Stringy-running-vacuum-model inflation: from primordial gravitational waves and stiff axion matter to dynamical dark energy

Abstract In previous works, we have derived a Running Vacuum Model (RVM) for string Universe, which provides an effective description of the evolution 4-dimensional string-inspired cosmologies from inflation till present epoch. context this “stringy RVM” version, it is assumed that early Universe characterised by purely gravitational degrees freedom, massless multiplet, including antisymmetric tensor field. The latter plays important role, since its dual gives rise to ‘stiff’ axion “matter”, in turn couples anomaly terms, be non-trivial at epochs. presence primordial wave (GW) perturbations, such anomalous couplings lead RVM-like dynamical inflation, without external inflatons. We review here framework and discuss potential scenarios generation GW, among formation unstable domain walls, eventually collapse non-spherical-symmetric manner, giving GW. also remark same type “stiff” axionic matter could provide, upon appropriate potentials during post-inflationary eras, (part of) Dark Matter (DM) well ultralight, depending on parameters model. All all, new (stringy) mechanism RVM preserves basic structure original (and more phenomenological) RVM, as main advantages: namely, graceful exit generating huge amount entropy capable explaining horizon problem. It predicts DM existence mild Energy (DE) quintessence universe, both being “living fossils” inflationary stages cosmic evolution. Altogether modern appears theoretically sound (string-based) approach cosmology with variety phenomenologically testable consequences.