String-Inspired Running Vacuum—The “Vacuumon”—And the Swampland Criteria

Nick E Mavromatos,Spyros Basilakos,Joan Solà Peracaula

doi:10.3390/universe6110218

Nick E Mavromatos, Spyros Basilakos + Show 1 more

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https://doi.org/10.3390/universe6110218

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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, 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, 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 ∼H4 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. Our study provides a particularly interesting example of a successful phenomenological theory beyond the ΛCDM, such as the RVM, in which the fulfilment of the swampland criteria by the associated scalar field potential, along with its compatibility with (an appropriate form of) the weak gravity conjecture, prove to be insufficient conditions for warranting consistency of the scalar vacuum field representation as a faithful ultraviolet complete representation of the RVM at the quantum gravity level.

Highlights

Embedding Effective Field Theory Models into Quantum Gravity and the Problems of CosmologyThe current work is motivated by the articles [1,2,3], where a string theory approach to the Running Vacuum Model (RVM) is presented, involving condensation of primordial gravitational waves.Despite significant advances in models of quantum gravity, including string/brane models [4,5,6,7], we are still far from an understanding of the microscopic theory that underlies the quantum structureUniverse 2020, 6, 218; doi:10.3390/universe6110218 www.mdpi.com/journal/universeUniverse 2020, 6, 218 of space-time at Planck scales
Understanding of the quantum field theory (QFT) of matter is still lacking in such background space times, even if one ignores the aspects of the quantisation of the gravitational field itself
From the point of view of the original four-dimensional string-inspired version of the RVM, based on the low-energy effective action of graviton and antisymmetric tensor fields of the massless string gravitational multiplet [1,2,3], condensates of graviton fluctuations provide dynamically ∼ H 4 contributions, which are responsible for the early de Sitter phase and the slow-roll condition is realised through the Kalb–Ramond axion field associated with the effective string action governing the inflationary regime

Summary

Introduction

Embedding Effective Field Theory Models into Quantum Gravity and the Problems of Cosmology. From the point of view of the original four-dimensional string-inspired version of the RVM, based on the low-energy effective action of graviton and antisymmetric tensor fields of the massless (bosonic) string gravitational multiplet [1,2,3], condensates of graviton fluctuations provide dynamically ∼ H 4 contributions, which are responsible for the early de Sitter phase and the slow-roll condition is realised through the Kalb–Ramond axion field associated with the effective string action governing the inflationary regime This implies that the swampland criteria per se, providing information for a possible embedding of the effective scalar vacuumon field description of the RVM to a consistent quantum gravity framework, themselves are not decisive enough to yield more information on the underlying microscopic string theory features, and in particular to provide any detailed information of the dynamics of the gravitational stringy condensates that underlie the stringy RVM dynamics, which are compatible with slow-roll inflation, in the sense of admitting approximately de Sitter solutions.

The Swampland Conjectures

The Weak Gravity Conjectures

RVM Cosmic Evolution

Embedding RVM in String Theory

The “Vacuumon” Representation of the Running Vacuum Model

String-Inspired RVM and the Swampland