Stringy-Running-Vacuum-Model Inflation: from primordial Gravitational Waves and stiff Axion Matter to Dynamical Dark Energy

Understand

In previous works we have derived a Running Vacuum Model (RVM) for a string Universe, which provides an effective description of the evolution of 4-dimensional string-inspired cosmologies from inflation till the present epoch.

• In the context of this "stringy RVM" version, it is assumed that the early Universe is characterised by purely gravitational degrees of freedom, from the massless gravitational string multiplet, including the antisymmetric tensor field.
• The latter plays an important role, since its dual gives rise to a `stiff' gravitational-axion "matter", which in turn couples to the gravitational anomaly terms, assumed to be non-trivial at early epochs.
• In the presence of primordial gravitational wave (GW) perturbations, such anomalous couplings lead to an RVM-like dynamical inflation, without external inflatons.