This approach can be dated back to a paper by Gabriele Veneziano[1] 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[2] 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.
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.
String cosmology appears to have difficulties in explaining this transition.
An inflationary cosmology implies the presence of a scalar field that drives inflation.
The other way round is to assume that a certain number of dimensions is compactified producing an effective four-dimensional theory to work with.
This section presents some of the relevant equations entering into string cosmology.
At the quantum level, this property is lost due to anomalies and the theory itself is not consistent, having no unitarity.
Indeed, the beta functions at two loops are and The assumption that conformal invariance holds implies that producing the corresponding equations of motion of low-energy physics.
, and from this cosmological models of a pre-big bang, scenario can be constructed.
One can also rewrite this action in a more familiar form by redefining the fields (Einstein frame) as and using