Condensate-Induced Inflation from Primordial Gravitational Waves in String-Inspired Chern-Simons Gravity

In this work, we elaborate further on a cosmological model of inflation that characterises Chern-Simons (CS) gravity models inspired from string theory. Such models are known to belong to the class of the so-called String-Inspired Running Vacuum Cosmologies. In particular, by applying methods of dynamical systems, commonly used in scalar-field cosmology, we examine in detail, for the first time, the passage from a pre-inflationary era dominated by a stiff-axion-matter equation of state, characteristic of the model, to inflation of Running Vacuum Model (RVM) type. By a careful discussion of the formation of the condensate of the CS gravitational anomaly term, induced by populations of primordial gravitational waves at the end of the stiff-axion-matter era, we show that an effectively linear axion-monodromy potential arises. This eventually causes the transition from the matter to the RVM inflation. By taking into account terms that have previously been ignored in the relevant literature of weak-graviton quantisation, we show that the effect of such terms is to diminish the value of the condensate by half, remaining however in the same order of magnitude. This, in turn, implies that the qualitative conclusions of previous works on the subject remain valid. Moreover, on assuming the approximate cosmic-time independence of the gravitational-CS condensate, we also provide an estimate of the number of sources of the primordial gravitational waves, upon the requirement of respecting the transplanckian conjecture.