door to a description of pre-Big Bang scenarios. The idea is related to a property of the bosonic string in a curve background, better known as nonlinear sigma model. First calculations from this model showed as the beta function, representing the running of the metric of the model as a function of an energy scale, is proportional to the Ricci tensor giving rise to a Ricci flow. As this model has conformal invariance and this must be kept to have a sensible quantum field theory, the beta function must be zero producing immediately the Einstein field equations. While Einstein equations seem to appear somewhat out of place, nevertheless this result is surely striking showing as a background two-dimensional model could produce higher-dimensional physics. An interesting point here is that such a string theory can be formulated without a requirement of criticality at 26 dimensions for consistency as happens on a flat background. This is a serious hint that the underlying physics of Einstein equations could be described by an effective two-dimensional conformal field theory. Indeed, the fact that we have evidence for an inflationary universe is an important support to string cosmology. In the evolution of the universe, after the inflationary phase, the expansion observed today sets in that is well described by Friedmann equations. A smooth transition is expected between these two different phases. String cosmology appears to have difficulties in explaining this transition. This is known in the literature as the graceful exit problem. An inflationary cosmology implies the presence of a scalar field that drives inflation. In string cosmology, this arises from the so-called dilaton field.