Abstract

In this short review, I discuss basic qualitative characteristics of quantum non-Abelian gauge dynamics in the non-stationary background of the expanding Universe in the framework of the standard Einstein–Yang–Mills formulation. A brief outlook of existing studies of cosmological Yang–Mills fields and their properties will be given. Quantum effects have a profound impact on the gauge field-driven cosmological evolution. In particular, a dynamical formation of the spatially-homogeneous and isotropic gauge field condensate may be responsible for both early and late-time acceleration, as well as for dynamical compensation of non-perturbative quantum vacua contributions to the ground state of the Universe. The main properties of such a condensate in the effective QCD theory at the flat Friedmann–Lemaítre–Robertson–Walker (FLRW) background will be discussed within and beyond perturbation theory. Finally, a phenomenologically consistent dark energy can be induced dynamically as a remnant of the QCD vacua compensation arising from leading-order graviton-mediated corrections to the QCD ground state.

Highlights

  • The cosmological constant (or, in general, dark energy (DE)) problem is one of the most controversial and debatable naturalness problems in theoretical physics and cosmology nowadays.It refers to an enigmatic anti-gravitating substance, which causes the Universe to expand with acceleration typical for de-Sitter cosmologies

  • This review aims at the search for a comprehensive answer to this fundamental question within the framework of strongly-coupled quantum Yang–Mills (YM) field theories with a non-trivial ground state, such as quantum chromodynamics (QCD)

  • Interpretations and theoretical developments that can be found within conventional quantum field theory (QFT) and particle physics concerning, in particular, YM theories with a non-trivial ground state

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Summary

Introduction

The cosmological constant (or, in general, dark energy (DE)) problem is one of the most controversial and debatable naturalness problems in theoretical physics and cosmology nowadays. For a comprehensive review of existing theoretical models and interpretations of the cosmological constant (or slowly-evolving DE), see, e.g., [15,16,17,18,19,20,21] and the references therein Given such a huge variety of DE models in the literature, there is an apparent deficit of phenomenological data capable of robustly constraining the possible time dependence of the DE density. The basic problem, is to describe various quantum vacuum (condensate) contributions to the ground state energy at macroscopic separations (IR limit), as well as their renormalization group (RG) running without having a complete high-energy QFT (UV limit) The latter would consistently unify all four different types of interactions in Nature, providing a naturally small positive Λ-term, as well as containing a suitable candidate for the inflaton field. This review aims at the search for a comprehensive answer to this fundamental question within the framework of strongly-coupled quantum Yang–Mills (YM) field theories with a non-trivial ground state, such as QCD

Vacuum Catastrophe
Yang–Mills Condensates in Cosmology
Yang–Mills Effective Action
Cosmological Evolution of the Yang–Mills Ground State
Exact Solutions of the One-Loop Effective Model
QCD Vacuum Compensation
Asymptotic Behavior of the QCD Vacuum Energy
Towards Non-Perturbative QCD
The Role of Gravity
Graviton-Exchange Correction to the QCD Ground State: A Pedagogical Outlook
Summary
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