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Non-Perturbative Yang-Mills Condensate as Dark Energy
General Relativity and Quantum Cosmology · Submitted 19 Sep 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using non-perturbative techniques mutated from the functional renormalization group procedure, we finally show that the minimum in $\theta$ of the effective Lagrangian exists, thus YMC can actually take place.
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The abstract, sentence by sentence
Models based on Yang-Mills condensate (YMC) have been advocated in the literature and claimed to be successful candidates to explain dark energy. Several instantiations of this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, results previously attained heavily relied on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically-free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in $\theta \!=\! - F_{\, \, \mu \nu}^a \, F^{a \mu \nu}/2$ exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using non-perturbative techniques mutated from the functional renormalization group procedure, we finally show that the minimum in $\theta$ of the effective Lagrangian exists, thus YMC can actually take place. The non-perturbative model has properties similar to the ones of the perturbative model. In the early stage of the universe, the YMC equation of state has an evolution that resembles the radiation component, i.e. $w_y \rightarrow 1/3$. However, in the late stage, $w_y$ naturally runs to the critical state with $w_y =-1$, and the universe transits from matter-dominated into dark energy dominated stage only recently, at a redshift the value of which depends on the initial conditions that are chosen while solving the dynamical system.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Models based on Yang-Mills condensate (YMC) have been advocated in the literature and claimed to be successful candidates to explain dark energy. | background 1.00 | 0.03 | 0.03 | asserted 0.54 |
| s1 | Several instantiations of this simple idea have been considered, the most promising of which are reviewed here. | background 0.94 | 0.23 | 0.02 | asserted 0.83 |
| s2 | Nevertheless, results previously attained heavily relied on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically-free limit, and were extended into a regime, the infrared limit, in which confinement is expected. | gap 0.77 | 0.06 | 0.03 | asserted 0.98 |
| s3 | We show that if a minimum of the effective Lagrangian in $\theta \!=\! - F_{\, \, \mu \nu}^a \, F^{a \mu \nu}/2$ exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. | result 0.83 | 0.77 | 0.36 | asserted 0.86 |
| s4 | The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. | result 0.75 | 0.35 | 0.04 | asserted 0.99 |
| s5 | Using non-perturbative techniques mutated from the functional renormalization group procedure, we finally show that the minimum in $\theta$ of the effective Lagrangian exists, thus YMC can actually take place. | result 0.55 | 0.96 | 0.52 | asserted 1.00 |
| s6 | The non-perturbative model has properties similar to the ones of the perturbative model. | result 0.82 | 0.69 | 0.09 | asserted 1.00 |
| s7 | In the early stage of the universe, the YMC equation of state has an evolution that resembles the radiation component, i.e. $w_y \rightarrow 1/3$. | result 1.00 | 0.80 | 0.06 | asserted 0.98 |
| s8 | However, in the late stage, $w_y$ naturally runs to the critical state with $w_y =-1$, and the universe transits from matter-dominated into dark energy dominated stage only recently, at a redshift the value of which depends on the initial conditions that are chosen while solving the dynamical system. | result 0.95 | 0.82 | 0.20 | asserted 1.00 |
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The paper
Original abstract
Models based on Yang-Mills condensate (YMC) have been advocated in the literature and claimed to be successful candidates to explain dark energy. Several instantiations of this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, results previously attained heavily relied on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically-free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in $\theta \!=\! - F_{\, \, \mu \nu}^a \, F^{a \mu \nu}/2$ exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using non-perturbative techniques mutated from the functional renormalization group procedure, we finally show that the minimum in $\theta$ of the effective Lagrangian exists, thus YMC can actually take place. The non-perturbative model has properties similar to the ones of the perturbative model. In the early stage of the universe, the YMC equation of state has an evolution that resembles the radiation component, i.e. $w_y \rightarrow 1/3$. However, in the late stage, $w_y$ naturally runs to the critical state with $w_y =-1$, and the universe transits from matter-dominated into dark energy dominated stage only recently, at a redshift the value of which depends on the initial conditions that are chosen while solving the dynamical system.
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References
How the literature uses it
9 arXiv papers cite this in 17 sentences
Papers citing it · 11 sentences without a confident label
Contests it 1 paper
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An alternative model to our approach has been recently suggested: the dark energy could be generated by an invisible Yang-Mills or Invisible QCD condensates [ref] In this case, the generation of a neutrino mass gap is similarly possible but it seems ruled out by observations of unconfined neutrinos.
Born-Infeld condensate as a possible origin of neutrino masses and dark energy · Conclusions and outlooks · contest 0.74
Builds on it 1 paper
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The effective action of the quantum YM gauge $SU(N)$($N=2,3,…$) theory consistently incorporating the vacuum polarisation effects and leading to the trace anomaly can be properly generalised to the FLRW background as follows [ref] (see also Ref. [ref] ) [equation] where the YM field and the corresponding stress tensor are defined as usual [equation] with internal (in adjoint representation) $a,b,c=1,… N^2-1$ and Lorentz $μ,ν=0,1,2,3$ indices and the gauge coupling $g̅=g̅(J)$ satisfying the RG evolution equation [ref] [equation] Depending on the sign of the invariant $J$, one distinguishes the chromoelectric $J>0$ and chromomagnetic $J<0$ YM fields.
Mirror QCD and Cosmological Constant · Effective Yang-Mills theory in expanding universe · 0.91
Cites it as background 4 papers
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In particular, an invisible QCD sector reconstructing Dark Energy was suggested in Refs. [ref] while a unified description of Dark Matter and Dark Energy originating from invisible QCD dynamics was proposed in Refs. [ref] .
Mirror QCD and Cosmological Constant · Introduction · 0.88
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The effects of a nonlinear electromagnetic theory in a cosmological setting have been studied by several authors (see e.g. Refs. [ref] ).
Dark Energy and Neutrino Superfluids · Dark Energy · 0.99
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One of these cases corresponding to $Q=+1$ has been discussed in the broad literature before (see e.g. Refs. [ref] ).
Time-crystal ground state and production of gravitational waves from QCD phase transition · Asymptotic attractor solution and Z2 symmetry restoration · 0.93
What it cites · 3 sentences without a confident label
Cites as background 5 papers
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The FRGE has been extensively applied to $SU(N)$ Yang-Mills theories, for further references see [ref] and for the application of the FRG to the study of YMC [ref] .
On the infrared behavior of Landau gauge Yang-Mills theory · Functional Renormalization Group · 0.96
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The FRGE has been extensively applied to $SU(N)$ Yang-Mills theories, for further references see [ref] and for the application of the FRG to the study of YMC [ref] .
Gluon condensation and scaling exponents for the propagators in Yang-Mills theory · Functional Renormalization Group · 0.96
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The FRGE has been extensively applied to $SU(N)$ Yang-Mills theories, for further references see [ref] and for the application of the FRG to the study of YMC [ref] .
Signatures of confinement in Landau gauge QCD · Functional Renormalization Group · 0.96
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