String-Inspired Running Vacuum, the "Vacuumon", and the Swampland Criteria

Abstract

We elaborate further on the compatibility of the "vacuumon potential" that characterises the inflationary phase of the Running Vacuum Model (RVM) with the Swampland criteria. The work is motivated by the fact that, as demonstrated recently by the authors [1-3], the RVM framework can be derived as an effective gravitational field theory stemming from underlying microscopic (critical) string theory models with gravitational anomalies, involving condensation of primordial gravitational waves. Although believed to be a classical scalar field description, not representing a fully fledged quantum field, nonetheless we show here that the vacuumon potential satisfies certain Swampland criteria for the relevant regime of parameters and field range. We link the criteria to the Gibbons-Hawking entropy that has been argued to characterise the RVM during the de Sitter phase. These results imply that the vacuumon may, after all, admit under certain conditions, a rôle as a quantum field during the inflationary (almost de Sitter) phase of the running vacuum. The conventional slow-roll interpretation of this field, however, fails just because it satisfies the Swampland criteria. The RVM effective theory derived from the low-energy effective action of string theory does, however, successfully describe inflation thanks to the $\sim H^4$ terms induced by the gravitational anomalous condensates. In addition, the stringy version of the RVM involves the Kalb-Ramond (KR) axion field, which, in contrast to the vacuumon, does perfectly satisfy the slow-roll condition. We conclude that the vacuumon description is not fully equivalent to the stringy formulation of the RVM.

arXiv comment37 pages revtex, 3 pdf figures incorporated; amended discussion on running-vacuum properties and evolution in sections IVA, IVC; References added. No effects on conclusions; version accepted for publication in Universe

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• Stringy-Running-Vacuum-Model Inflation: from primordial Gravitational Waves and stiff Axion Matter to Dynamical Dark Energy
• Inflationary physics and transplanckian conjecture in the Stringy Running-Vacuum-Model: from the phantom vacuum to the true vacuum
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Multi-field cold and warm inflation and the de Sitter swampland conjectures
• Dilatonic (Anti-)de Sitter Black Holes and Weak Gravity Conjecture
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• Running vacuum and H^4-inflation
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme